Namespaces
	detail

	experimental

	internal

Classes
class	BezierCurve
	Represents a Bezier curve defined by an array of control points. More...

class	BezierPatch
	Represents a 3D Bezier patch defined by a 2D array of control points. More...

class	BoundingBox

class	Cone
	Represents a cone defined by a base radius, a top radius, the length, the orientation and the location of the base center. More...

class	CurvedPolygon
	Represents a polygon with generic curves for edges. More...

class	Hexahedron
	Represents an hexahedral geometric shape defined by eight points. More...

class	KnotVector
	Represents the knot vector for a B-Spline/NURBS Curve/Surface. More...

class	Line
	Represents a line, \( L(t) \in \mathcal{R}^d \) , defined by an origin point, \( P \) and a normalized direction vector, \( \vec{d} \), \( \ni L(t)= P + t\vec{d} \forall t \in \mathcal{R} \). More...

class	NURBSCurve
	Represents a NURBS curve defined by an array of control points, weights and knots. More...

class	NURBSPatch
	Represents a NURBS patch defined by a 2D array of control points. More...

class	TrimmingCurveQuadratureData

class	Octahedron
	Represents an octahedral geometric shape defined by six points. More...

class	OrientedBoundingBox
	OrientedBoundingBox represents an oriented bounding box defined by its centroid, axes, and extents. More...

class	Plane
	Defines an oriented plane within a 2-D or 3-D Euclidean space and provides associated operators, such as, projection, signed distance, orientation, etc. More...

class	Point
	The point class represents a point, \( p \in \mathcal{R}^d \) . It provides access methods to set and query the point coordinates. More...

class	Polygon
	Represents a polygon defined by an array of points. More...

class	Polyhedron
	Represents a convex polyhedron defined by an array of points and optionally their neighbors (a point is a neighbor of another point if there is an edge between them) More...

class	NeighborCollection
	Represents a collection of neighbor relations between vertices. More...

class	Quadrilateral
	Represents a quadrilateral geometric shape defined by four points. More...

class	Ray

class	Segment

class	Sphere
	Defines an oriented Sphere in 2-D (i.e., a circle) or 3-D given by its center, \( \mathcal{X} \) and radius \( \mathcal{R} \). The Sphere object provides associated operations on a sphere, such as, signed distance and orientation. More...

class	Tetrahedron
	Represents a tetrahedral geometric shape defined by four points. More...

class	Triangle
	Represents a triangular geometric shape defined by three points. More...

class	Vector
	Represents a vector, \( v \in \mathcal{R}^d \). It provides access methods for setting and querying the vector components as well as vector math operators, e.g., adding, subtracting, dot_product and cross_product. More...

struct	WindingTolerances
	Struct containing tolerances shared across GWN values with sensible defaults. More...

Typedefs
Pre-defined point types
using	Point2D = Point< double, 2 >

using	Point3D = Point< double, 3 >

Pre-defined Vector types
using	Vector2D = Vector< double, 2 >

using	Vector3D = Vector< double, 3 >

Enumerations
enum	OrientationResult { ON_BOUNDARY , ON_POSITIVE_SIDE , ON_NEGATIVE_SIDE }
	Enumerates possible return values for orientation tests. More...

enum class	PolygonArray { Dynamic , Static }

Functions
template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const BezierCurve< T, NDIMS > &bCurve)
	Overloaded output operator for Bezier Curves. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const BezierPatch< T, NDIMS > &bPatch)
	Overloaded output operator for Bezier Patches. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Cone< T, NDIMS > &Cone)
	Free functions implementing Cone's operators. More...

template<typename T , int NDIMS, PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>
Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >	regular_polygon (int nSides, T radius=T {1}, const axom::numerics::Matrix< T > &transform=axom::numerics::Matrix< T >::identity(NDIMS))
	Create a regular polygon. More...

template<typename T >
Polyhedron< T, 3 >	regular_prism (int numSides, T radius=1, T height=1, const axom::numerics::Matrix< T > &transform=axom::numerics::Matrix< T >::identity(4))
	Construct a regular 3D prism. More...

template<typename CurveType >
std::ostream &	operator<< (std::ostream &os, const CurvedPolygon< CurveType > &poly)
	Overloaded output operator for polygons. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Hexahedron< T, NDIMS > &hex)
	Free functions implementing Hexahedron's operators. More...

template<typename T >
std::ostream &	operator<< (std::ostream &os, const KnotVector< T > &kVec)
	Overloaded output operator for knot vectors. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Line< T, NDIMS > &line)
	Overloaded output operator for lines. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const NURBSCurve< T, NDIMS > &bCurve)
	Overloaded output operator for NURBS Curves. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const NURBSPatch< T, NDIMS > &nPatch)
	Overloaded output operator for NURBS Patches. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Octahedron< T, NDIMS > &oct)
	Free functions implementing Octahedron's operators. More...

template<typename T , int NDIMS>
Point< T, NDIMS >	transform_point (const Point< T, NDIMS > &pt, const axom::numerics::Matrix< T > &transform=axom::numerics::Matrix< T >::identity(NDIMS))
	Transform a point using a transformation matrix. More...

template<typename T , int NDIMS, axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>
std::ostream &	operator<< (std::ostream &os, const Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS > &poly)
	Overloaded output operator for polygons. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Polyhedron< T, NDIMS > &poly)
	Overloaded output operator for polyhedrons. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Quadrilateral< T, NDIMS > &quad)
	Overloaded output operator for quadrilaterals. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Ray< T, NDIMS > &ray)
	Overloaded output operator for rays. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Tetrahedron< T, NDIMS > &tet)
	Free functions implementing Tetrahedron's operators. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Triangle< T, NDIMS > &tri)
	Overloaded output operator for triangles. More...

template<typename T >
Polygon< T, 3 >	clip (const Triangle< T, 3 > &tri, const BoundingBox< T, 3 > &bbox)
	Clips a 3D triangle against an axis-aligned bounding box in 3D. More...

template<typename T , axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>
AXOM_SUPPRESS_HD_WARN AXOM_HOST_DEVICE Polygon< T, 2, ARRAY_TYPE, MAX_VERTS >	clip (const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &subjectPolygon, const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &clipPolygon, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 2D subject polygon against a clip polygon in 2D, returning their geometric intersection as a polygon. More...

template<typename T , axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>
AXOM_HOST_DEVICE Polygon< T, 2, ARRAY_TYPE, MAX_VERTS >	clip (const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &subjectPolygon, const Plane< T, 2 > &clipPlane, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 2D subject polygon against a clip plane in 2D, returning their geometric intersection as a polygon. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Hexahedron< T, 3 > &hex, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D hexahedron against a tetrahedron in 3D, returning the geometric intersection of the hexahedron and the tetrahedron as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Tetrahedron< T, 3 > &tet, const Hexahedron< T, 3 > &hex, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D hexahedron against a tetrahedron in 3D, returning the geometric intersection of the hexahedron and the tetrahedron as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Hexahedron< T, 3 > &hex1, const Hexahedron< T, 3 > &hex2, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D hexahedron against a hexahedron in 3D, returning the geometric intersection of the hexahedron and the hexahedron as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Octahedron< T, 3 > &oct, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D octahedron against a tetrahedron in 3D, returning the geometric intersection of the octahedron and the tetrahedron as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Tetrahedron< T, 3 > &tet, const Octahedron< T, 3 > &oct, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D octahedron against a tetrahedron in 3D, returning the geometric intersection of the octahedron and the tetrahedron as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Tetrahedron< T, 3 > &tet1, const Tetrahedron< T, 3 > &tet2, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D tetrahedron against another tetrahedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Tetrahedron< T, 3 > &tet, const Polyhedron< T, 3 > &poly, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Polyhedron< T, 3 > &poly, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Hexahedron< T, 3 > &hex, const Polyhedron< T, 3 > &poly, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D hexahedron against a polyhedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Polyhedron< T, 3 > &poly, const Hexahedron< T, 3 > &hex, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D polyhedron against a hexahedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Polyhedron< T, 3 > &poly1, const Polyhedron< T, 3 > &poly2, double eps=1.e-10)
	Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Tetrahedron< T, 3 > &tet, const Plane< T, 3 > &plane, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D tetrahedron against the half-space defined by a plane and returns the resulting polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Plane< T, 3 > &plane, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D tetrahedron against the half-space defined by a plane and returns the resulting polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Polyhedron< T, 3 > &poly, const Plane< T, 3 > &plane, double eps=1.e-10)
	Clips a 3D polyhedron against the half-space defined by a plane and returns the resulting polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Plane< T, 3 > &plane, const Polyhedron< T, 3 > &poly, double eps=1.e-10)
	Clips a 3D polyhedron against the half-space defined by a plane and returns the resulting polyhedron. More...

template<typename T >
AXOM_HOST_DEVICE Polyhedron< T, 3 >	clip (const Hexahedron< T, 3 > &hex, const Plane< T, 3 > &plane, double eps=1.e-10, bool tryFixOrientation=false)
	Clips a 3D hexahedron against the half-space defined by a plane and returns the resulting polyhedron. More...

template<typename T , int NDIMS>
OrientedBoundingBox< T, NDIMS >	merge_boxes (const OrientedBoundingBox< T, NDIMS > &l, const OrientedBoundingBox< T, NDIMS > &r)
	Creates an oriented bounding box which contains the passed in OBBs. More...

template<typename T , int NDIMS>
BoundingBox< T, NDIMS >	merge_boxes (const BoundingBox< T, NDIMS > &l, const BoundingBox< T, NDIMS > &r)
	Constructor. Creates a bounding box which contains the passed in bounding boxes. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Triangle< T, NDIMS > &tri)
	Creates a bounding box around a Triangle. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Quadrilateral< T, NDIMS > &quad)
	Creates a bounding box around a Quadrilateral. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Octahedron< T, NDIMS > &oct)
	Creates a bounding box around an Octahedron. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Hexahedron< T, NDIMS > &hex)
	Creates a bounding box around a Hexahedron. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Polyhedron< T, NDIMS > &poly)
	Creates a bounding box around a Polyhedron. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Tetrahedron< T, NDIMS > &tet)
	Creates a bounding box around a Tetrahedron. More...

template<typename T , int NDIMS, PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>
AXOM_HOST_DEVICE BoundingBox< T, NDIMS >	compute_bounding_box (const Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS > &poly)
	Creates a bounding box around a Polygon. More...

template<typename T >
T	sector_area (const primal::BezierCurve< T, 2 > &curve)
	Calculates the signed sector area of a planar, nonrational Bezier curve. More...

template<typename T >
primal::Point< T, 2 >	sector_centroid (const primal::BezierCurve< T, 2 > &curve)
	Calculates the area-weighted centroid numerator of a planar, nonrational Bezier curve. More...

template<typename T >
T	area (const primal::CurvedPolygon< BezierCurve< T, 2 >> &poly, double tol=1e-8)
	Returns the area enclosed by the CurvedPolygon. More...

template<typename T >
primal::Point< T, 2 >	centroid (const primal::CurvedPolygon< BezierCurve< T, 2 >> &poly, double tol=1e-8)
	Returns the centroid of the CurvedPolygon. More...

template<typename T , typename CurveType >
bool	in_curved_polygon (const Point< T, 2 > &query, const CurvedPolygon< CurveType > &cpoly, bool useNonzeroRule=true, double edge_tol=1e-8, double EPS=1e-8)
	Robustly determine if query point is interior to a curved polygon. More...

template<typename T >
bool	in_polygon (const Point< T, 2 > &query, const Polygon< T, 2 > &poly, bool includeBoundary=false, bool useNonzeroRule=true, double edge_tol=1e-8)
	Determines containment for a point in a polygon. More...

template<typename T >
bool	in_polyhedron (const Point< T, 3 > &query, const Polyhedron< T, 3 > &poly, bool includeBoundary=false, bool useNonzeroRule=true, double edge_tol=1e-8, double EPS=1e-8)
	Determines containment for a point in a polygon. More...

template<typename T >
bool	in_sphere (const Point< T, 2 > &q, const Point< T, 2 > &p0, const Point< T, 2 > &p1, const Point< T, 2 > &p2, double EPS=1e-8)
	Tests whether a query point lies inside a 2D triangle's circumcircle. More...

template<typename T >
bool	in_sphere (const Point< T, 2 > &q, const Triangle< T, 2 > &tri, double EPS=1e-8)
	Tests whether a query point lies inside a 2D triangle's circumcircle. More...

template<typename T >
bool	in_sphere (const Point< T, 3 > &q, const Point< T, 3 > &p0, const Point< T, 3 > &p1, const Point< T, 3 > &p2, const Point< T, 3 > &p3, double EPS=1e-8)
	Tests whether a query point lies inside a 3D tetrahedron's circumsphere. More...

template<typename T >
bool	in_sphere (const Point< T, 3 > &q, const Tetrahedron< T, 3 > &tet, double EPS=1e-8)
	Tests whether a query point lies inside a 3D tetrahedron's circumsphere. More...

template<typename T >
bool	in_sphere (const BoundingBox< T, 2 > &bb, const Sphere< T, 2 > &circle)
	Tests whether a bounding box lies inside a 2D sphere. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Segment< T, 3 > &P, const Segment< T, 3 > &Q, Point< T, 3 > &intersection, const T EPS=static_cast< T >(1e-08))
	Determines if two 3D segments intersect. More...

template<typename T >
bool	intersect (const Ray< T, 3 > &ray, const BezierPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol, double EPS, bool isHalfOpen, bool &success)
	Determines if a ray intersects a Bezier patch. More...

template<typename T >
bool	intersect (const Ray< T, 3 > &ray, const BezierPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol=1e-8, double EPS=1e-8, bool isHalfOpen=false)
	! More...

template<typename T >
bool	intersect (const Line< T, 3 > &line, const BezierPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol, double EPS, bool isHalfOpen, bool &success)
	Determines if a line (two-sided ray) intersects a Bezier patch. More...

template<typename T >
bool	intersect (const Line< T, 3 > &line, const BezierPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol=1e-8, double EPS=1e-8, bool isHalfOpen=false)
	! More...

template<typename T >
bool	intersect (const Ray< T, 3 > &ray, const NURBSPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol, double EPS, bool countUntrimmed, bool isHalfOpen, bool &success)
	Determines if a ray intersects a NURBS patch. More...

template<typename T >
bool	intersect (const Ray< T, 3 > &ray, const NURBSPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol=1e-8, double EPS=1e-8, bool countUntrimmed=true, bool isHalfOpen=false)
	! More...

template<typename T >
bool	intersect (const Line< T, 3 > &line, const NURBSPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol, double EPS, bool countUntrimmed, bool isHalfOpen, bool &success)
	Determines if a line (two-sided ray) intersects a NURBS patch. More...

template<typename T >
bool	intersect (const Line< T, 3 > &line, const NURBSPatch< T, 3 > &patch, axom::Array< T > &t, axom::Array< T > &u, axom::Array< T > &v, double tol=1e-8, double EPS=1e-8, bool countUntrimmed=true, bool isHalfOpen=false)
	! More...

template<typename T >
bool	intersect (const NURBSCurve< T, 2 > &n1, const NURBSCurve< T, 2 > &n2, axom::Array< T > &p1, axom::Array< T > &p2, double tol=1.0E-8)
	Finds the intersection points for two NURBS curves in 2D. More...

template<typename T >
AXOM_HOST_DEVICE T	intersection_volume (const Hexahedron< T, 3 > &hex, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Finds the absolute (unsigned) intersection volume between a hexahedron and a tetrahedron. More...

template<typename T >
AXOM_HOST_DEVICE T	intersection_volume (const Tetrahedron< T, 3 > &tet, const Hexahedron< T, 3 > &hex, double eps=1.e-10, bool tryFixOrientation=false)
	Finds the absolute (unsigned) intersection volume between a tetrahedron and a hexahedron. More...

template<typename T >
AXOM_HOST_DEVICE T	intersection_volume (const Octahedron< T, 3 > &oct, const Tetrahedron< T, 3 > &tet, double eps=1.e-10, bool tryFixOrientation=false)
	Finds the absolute (unsigned) intersection volume between a octahedron and a tetrahedron. More...

template<typename T >
AXOM_HOST_DEVICE T	intersection_volume (const Tetrahedron< T, 3 > &tet, const Octahedron< T, 3 > &oct, double eps=1.e-10, bool tryFixOrientation=false)
	Finds the absolute (unsigned) intersection volume between a tetrahedron and a octahedron. More...

template<typename T >
AXOM_HOST_DEVICE T	intersection_volume (const Tetrahedron< T, 3 > &tet1, const Tetrahedron< T, 3 > &tet2, double eps=1.e-10, bool tryFixOrientation=false)
	Finds the absolute (unsigned) intersection volume between a tetrahedron and another tetrahedron. More...

template<typename T >
bool	is_convex (const Polygon< T, 2 > &poly, double EPS=1e-8)
	Determines if a polygon defined by ordered vertices is convex. More...

template<typename T >
int	orientation (const Point< T, 3 > &p, const Triangle< T, 3 > &tri, double EPS=1e-9)
	Computes the orientation of a point p with respect to an oriented triangle tri. More...

template<typename T >
int	orientation (const Point< T, 2 > &p, const Segment< T, 2 > &seg, double EPS=1e-9)
	Computes the orientation of a point p with respect to an oriented segment. More...

template<typename T , PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>
AXOM_HOST_DEVICE primal::Polygon< T, 3, ARRAY_TYPE, MAX_VERTS >	slice (const primal::Tetrahedron< T, 3 > &tet, const primal::Plane< T, 3 > &plane)
	Slices a 3D tetrahedron with a plane and returns the resulting polygon. More...

template<typename Tp >
void	split (const Octahedron< Tp, 3 > &oct, axom::Array< Tetrahedron< Tp, 3 >> &out)
	Splits an Octahedron into eight Tetrahedrons. More...

template<typename Tp >
AXOM_HOST_DEVICE void	split (const Octahedron< Tp, 3 > &oct, Tetrahedron< Tp, 3 > *outPtr)
	Splits an Octahedron into eight Tetrahedrons. More...

double	squared_distance (const double A, const double B, int N)
	Computes the squared distance from point A to point B, represented by arrays of length N. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE double	squared_distance (const Point< T, NDIMS > &A, const Point< T, NDIMS > &B)
	Computes the squared distance from point A to point B. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE double	squared_distance (const Point< T, NDIMS > &P, const BoundingBox< T, NDIMS > &B)
	Computes the minimum squared distance from a query point, P, to a given axis-aligned bounding box B. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE double	squared_distance (const BoundingBox< T, NDIMS > &A, const BoundingBox< T, NDIMS > &B)
	Computes the minimum squared distance between 2 axis-aligned boxes. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE double	squared_distance (const Point< T, NDIMS > &P, const Segment< T, NDIMS > &S)
	Computes the minimum squared distance from a query point, P, to the given segment, S. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE double	squared_distance (const Point< T, NDIMS > &P, const Triangle< T, NDIMS > &tri)
	Computes the minimum squared distance from a query point, P, to the closest point on the given triangle. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const Segment< T, 2 > &s, double edge_tol=1e-8)
	Compute the GWN for a 2D point wrt a 2D line segment. More...

template<typename T >
int	winding_number (const Point< T, 2 > &q, const Triangle< T, 2 > &tri, bool includeBoundary=false, double edge_tol=1e-8)
	Compute the winding number for a 2D point wrt a 2D triangle. More...

template<typename T >
int	winding_number (const Point< T, 2 > &R, const Polygon< T, 2 > &P, bool &isOnEdge, bool includeBoundary=false, double edge_tol=1e-8)
	Computes the winding number for a 2D point wrt a 2D polygon. More...

template<typename T >
int	winding_number (const Point< T, 2 > &R, const Polygon< T, 2 > &P, bool includeBoundary=false, double edge_tol=1e-8)
	Computes the winding number for a 2D point wrt a 2D polygon. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const NURBSCurve< T, 2 > &n, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt a 2D NURBS curve. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const BezierCurve< T, 2 > &bezier, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt a 2D NURBS curve. More...

template<typename T , typename CurveType >
double	winding_number (const Point< T, 2 > &q, const CurvedPolygon< CurveType > &cpoly, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt to a 2D curved polygon. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const axom::Array< BezierCurve< T, 2 >> &carray, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt to a collection of 2D Bezier curves. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const axom::Array< NURBSCurve< T, 2 >> &narray, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt to a collection of 2D NURBS curves. More...

template<typename T >
double	winding_number (const Point< T, 2 > &query, const detail::NURBSCurveGWNCache< T > &nurbs_cache, bool &isOnCurve, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt memoized data for a 2D NURBS curve. More...

template<typename T >
double	winding_number (const Point< T, 2 > &q, const detail::NURBSCurveGWNCache< T > &nurbs_cache, double edge_tol=1e-8, double EPS=1e-8)
	Overload without optional return parameter. More...

template<typename T >
double	winding_number (const Point< T, 2 > &query, const axom::Array< detail::NURBSCurveGWNCache< T >> &nurbs_cache_arr, bool &isOnCurve, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for a 2D point wrt an array of memoized data for 2D NURBS curves. More...

template<typename T >
double	winding_number (const Point< T, 2 > &query, const axom::ArrayView< const detail::NURBSCurveGWNCache< T >> &nurbs_curve_arr, double edge_tol=1e-8, double EPS=1e-8)
	Overload for views. More...

template<typename T >
double	winding_number (const Point< T, 2 > &query, const axom::Array< detail::NURBSCurveGWNCache< T >> &nurbs_curve_arr, double edge_tol=1e-8, double EPS=1e-8)
	Overload without optional return parameter. More...

template<typename T >
axom::Array< double >	winding_number (const axom::Array< Point< T, 2 >> &query_arr, const axom::Array< detail::NURBSCurveGWNCache< T >> &nurbs_cache_arr, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for an array of 2D points wrt an array of cached data for 2D NURBS curves. More...

template<typename T , typename CurveType >
axom::Array< double >	winding_number (const axom::Array< Point< T, 2 >> &query_arr, const axom::Array< CurveType > &curve_arr, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for an array of 2D points wrt an array of generic 2D curves. More...

template<typename T , typename CurveType >
axom::Array< double >	winding_number (const axom::Array< Point< T, 2 >> &q_arr, const CurvedPolygon< CurveType > &cpoly, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for an array of 2D points wrt to a 2D curved polygon. More...

template<typename T >
axom::Array< double >	winding_number (const axom::Array< Point< T, 2 >> &q_arr, const CurvedPolygon< detail::NURBSCurveGWNCache< T >> &cpoly, double edge_tol=1e-8, double EPS=1e-8)
	Computes the GWN for an array of 2D points wrt to a 2D curved polygon. More...

Forward Declared Overloaded Operators
template<typename T , int NDIMS>
AXOM_HOST_DEVICE bool	operator== (const BoundingBox< T, NDIMS > &lhs, const BoundingBox< T, NDIMS > &rhs)
	Equality comparison operator for bounding boxes. Two bounding boxes are equal when they have the same bounds. More...

template<typename T , int NDIMS>
bool	operator!= (const BoundingBox< T, NDIMS > &lhs, const BoundingBox< T, NDIMS > &rhs)
	Inequality comparison operator for bounding boxes. Two bounding boxes are unequal when they have different bounds. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const BoundingBox< T, NDIMS > &bb)
	Overloaded output operator for bounding boxes. More...

template<typename T , int NDIMS>
bool	operator== (const OrientedBoundingBox< T, NDIMS > &lhs, const OrientedBoundingBox< T, NDIMS > &rhs)
	Equality comparison operator for oriented bounding boxes. More...

template<typename T , int NDIMS>
bool	operator!= (const OrientedBoundingBox< T, NDIMS > &lhs, const OrientedBoundingBox< T, NDIMS > &rhs)
	Inequality comparison operator for oriented bounding boxes. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const OrientedBoundingBox< T, NDIMS > &box)
	Overloaded output operator for oriented bounding boxes. More...

template<typename T , int NDIMS>
OrientedBoundingBox< T, NDIMS >	compute_oriented_bounding_box (const Point< T, NDIMS > *pts, int n)
	Creates a bounding box which contains the collection of passed in points. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Plane< T, NDIMS > &p)

template<typename T , int NDIMS>
AXOM_HOST_DEVICE bool	operator== (const Point< T, NDIMS > &lhs, const Point< T, NDIMS > &rhs)
	Equality comparison operator for points. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE bool	operator!= (const Point< T, NDIMS > &lhs, const Point< T, NDIMS > &rhs)
	Inequality comparison operator for points. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Point< T, NDIMS > &pt)
	Overloaded output operator for points. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE bool	operator== (const Segment< T, NDIMS > &lhs, const Segment< T, NDIMS > &rhs)
	Equality comparison operator for Segment. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE bool	operator!= (const Segment< T, NDIMS > &lhs, const Segment< T, NDIMS > &rhs)
	Inequality comparison operator for Segment. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Segment< T, NDIMS > &seg)
	Overloaded output operator for Segment. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Sphere< T, NDIMS > &s)

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator+ (const Vector< T, NDIMS > &A, const Vector< T, NDIMS > &B)
	Adds vectors A, B and stores the result into a new vector C. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Point< T, NDIMS >	operator+ (const Point< T, NDIMS > &P, const Vector< T, NDIMS > &V)
	Adds vector V to point P and stores the result into a new point. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Point< T, NDIMS >	operator+ (const Vector< T, NDIMS > &V, const Point< T, NDIMS > &P)
	Adds vector V to point P and stores the result into a new point. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Point< T, NDIMS >	operator- (const Point< T, NDIMS > &P, const Vector< T, NDIMS > &V)
	Subtracts vector V from point P and stores the result into a new point. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator- (const Vector< T, NDIMS > &A, const Vector< T, NDIMS > &B)
	Subtracts vectors A, B and stores the result into a new vector C. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator- (const Point< T, NDIMS > &h, const Point< T, NDIMS > &t)
	Subtracts Point t from Point h, yielding a vector. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator- (const Vector< T, NDIMS > &vec1)
	Unary negation of a vector instance. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator* (const Vector< T, NDIMS > &vec, const T scalar)
	Scalar multiplication of vector; Scalar on rhs. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator* (const T scalar, const Vector< T, NDIMS > &vec)
	Scalar multiplication of vector; Scalar on lhs. More...

template<typename T , int NDIMS>
AXOM_HOST_DEVICE Vector< T, NDIMS >	operator/ (const Vector< T, NDIMS > &vec, const T scalar)
	Scalar division of vector; Scalar on rhs. More...

template<typename T , int NDIMS>
std::ostream &	operator<< (std::ostream &os, const Vector< T, NDIMS > &vec)
	Overloaded output operator for vectors. More...

Forward-declared helper functions
template<typename T >
AXOM_HOST_DEVICE Plane< T, 2 >	make_plane (const Point< T, 2 > &x1, const Point< T, 2 > &x2)
	Constructs a Plane in 2D that goes through the specified points. More...

template<typename T >
AXOM_HOST_DEVICE Plane< T, 3 >	make_plane (const Point< T, 3 > &x1, const Point< T, 3 > &x2, const Point< T, 3 > &x3)
	Constructs a Plane in 3D that goes through the specified points. More...

Evaluates scalar-field line integrals for functions f : R^n -> R^m
template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>
LambdaRetType	evaluate_line_integral (const primal::CurvedPolygon< CurveType > &cpoly, Lambda &&integrand, int npts)
	Evaluate a line integral along the boundary of a CurvedPolygon object for a function with an arbitrary return type. More...

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>
LambdaRetType	evaluate_line_integral (const CurveType &c, Lambda &&integrand, int npts)
	Evaluate a line integral along the boundary of a generic curve for a function with an arbitrary return type. More...

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>
LambdaRetType	evaluate_line_integral (const axom::Array< CurveType > &carray, Lambda &&integrand, int npts)
	Evaluate a line integral on an array of NURBS curves on a scalar field for a function with an arbitrary return type. More...

Evaluates vector-field line integrals for functions f : R^n -> R^n
template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>
FuncRetType	evaluate_vector_line_integral (const CurvedPolygon< CurveType > &cpoly, Lambda &&vector_integrand, int npts)
	Evaluate a vector-field line integral along the boundary of a CurvedPolygon object. More...

template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>
FuncRetType	evaluate_vector_line_integral (const CurveType &c, Lambda &&vector_integrand, int npts)
	Evaluate a vector-field line integral on a single generic curve. More...

template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>
FuncRetType	evaluate_vector_line_integral (const axom::Array< CurveType > &carray, Lambda &&vector_integrand, int npts)
	Evaluate a line integral on an array of generic curves on a vector field. More...

Evaluates scalar-field 2D area integrals for functions f : R^2 -> R^m
template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>
LambdaRetType	evaluate_area_integral (const primal::CurvedPolygon< CurveType > &cpoly, Lambda &&integrand, int npts_Q, int npts_P=0)
	Evaluate an integral on the interior of a CurvedPolygon object. More...

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>
LambdaRetType	evaluate_area_integral (const axom::Array< CurveType > &carray, Lambda &&integrand, int npts_Q, int npts_P=0)
	Evaluate an integral on the interior of a region bound by 2D curves. More...

Evaluates scalar-field surface integrals for functions f : R^3 -> R^m
template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>
LambdaRetType	evaluate_surface_integral (const primal::BezierPatch< T, 3 > &patch, Lambda &&integrand, int npts)
	Evaluate a scalar surface integral on a single Bezier patch. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>
LambdaRetType	evaluate_surface_integral (const primal::NURBSPatch< T, 3 > &patch, Lambda &&integrand, int npts_Q, int npts_P=0)
	Evaluate a scalar surface integral on a single NURBS patch. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>
LambdaRetType	evaluate_surface_integral (const axom::Array< BezierPatch< T, 3 >> &patches, Lambda &&integrand, int npts)
	Evaluate a scalar surface integral on a collection of Bezier patches. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>
LambdaRetType	evaluate_surface_integral (const axom::Array< NURBSPatch< T, 3 >> &patches, Lambda &&integrand, int npts_Q, int npts_P=0)
	Evaluate a scalar surface integral on a collection of NURBS patches. More...

Evaluates scalar-field volume integrals for functions f : R^3 -> R^m
template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>
LambdaRetType	evaluate_volume_integral (const primal::BezierPatch< T, 3 > &patch, Lambda &&integrand, T lower_bound_z, int npts_uv, int npts_z=0)
	Evaluate a scalar volume-integral contribution from a single Bezier patch. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>
LambdaRetType	evaluate_volume_integral (const primal::NURBSPatch< T, 3 > &patch, Lambda &&integrand, T lower_bound_z, int npts_Q, int npts_P=0, int npts_Z=0)
	Evaluate a scalar volume-integral contribution from a single NURBS patch. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>
LambdaRetType	evaluate_volume_integral (const axom::Array< BezierPatch< T, 3 >> &patches, Lambda &&integrand, int npts_uv, int npts_z=0)
	Evaluate a scalar volume integral over a collection of Bezier patches. More...

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>
LambdaRetType	evaluate_volume_integral (const axom::Array< NURBSPatch< T, 3 >> &patches, Lambda &&integrand, int npts_Q, int npts_P=0, int npts_Z=0)
	Evaluate a scalar volume integral over a collection of NURBS patches. More...

Triangle Intersection Routines

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Triangle< T, 3 > &t1, const Triangle< T, 3 > &t2, bool includeBoundary=false, double EPS=1E-08)
	Tests if 3D Triangles t1 and t2 intersect. More...

template<typename T >
bool	intersect (const Triangle< T, 2 > &t1, const Triangle< T, 2 > &t2, bool includeBoundary=false, double EPS=1E-08)
	Tests if 2D Triangles t1 and t2 intersect. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Triangle< T, 3 > &tri, const BoundingBox< T, 3 > &bb)
	Determines if a triangle and a bounding box intersect. More...

template<typename T >
bool	intersect (const Triangle< T, 3 > &tri, const Ray< T, 3 > &ray)
	Determines if a 3D triangle intersects a 3D ray. More...

template<typename T >
bool	intersect (const Triangle< T, 3 > &tri, const Ray< T, 3 > &ray, T &t)
	Determines if a 3D triangle intersects a 3D ray. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Triangle< T, 3 > &tri, const Ray< T, 3 > &ray, T &t, Point< double, 3 > &p)
	Determines if a 3D triangle intersects a 3D ray. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Triangle< T, 3 > &tri, const Segment< T, 3 > &seg)
	Determines if a 3D triangle intersects a 3D segment. More...

template<typename T >
bool	intersect (const Triangle< T, 3 > &tri, const Segment< T, 3 > &seg, T &t)
	Determines if a 3D triangle intersects a 3D segment. More...

template<typename T >
bool	intersect (const Triangle< T, 3 > &tri, const Segment< T, 3 > &seg, T &t, Point< double, 3 > &p)
	Determines if a 3D triangle intersects a 3D segment. More...

Ray Intersection Routines
template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Ray< T, 2 > &R, const Segment< T, 2 > &S, T &ray_param, T &seg_param, const T EPS=1e-8)
	Computes the intersection of the given ray, R, with the segment, S. More...

template<typename T >
bool	intersect (const Ray< T, 2 > &R, const Segment< T, 2 > &S, T &ray_param)
	Computes the intersection of the given ray, R, with the segment, S. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Ray< T, 2 > &R, const Segment< T, 2 > &S)
	Computes the intersection of the given ray, R, with the segment, S. More...

template<typename T >
bool	intersect (const Ray< T, 2 > &R, const Segment< T, 2 > &S, Point< T, 2 > &ip, const T EPS=1e-8)
	Computes the intersection of the given ray, R, with the segment, S. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Ray< T, DIM > &R, const BoundingBox< T, DIM > &bb, Point< T, DIM > &ip)
	Computes the intersection of the given ray, R, with the Box, bb. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Ray< T, DIM > &R, const BoundingBox< T, DIM > &bb)
	Computes the intersection of the given ray, R, with the Box, bb. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Line< T, DIM > &L, const BoundingBox< T, DIM > &bb, Point< T, DIM > &ip)
	Computes the intersection of the given line, L, with the Box, bb. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Line< T, DIM > &L, const BoundingBox< T, DIM > &bb)
	Computes the intersection of the given line, L, with the Box, bb. More...

Segment-BoundingBox Intersection Routines
template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Segment< T, DIM > &S, const BoundingBox< T, DIM > &bb, T &tmin, T &tmax, const double &EPS=1e-8)
	Computes the intersection of the given segment, S, with the Box, bb. If an intersection is found, output parameter ip contains an intersection point. More...

template<typename T , int DIM>
bool	intersect (const Segment< T, DIM > &S, const BoundingBox< T, DIM > &bb, Point< T, DIM > &ip, const double &EPS=1e-8)
	This variant returns a point within the intersection as an OUT parameters. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Segment< T, DIM > &S, const BoundingBox< T, DIM > &bb)

Axis-Aligned Bounding Box Intersection Routines
template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const BoundingBox< T, DIM > &bb1, const BoundingBox< T, DIM > &bb2)
	Determines if two axis aligned bounding boxes intersect. More...

Sphere Intersection Routines
template<typename T , int DIM>
bool	intersect (const Sphere< T, DIM > &s1, const Sphere< T, DIM > &s2, double TOL=1.e-9)
	Determines if two spheres intersect. More...

template<typename T >
bool	intersect (const Sphere< T, 2 > &circle, const BoundingBox< T, 2 > &bb)
	Determines if a 2D sphere intersects (overlaps with) a bounding box. More...

template<typename T >
bool	intersect (const Sphere< T, 2 > &circle, const NURBSCurve< T, 2 > &curve, axom::Array< T > &circle_params, axom::Array< T > &curve_params, double tol=1e-8, double EPS=1e-8)
	Determines if a 2D sphere intersects a NURBS Curve. More...

Oriented Bounding Box Intersection Routines
template<typename T >
bool	intersect (const OrientedBoundingBox< T, 1 > &b1, const OrientedBoundingBox< T, 1 > &b2)

template<typename T >
bool	intersect (const OrientedBoundingBox< T, 2 > &b1, const OrientedBoundingBox< T, 2 > &b2)
	Determines if a 2D OBB intersects a 2D OBB. More...

template<typename T >
bool	intersect (const OrientedBoundingBox< T, 3 > &b1, const OrientedBoundingBox< T, 3 > &b2, double EPS=1E-4)
	Determines if a 3D OBB intersects a 3D OBB. More...

Bezier Curve Intersection Routines
template<typename T >
bool	intersect (const BezierCurve< T, 2 > &c1, const BezierCurve< T, 2 > &c2, axom::Array< T > &sp, axom::Array< T > &tp, double tol=1E-8)
	Tests if two Bezier Curves c1 and c2 intersect. More...

template<typename T >
bool	intersect (const Ray< T, 2 > &r, const BezierCurve< T, 2 > &c, axom::Array< T > &rp, axom::Array< T > &cp, double tol=1E-8, double EPS=1E-8)
	Function to find intersections between a ray and a Bezier curve. More...

template<typename T >
bool	intersect (const Ray< T, 2 > &r, const NURBSCurve< T, 2 > &n, axom::Array< T > &rp, axom::Array< T > &np, double tol=1E-8, double EPS=1E-8)
	Function to find intersections between a ray and a NURBS curve. More...

Plane Intersection Routines
template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Plane< T, 3 > &p, const BoundingBox< T, 3 > &bb, bool checkOverlaps=false, double EPS=1E-08)
	Determines if a 3D plane intersects a 3D bounding box. By default (checkOverlaps is false), checks if \|s\| <= r, where "s" is the distance of the bounding box center to the plane, and "r" is the projected radius of the bounding box along the line parallel to the plane normal and going through the box center. If checkOverlaps is true, checks if \|s\| < r, where the bounding box overlaps both half spaces of the plane. More...

template<typename T , int DIM>
AXOM_HOST_DEVICE bool	intersect (const Plane< T, DIM > &plane, const Segment< T, DIM > &seg, T &t, const double &EPS=1e-12)
	Determines if a plane intersects a segment. More...

template<typename T >
AXOM_HOST_DEVICE bool	intersect (const Plane< T, 3 > &p, const Tetrahedron< T, 3 > &tet, Polygon< T, 3 > &intersection)
	Determines if a 3D plane intersects a tetrahedron. More...

Winding number operations between 3D points and primitives
template<typename T >
double	winding_number (const Point< T, 3 > &q, const Triangle< T, 3 > &tri, bool &isOnFace, const double edge_tol=1e-8, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a 3D triangle. More...

template<typename T >
double	winding_number (const Point< T, 3 > &q, const Triangle< T, 3 > &tri, const double edge_tol=1e-8, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a 3D triangle. More...

template<typename T >
double	winding_number (const Point< T, 3 > &q, const Polygon< T, 3 > &poly, bool &isOnFace, const double edge_tol=1e-8, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a 3D planar polygon. More...

template<typename T >
double	winding_number (const Point< T, 3 > &q, const Polygon< T, 3 > &poly, const double edge_tol=1e-8, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a 3D planar polygon. More...

template<typename T >
int	winding_number (const Point< T, 3 > &q, const Polyhedron< T, 3 > &poly, bool includeBoundary=false, double edge_tol=1e-8, double EPS=1e-8)
	Computes the winding number for a 3D point wrt a 3D convex polyhedron. More...

template<typename T >
double	winding_number (const Point< T, 3 > &query, const detail::NURBSPatchGWNCache< T > &nurbs, const double edge_tol=1e-8, const double ls_tol=1e-8, const double quad_tol=1e-8, const double disk_size=0.01, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a 3D NURBS patch with precomputed data. More...

template<typename T >
double	winding_number (const Point< T, 3 > &query, const axom::ArrayView< const detail::NURBSPatchGWNCache< T >> &nurbs_arr, const double edge_tol=1e-8, const double ls_tol=1e-8, const double quad_tol=1e-8, const double disk_size=0.01, const double EPS=1e-8)
	Overload for a single query and an ArrayView. More...

template<typename T , typename SurfaceType >
double	winding_number (const Point< T, 3 > &query, const SurfaceType &surf, const double edge_tol=1e-8, const double ls_tol=1e-8, const double quad_tol=1e-8, const double disk_size=0.01, const double EPS=1e-8)
	Computes the GWN for a 3D point wrt a generic 3D surface object. More...

template<typename T >
axom::Array< double >	winding_number (const axom::Array< Point< T, 3 >> &query_arr, const axom::Array< detail::NURBSPatchGWNCache< T >> &nurbs_arr, const double edge_tol=1e-8, const double ls_tol=1e-8, const double quad_tol=1e-8, const double disk_size=0.01, const double EPS=1e-8)
	Computes the GWN for an array of 3D point wrt an array of NURBS patch cache data. More...

template<typename T , typename SurfaceType >
axom::Array< double >	winding_number (const axom::Array< Point< T, 3 >> &query_arr, const axom::Array< SurfaceType > &surf_arr, const double edge_tol=1e-8, const double ls_tol=1e-8, const double quad_tol=1e-8, const double disk_size=0.01, const double EPS=1e-8)
	Computes the GWN for an array an array of 3D points wrt an array of generic surfaces. More...

Typedef Documentation

◆ Point2D

using axom::primal::Point2D = typedef Point<double, 2>

◆ Point3D

using axom::primal::Point3D = typedef Point<double, 3>

◆ Vector2D

using axom::primal::Vector2D = typedef Vector<double, 2>

◆ Vector3D

using axom::primal::Vector3D = typedef Vector<double, 3>

Enumeration Type Documentation

◆ OrientationResult

enum axom::primal::OrientationResult

Enumerates possible return values for orientation tests.

Enumerator
ON_BOUNDARY	primitive is on the boundary of a primitive
ON_POSITIVE_SIDE	primitive is on the positive side of a primitive
ON_NEGATIVE_SIDE	primitive is on the negative side of a primitive

◆ PolygonArray

enum axom::primal::PolygonArray

strong

The polygon can have a dynamic or static array to store vertices

Enumerator
Dynamic
Static

Function Documentation

◆ operator<<() [1/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const BezierCurve< T, NDIMS > &	bCurve
	)

Overloaded output operator for Bezier Curves.

Free functions related to BezierCurve.

References axom::primal::BezierCurve< T, NDIMS >::print().

◆ operator<<() [2/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const BezierPatch< T, NDIMS > &	bPatch
	)

Overloaded output operator for Bezier Patches.

Free functions related to BezierPatch.

References axom::primal::BezierPatch< T, NDIMS >::print().

◆ operator==() [1/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::operator==	(	const BoundingBox< T, NDIMS > &	lhs,
		const BoundingBox< T, NDIMS > &	rhs
	)

Equality comparison operator for bounding boxes. Two bounding boxes are equal when they have the same bounds.

Free functions implementing comparison and arithmetic operators.

References axom::primal::BoundingBox< T, NDIMS >::getMax(), and axom::primal::BoundingBox< T, NDIMS >::getMin().

◆ operator!=() [1/4]

template<typename T , int NDIMS>

bool axom::primal::operator!=	(	const BoundingBox< T, NDIMS > &	lhs,
		const BoundingBox< T, NDIMS > &	rhs
	)

Inequality comparison operator for bounding boxes. Two bounding boxes are unequal when they have different bounds.

◆ operator<<() [3/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const BoundingBox< T, NDIMS > &	bb
	)

Overloaded output operator for bounding boxes.

References axom::primal::BoundingBox< T, NDIMS >::print().

◆ operator<<() [4/23]

template<typename T , int NDIMS>

std::ostream& axom::primal::operator<<	(	std::ostream &	os,
		const Cone< T, NDIMS > &	Cone
	)

Free functions implementing Cone's operators.

References axom::primal::Cone< T, NDIMS >::print().

◆ regular_polygon()

template<typename T , int NDIMS, PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>

Polygon<T, NDIMS, ARRAY_TYPE, MAX_VERTS> axom::primal::regular_polygon	(	int	nSides,
		T	radius = `T {1}`,
		const axom::numerics::Matrix< T > &	transform = `axom::numerics::Matrix<T>::identity(NDIMS)`
	)

Create a regular polygon.

Parameters

nSides	The number of sides in the polygon.
radius	The radius of the polgon from the origin to a point.
transform	An optional transformation matrix, which defaults to the identity matrix for the dimension NDIMS.

Returns: A new regular polygon with nSides sides and radius \radius, transformed by the supplied tranformation matrix.

Note: This is host-only function.

◆ regular_prism()

template<typename T >

Polyhedron<T, 3> axom::primal::regular_prism	(	int	numSides,
		T	radius = `1`,
		T	height = `1`,
		const axom::numerics::Matrix< T > &	transform = `axom::numerics::Matrix<T>::identity(4)`
	)

Construct a regular 3D prism.

Parameters

numSides	The number of sides on the base polygon.
radius	The radius of the base polygon.
height	The height of the prism.
transform	An optional 4x4 matrix transformation.

Returns: A Polyhedron that represents the regular prism.

References axom::primal::Polyhedron< T, NDIMS >::addNeighbors(), axom::primal::Polyhedron< T, NDIMS >::addVertex(), axom::numerics::Matrix< T >::getNumColumns(), axom::numerics::Matrix< T >::getNumRows(), axom::numerics::matrix_multiply(), SLIC_ASSERT, and axom::numerics::Matrix< T >::zeros().

◆ operator<<() [5/23]

template<typename CurveType >

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const CurvedPolygon< CurveType > &	poly
	)

Overloaded output operator for polygons.

Free functions implementing Polygon's operators.

References axom::primal::CurvedPolygon< CurveType >::print().

◆ operator<<() [6/23]

template<typename T , int NDIMS>

std::ostream& axom::primal::operator<<	(	std::ostream &	os,
		const Hexahedron< T, NDIMS > &	hex
	)

Free functions implementing Hexahedron's operators.

References axom::primal::Hexahedron< T, NDIMS >::print().

◆ operator<<() [7/23]

template<typename T >

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const KnotVector< T > &	kVec
	)

Overloaded output operator for knot vectors.

Free functions related to KnotVector.

References axom::primal::KnotVector< T >::print().

◆ operator<<() [8/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Line< T, NDIMS > &	line
	)

Overloaded output operator for lines.

Free functions implementing Line's operators.

References axom::primal::Line< T, NDIMS >::print().

◆ operator<<() [9/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const NURBSCurve< T, NDIMS > &	bCurve
	)

Overloaded output operator for NURBS Curves.

Free functions related to NURBSCurve.

References axom::primal::NURBSCurve< T, NDIMS >::print().

◆ operator<<() [10/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const NURBSPatch< T, NDIMS > &	nPatch
	)

Overloaded output operator for NURBS Patches.

Free functions related to NURBSPatch.

References axom::primal::NURBSPatch< T, NDIMS >::print().

◆ operator<<() [11/23]

template<typename T , int NDIMS>

std::ostream& axom::primal::operator<<	(	std::ostream &	os,
		const Octahedron< T, NDIMS > &	oct
	)

Free functions implementing Octahedron's operators.

References axom::primal::Octahedron< T, NDIMS >::print().

◆ operator==() [2/4]

template<typename T , int NDIMS>

bool axom::primal::operator==	(	const OrientedBoundingBox< T, NDIMS > &	lhs,
		const OrientedBoundingBox< T, NDIMS > &	rhs
	)

Equality comparison operator for oriented bounding boxes.

Free functions implementing comparison and arithmetic operators.

Two oriented bounding boxes are equal when they have the same bounds and axes.

References axom::primal::OrientedBoundingBox< T, NDIMS >::contains().

◆ operator!=() [2/4]

template<typename T , int NDIMS>

bool axom::primal::operator!=	(	const OrientedBoundingBox< T, NDIMS > &	lhs,
		const OrientedBoundingBox< T, NDIMS > &	rhs
	)

Inequality comparison operator for oriented bounding boxes.

Two bounding boxes are unequal when they have different bounds

◆ operator<<() [12/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const OrientedBoundingBox< T, NDIMS > &	box
	)

Overloaded output operator for oriented bounding boxes.

References axom::primal::OrientedBoundingBox< T, NDIMS >::print().

◆ compute_oriented_bounding_box()

template<typename T , int NDIMS>

OrientedBoundingBox< T, NDIMS > axom::primal::compute_oriented_bounding_box	(	const Point< T, NDIMS > *	pts,
		int	n
	)

Creates a bounding box which contains the collection of passed in points.

Call srand() to initialize the random number generator before using this function.

Parameters

[in]	pts	array of points
[in]	n	number of points

Note: if n <= 0, invokes default constructor

◆ operator<<() [13/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Plane< T, NDIMS > &	p
	)

References axom::primal::Plane< T, NDIMS >::print().

◆ make_plane() [1/2]

template<typename T >

AXOM_HOST_DEVICE Plane< T, 2 > axom::primal::make_plane	(	const Point< T, 2 > &	x1,
		const Point< T, 2 > &	x2
	)

Constructs a Plane in 2D that goes through the specified points.

Parameters

[in]	x1	coordinates of the first point.
[in]	x2	coordinates of the second point.

Returns: plane the plane/line defined by the two points

Precondition: x1 should not be equal to x2

References axom::primal::Vector< T, NDIMS >::is_zero(), and SLIC_CHECK_MSG.

◆ make_plane() [2/2]

template<typename T >

AXOM_HOST_DEVICE Plane< T, 3 > axom::primal::make_plane	(	const Point< T, 3 > &	x1,
		const Point< T, 3 > &	x2,
		const Point< T, 3 > &	x3
	)

Constructs a Plane in 3D that goes through the specified points.

Parameters

[in]	x1	coordinates of the first point.
[in]	x2	coordinates of the second point.
[in]	x3	coordinates of the third point.

Returns: plane the plane defined by the three points

Precondition: The user-supplied points, x1, x2, x3 should not be collinear.

References axom::primal::Vector< T, NDIMS >::cross_product(), axom::primal::Vector< T, NDIMS >::is_zero(), and SLIC_CHECK_MSG.

◆ operator==() [3/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::operator==	(	const Point< T, NDIMS > &	lhs,
		const Point< T, NDIMS > &	rhs
	)

Equality comparison operator for points.

◆ operator!=() [3/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::operator!=	(	const Point< T, NDIMS > &	lhs,
		const Point< T, NDIMS > &	rhs
	)

Inequality comparison operator for points.

Inequality operator for points.

◆ operator<<() [14/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Point< T, NDIMS > &	pt
	)

Overloaded output operator for points.

Free functions implementing Point's operators.

References axom::primal::Point< T, NDIMS >::print().

◆ transform_point()

template<typename T , int NDIMS>

Point<T, NDIMS> axom::primal::transform_point	(	const Point< T, NDIMS > &	pt,
		const axom::numerics::Matrix< T > &	transform = `axom::numerics::Matrix<T>::identity(NDIMS)`
	)

Transform a point using a transformation matrix.

Parameters

pt	The point to be transformed.
transform	The transformation matrix.

Returns: The transformed point.

Note: We allow a matrix 1 rank larger than NDIMS so we can perform translations.

References axom::numerics::matrix_vector_multiply(), and SLIC_ASSERT.

◆ operator<<() [15/23]

template<typename T , int NDIMS, axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS > &	poly
	)

Overloaded output operator for polygons.

Free functions implementing Polygon's operators.

References axom::primal::Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >::print().

◆ operator<<() [16/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Polyhedron< T, NDIMS > &	poly
	)

Overloaded output operator for polyhedrons.

Free functions implementing Polyhedron's operators.

References axom::primal::Polyhedron< T, NDIMS >::print().

◆ operator<<() [17/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Quadrilateral< T, NDIMS > &	quad
	)

Overloaded output operator for quadrilaterals.

Free functions implementing Quadrilateral's operators.

References axom::primal::Quadrilateral< T, NDIMS >::print().

◆ operator<<() [18/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Ray< T, NDIMS > &	ray
	)

Overloaded output operator for rays.

Free functions implementing Ray's operators.

References axom::primal::Ray< T, NDIMS >::print().

◆ operator==() [4/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::operator==	(	const Segment< T, NDIMS > &	lhs,
		const Segment< T, NDIMS > &	rhs
	)

Equality comparison operator for Segment.

Equality comparison operator for segments.

◆ operator!=() [4/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::operator!=	(	const Segment< T, NDIMS > &	lhs,
		const Segment< T, NDIMS > &	rhs
	)

Inequality comparison operator for Segment.

Inequality operator for segments.

◆ operator<<() [19/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Segment< T, NDIMS > &	seg
	)

Overloaded output operator for Segment.

Free functions implementing Segments's operators.

References axom::primal::Segment< T, NDIMS >::print().

◆ operator<<() [20/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Sphere< T, NDIMS > &	s
	)

References axom::primal::Sphere< T, NDIMS >::print().

◆ operator<<() [21/23]

template<typename T , int NDIMS>

std::ostream& axom::primal::operator<<	(	std::ostream &	os,
		const Tetrahedron< T, NDIMS > &	tet
	)

Free functions implementing Tetrahedron's operators.

References axom::primal::Tetrahedron< T, NDIMS >::print().

◆ operator<<() [22/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Triangle< T, NDIMS > &	tri
	)

Overloaded output operator for triangles.

Free functions implementing Triangle's operators.

References axom::primal::Triangle< T, NDIMS >::print().

◆ operator+() [1/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator+	(	const Vector< T, NDIMS > &	A,
		const Vector< T, NDIMS > &	B
	)

inline

Adds vectors A, B and stores the result into a new vector C.

Parameters

[in]	A	vector on the left-hand side.
[in]	B	vector on the right-hand side.

Returns: C resulting vector, \( C_i = A_i + B_i \forall i \)

◆ operator+() [2/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Point< T, NDIMS > axom::primal::operator+	(	const Point< T, NDIMS > &	P,
		const Vector< T, NDIMS > &	V
	)

Adds vector V to point P and stores the result into a new point.

Parameters

[in]	P	point on the left-hand side.
[in]	V	vector on the right-hand side.

Returns: resulting point, \( p'_i = p_i + v_i \forall i \)

References axom::primal::Point< T, NDIMS >::array(), and axom::primal::Vector< T, NDIMS >::array().

◆ operator+() [3/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Point< T, NDIMS > axom::primal::operator+	(	const Vector< T, NDIMS > &	V,
		const Point< T, NDIMS > &	P
	)

Adds vector V to point P and stores the result into a new point.

Parameters

[in]	V	vector on the left-hand side.
[in]	P	point on the right-hand side.

Returns: resulting point, \( p'_i = v_i + p_i \forall i \)

◆ operator-() [1/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Point< T, NDIMS > axom::primal::operator-	(	const Point< T, NDIMS > &	P,
		const Vector< T, NDIMS > &	V
	)

Subtracts vector V from point P and stores the result into a new point.

Parameters

[in]	P	point on the left-hand side.
[in]	V	vector on the right-hand side.

Returns: resulting point, \( p'_i = p_i + v_i \forall i \)

References axom::primal::Point< T, NDIMS >::array(), and axom::primal::Vector< T, NDIMS >::array().

◆ operator-() [2/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator-	(	const Vector< T, NDIMS > &	A,
		const Vector< T, NDIMS > &	B
	)

inline

Subtracts vectors A, B and stores the result into a new vector C.

Parameters

[in]	A	vector on the left-hand side.
[in]	B	vector on the right-hand side.

Returns: C resulting vector, \( C_i = A_i - B_i \forall i \)

◆ operator-() [3/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator-	(	const Point< T, NDIMS > &	h,
		const Point< T, NDIMS > &	t
	)

Subtracts Point t from Point h, yielding a vector.

Parameters

[in]	h	the head of the resulting vector
[in]	t	the tail of the resulting vector

Returns: resulting vector, \( V_i = h_i - t_i \forall i \)

◆ operator-() [4/4]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator- ( const Vector< T, NDIMS > & vec1 )

inline

Unary negation of a vector instance.

Parameters

[in] vec1 vector instance to negate.

Returns: C resulting vector from unary negation.

References axom::primal::Vector< T, NDIMS >::negate().

◆ operator*() [1/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator*	(	const Vector< T, NDIMS > &	vec,
		const T	scalar
	)

inline

Scalar multiplication of vector; Scalar on rhs.

Free functions involving vectors.

Parameters

[in]	vec	vector instance.
[in]	scalar	user-supplied scalar.

Returns: C resulting vector, \( \ni: C_i = scalar*vec_i, \forall i\)

◆ operator*() [2/2]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator*	(	const T	scalar,
		const Vector< T, NDIMS > &	vec
	)

inline

Scalar multiplication of vector; Scalar on lhs.

Parameters

[in]	scalar	user-supplied scalar.
[in]	vec	vector instance.

Returns: C resulting vector, \( \ni: C_i = scalar*vec_i, \forall i\)

◆ operator/()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Vector< T, NDIMS > axom::primal::operator/	(	const Vector< T, NDIMS > &	vec,
		const T	scalar
	)

inline

Scalar division of vector; Scalar on rhs.

Parameters

[in]	vec	vector instance
[in]	scalar	user-supplied scalar.

Returns: C resulting vector, \( \ni: C_i = vec_i / scalar, \forall i\)

Precondition: scalar != 0.0

◆ operator<<() [23/23]

template<typename T , int NDIMS>

std::ostream & axom::primal::operator<<	(	std::ostream &	os,
		const Vector< T, NDIMS > &	vec
	)

Overloaded output operator for vectors.

Parameters

[in]	os	C++ output stream
[in]	vec	vector instance

References axom::primal::Vector< T, NDIMS >::print().

◆ clip() [1/19]

template<typename T >

Polygon<T, 3> axom::primal::clip	(	const Triangle< T, 3 > &	tri,
		const BoundingBox< T, 3 > &	bbox
	)

Clips a 3D triangle against an axis-aligned bounding box in 3D.

Parameters

[in]	tri	The triangle to clip
[in]	bbox	The bounding box to clip against

Returns: A planar polygon of the triangle clipped against the bounding box. If the triangle is completely outside the bounding box, the returned polygon is empty (i.e. it has no vertices).

Note: Using a specialization of the Sutherland-Hodgeman clipping algorithm for axis aligned planes

References axom::primal::BoundingBox< T, NDIMS >::contains(), axom::primal::BoundingBox< T, NDIMS >::getMax(), axom::primal::BoundingBox< T, NDIMS >::getMin(), axom::primal::BoundingBox< T, NDIMS >::intersectsWith(), and axom::utilities::swap().

◆ clip() [2/19]

template<typename T , axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>

AXOM_SUPPRESS_HD_WARN AXOM_HOST_DEVICE Polygon<T, 2, ARRAY_TYPE, MAX_VERTS> axom::primal::clip	(	const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &	subjectPolygon,
		const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &	clipPolygon,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 2D subject polygon against a clip polygon in 2D, returning their geometric intersection as a polygon.

This function clips the subject polygon by the planes obtained from the clip polygon's edges (normals point inward). Clipping the subject polygon by each plane gives the polygon above that plane. Clipping the polygon by a plane involves finding new vertices at the intersection of the polygon edges and the plane, and removing vertices from the polygon that are below the plane.

Parameters

[in]	subjectPolygon	The subject polygon
[in]	clipPolygon	The clip polygon
[in]	eps	The tolerance for plane point orientation. Defaults to 1.e-10.
[in]	tryFixOrientation	If true, takes each shape with a negative signed area and swaps the order of some vertices in that shape to try to obtain a nonnegative signed area. Defaults to false.

Returns: A polygon of the subject polygon clipped against the clip polygon.

Note: Function is based off the Sutherland–Hodgman algorithm.

Warning: Polygons with static array types must have enough vertices preallocated for the output polygon. It is mandatory that MAX_VERTS >= subjectPolygon.numVertices() + clipPolygon.numVertices() for the output polygon with the largest possible vertex count. Otherwise, if there is not enough preallocated vertices, output polygon will have missing vertices.

See also: axom::primal::Polygon::addVertex(), axom::StaticArray::push_back() for behavior when there is not enough preallocated vertices.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polygon will have a non-positive and/or unexpected area.; If tryFixOrientation flag is false and some of the shapes have a negative signed area, the returned Polygon will have a non-positive and/or unexpected area.

◆ clip() [3/19]

template<typename T , axom::primal::PolygonArray ARRAY_TYPE, int MAX_VERTS>

AXOM_HOST_DEVICE Polygon<T, 2, ARRAY_TYPE, MAX_VERTS> axom::primal::clip	(	const Polygon< T, 2, ARRAY_TYPE, MAX_VERTS > &	subjectPolygon,
		const Plane< T, 2 > &	clipPlane,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 2D subject polygon against a clip plane in 2D, returning their geometric intersection as a polygon.

This function makes a clip polygon line segment from the plane and delegates clipping to the polygon-polygon clipper.

Parameters

[in]	subjectPolygon	The subject polygon
[in]	clipPlane	The clip plane
[in]	eps	The tolerance for plane point orientation. Defaults to 1.e-10.
[in]	tryFixOrientation	If true, takes each shape with a negative signed area and swaps the order of some vertices in that shape to try to obtain a nonnegative signed area. Defaults to false.

Returns: A polygon of the subject polygon clipped against the clip plane.

◆ clip() [4/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Hexahedron< T, 3 > &	hex,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D hexahedron against a tetrahedron in 3D, returning the geometric intersection of the hexahedron and the tetrahedron as a polyhedron.

This function clips the hexahedron by the 4 planes obtained from the tetrahedron's faces (normals point inward). Clipping the hexahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	hex	The hexahedron to clip
[in]	tet	The tetrahedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the hexahedron clipped against the tetrahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [5/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Tetrahedron< T, 3 > &	tet,
		const Hexahedron< T, 3 > &	hex,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D hexahedron against a tetrahedron in 3D, returning the geometric intersection of the hexahedron and the tetrahedron as a polyhedron.

This function clips the hexahedron by the 4 planes obtained from the tetrahedron's faces (normals point inward). Clipping the hexahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet	The tetrahedron to clip against
[in]	hex	The hexahedron to clip
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the hexahedron clipped against the tetrahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

References clip().

◆ clip() [6/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Hexahedron< T, 3 > &	hex1,
		const Hexahedron< T, 3 > &	hex2,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D hexahedron against a hexahedron in 3D, returning the geometric intersection of the hexahedron and the hexahedron as a polyhedron.

This function clips the hexahedron by the 6 planes obtained from the hexahedron's faces (normals point inward). Clipping the hexahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	hex1	The hexahedron to clip
[in]	hex2	The hexahedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the hexahedron clipped against the hexahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.; hex1 and hex2 are assumed to be convex.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [7/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Octahedron< T, 3 > &	oct,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D octahedron against a tetrahedron in 3D, returning the geometric intersection of the octahedron and the tetrahedron as a polyhedron.

This function clips the octahedron by the 4 planes obtained from the tetrahedron's faces (normals point inward). Clipping the octahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	oct	The octahedron to clip
[in]	tet	The tetrahedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the octahedron clipped against the tetrahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [8/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Tetrahedron< T, 3 > &	tet,
		const Octahedron< T, 3 > &	oct,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D octahedron against a tetrahedron in 3D, returning the geometric intersection of the octahedron and the tetrahedron as a polyhedron.

This function clips the octahedron by the 4 planes obtained from the tetrahedron's faces (normals point inward). Clipping the octahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet	The tetrahedron to clip against
[in]	oct	The octahedron to clip
[in]	tet	The tetrahedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the octahedron clipped against the tetrahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

References clip().

◆ clip() [9/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Tetrahedron< T, 3 > &	tet1,
		const Tetrahedron< T, 3 > &	tet2,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D tetrahedron against another tetrahedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the first tetrahedron by the 4 planes obtained from the second tetrahedron's faces (normals point inward). Clipping the tetrahedron/polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet1	The tetrahedron to clip
[in]	tet2	The tetrahedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the tetrahedron clipped against the other tetrahedron.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [10/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Tetrahedron< T, 3 > &	tet,
		const Polyhedron< T, 3 > &	poly,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the first polyhedron by the planes obtained from the second polyhedron's faces (normals point inward). Clipping the polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet	The tetrahedron to clip
[in]	poly	The polyhedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the clip results

Note: poly is assumed to be convex. Any non-planar faces in poly will result in multiple clipping planes for the face.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [11/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Polyhedron< T, 3 > &	poly,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the first polyhedron by the planes obtained from the second polyhedron's faces (normals point inward). Clipping the polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet	The tetrahedron to clip
[in]	poly	The polyhedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the clip results

Note: poly is assumed to be convex. Any non-planar faces in poly will result in multiple clipping planes for the face.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [12/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Hexahedron< T, 3 > &	hex,
		const Polyhedron< T, 3 > &	poly,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D hexahedron against a polyhedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the polyhedron by the planes obtained from the hexahedron's faces (normals point inward). Clipping the polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	hex	The hexahedron to clip
[in]	poly	The polyhedron to clip against
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the clip results

Note: hex and poly shapes are assumed to be convex. The hex shape is clipped as a polyhedron. Any non-planar faces may give rise to non-planar clipped faces. The poly shape's faces are used as clipping planes for hex. Any non-planar faces in poly will result in multiple clipping planes for the face.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [13/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Polyhedron< T, 3 > &	poly,
		const Hexahedron< T, 3 > &	hex,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D polyhedron against a hexahedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the polyhedron by the planes obtained from the hexahedron's faces (normals point inward). Clipping the polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	poly	The polyhedron to clip against
[in]	hex	The hexahedron to clip
[in]	eps	The epsilon value
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A polyhedron of the clip results

Note: hex and poly shapes are assumed to be convex. Any non-planar faces may give rise to non-planar clipped faces. The hex shape's faces are used as clipping planes for poly. Any non-planar faces in hex will result in multiple clipping planes for the face.

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned Polyhedron will have a non-positive and/or unexpected volume.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned Polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [14/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Polyhedron< T, 3 > &	poly1,
		const Polyhedron< T, 3 > &	poly2,
		double	eps = `1.e-10`
	)

Clips a 3D polyhedron against another polyhedron in 3D, returning the geometric intersection as a polyhedron.

This function clips the first polyhedron by the planes obtained from the second polyhedron's faces (normals point inward). Clipping the polyhedron by each plane gives the polyhedron above that plane. Clipping the polyhedron by a plane involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	poly1	The polyhedron to clip
[in]	poly2	The polyhedron to clip against
[in]	eps	The epsilon value

Returns: A polyhedron of the clip results

Note: poly1 and poly2 shapes are assumed to be convex. Any non-planar faces may give rise to non-planar clipped faces. The poly2 shape's faces are used as clipping planes for poly1. Any non-planar faces in poly2 will result in multiple clipping planes for the face.

◆ clip() [15/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Tetrahedron< T, 3 > &	tet,
		const Plane< T, 3 > &	plane,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D tetrahedron against the half-space defined by a plane and returns the resulting polyhedron.

This function clips a tetrahedron against the half-space defined by a plane. This involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	tet	The tetrahedron to clip
[in]	plane	The plane defining the half-space used to clip the tetrahedron
[in]	eps	The tolerance for plane point orientation
[in]	tryFixOrientation	If true and the tetrahedron has a negative signed volume, swaps the order of some vertices in the tetrathedron to try to obtain a nonnegative signed volume. Defaults to false.

Returns: The polyhedron obtained from clipping a tetrahedron against the half-space defined by a plane.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the tetrahedron's vertex order will be valid. It is the responsiblity of the caller to pass a tetrahedron with a valid vertex order. Otherwise, the returned polyhedron will have a non-positive and/or unexpected volume.; If the tryFixOrientation flag is false and the tetrahedron has a negative signed volume, the returned polyhedron will have a non-positive and/or unexpected volume.

◆ clip() [16/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Plane< T, 3 > &	plane,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D tetrahedron against the half-space defined by a plane and returns the resulting polyhedron.

This function clips a tetrahedron against the half-space defined by a plane. This involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	plane	The plane defining the half-space used to clip the tetrahedron
[in]	tet	The tetrahedron to clip
[in]	eps	The tolerance for plane point orientation
[in]	tryFixOrientation	If true and the tetrahedron has a negative signed volume, swaps the order of some vertices in the tetrathedron to try to obtain a nonnegative signed volume. Defaults to false.

Returns: The polyhedron obtained from clipping a tetrahedron against the half-space defined by a plane.

Note: Function is based off clipPolyhedron() in Mike Owen's PolyClipper.

Warning: tryFixOrientation flag does not guarantee the tetrahedron's vertex order will be valid. It is the responsiblity of the caller to pass a tetrahedron with a valid vertex order. Otherwise, the returned polyhedron will have a non-positive and/or unexpected volume.; If the tryFixOrientation flag is false and the tetrahedron has a negative signed volume, the returned polyhedron will have a non-positive and/or unexpected volume.

References clip().

◆ clip() [17/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Polyhedron< T, 3 > &	poly,
		const Plane< T, 3 > &	plane,
		double	eps = `1.e-10`
	)

Clips a 3D polyhedron against the half-space defined by a plane and returns the resulting polyhedron.

This function clips a polyhedron against the half-space defined by a plane. This involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	plane	The plane defining the half-space used to clip the tetrahedron
[in]	poly	The polyhedron to clip
[in]	eps	The tolerance for plane point orientation

Returns: The polyhedron obtained from clipping a polyhedron against the half-space defined by a plane.

◆ clip() [18/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Plane< T, 3 > &	plane,
		const Polyhedron< T, 3 > &	poly,
		double	eps = `1.e-10`
	)

Clips a 3D polyhedron against the half-space defined by a plane and returns the resulting polyhedron.

This function clips a polyhedron against the half-space defined by a plane. This involves finding new vertices at the intersection of the polyhedron edges and the plane, removing vertices from the polyhedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	poly	The polyhedron to clip
[in]	plane	The plane defining the half-space used to clip the polyhedron.
[in]	eps	The tolerance for plane point orientation

Returns: The polyhedron obtained from clipping a polyhedron against the half-space defined by a plane.

◆ clip() [19/19]

template<typename T >

AXOM_HOST_DEVICE Polyhedron<T, 3> axom::primal::clip	(	const Hexahedron< T, 3 > &	hex,
		const Plane< T, 3 > &	plane,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Clips a 3D hexahedron against the half-space defined by a plane and returns the resulting polyhedron.

This function clips a hexahedron against the half-space defined by a plane. This involves finding new vertices at the intersection of the hexahedron edges and the plane, removing vertices from the hexahedron that are below the plane, and redefining the neighbors for each vertex (a vertex is a neighbor of another vertex if there is an edge between them).

Parameters

[in]	hex	The hexahedron to clip
[in]	plane	The plane defining the half-space used to clip the hexahedron.
[in]	eps	The tolerance for plane point orientation
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: The polyhedron obtained from clipping a hexahedron against the half-space defined by a plane.

References clip(), and axom::primal::Polyhedron< T, NDIMS >::from_primitive().

◆ merge_boxes() [1/2]

template<typename T , int NDIMS>

OrientedBoundingBox<T, NDIMS> axom::primal::merge_boxes	(	const OrientedBoundingBox< T, NDIMS > &	l,
		const OrientedBoundingBox< T, NDIMS > &	r
	)

Creates an oriented bounding box which contains the passed in OBBs.

Call srand() to initialize the random number generator before using this function.

Parameters

[in]	l	left obb
[in]	r	right obb

References axom::primal::OrientedBoundingBox< T, NDIMS >::contains(), and axom::primal::OrientedBoundingBox< T, NDIMS >::vertices().

◆ merge_boxes() [2/2]

template<typename T , int NDIMS>

BoundingBox<T, NDIMS> axom::primal::merge_boxes	(	const BoundingBox< T, NDIMS > &	l,
		const BoundingBox< T, NDIMS > &	r
	)

Constructor. Creates a bounding box which contains the passed in bounding boxes.

Parameters

[in]	l	left bb
[in]	r	right bb

References axom::primal::BoundingBox< T, NDIMS >::addBox().

◆ compute_bounding_box() [1/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Triangle< T, NDIMS > & tri )

Creates a bounding box around a Triangle.

Parameters

[in] tri The Triangle

◆ compute_bounding_box() [2/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Quadrilateral< T, NDIMS > & quad )

Creates a bounding box around a Quadrilateral.

Parameters

[in] quad The Quadrilateral

◆ compute_bounding_box() [3/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Octahedron< T, NDIMS > & oct )

Creates a bounding box around an Octahedron.

Parameters

[in] oct The Octahedron

◆ compute_bounding_box() [4/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Hexahedron< T, NDIMS > & hex )

Creates a bounding box around a Hexahedron.

Parameters

[in] hex The Hexahedron

◆ compute_bounding_box() [5/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Polyhedron< T, NDIMS > & poly )

Creates a bounding box around a Polyhedron.

Parameters

[in] poly The Polyhedron

References axom::primal::BoundingBox< T, NDIMS >::addPoint(), and axom::primal::Polyhedron< T, NDIMS >::numVertices().

◆ compute_bounding_box() [6/7]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Tetrahedron< T, NDIMS > & tet )

Creates a bounding box around a Tetrahedron.

Parameters

[in] tet The tetrahedron

◆ compute_bounding_box() [7/7]

template<typename T , int NDIMS, PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>

AXOM_HOST_DEVICE BoundingBox<T, NDIMS> axom::primal::compute_bounding_box ( const Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS > & poly )

Creates a bounding box around a Polygon.

Parameters

[in] poly The polygon

References axom::primal::BoundingBox< T, NDIMS >::addPoint(), and axom::primal::Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >::numVertices().

◆ sector_area()

template<typename T >

T axom::primal::sector_area ( const primal::BezierCurve< T, 2 > & curve )

Calculates the signed sector area of a planar, nonrational Bezier curve.

The sector area is the signed area between the curve and the origin. The equation and derivation are described in: Ueda, K. "Signed area of sectors between spline curves and the origin" IEEE International Conference on Information Visualization, 1999.

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and SLIC_ASSERT.

◆ sector_centroid()

template<typename T >

primal::Point<T, 2> axom::primal::sector_centroid ( const primal::BezierCurve< T, 2 > & curve )

Calculates the area-weighted centroid numerator of a planar, nonrational Bezier curve.

This is the first raw moment of the region between the curve and the origin. Divide by sector_area() to recover the centroid. The equation and derivation are generalizations of: Ueda, K. "Signed area of sectors between spline curves and the origin" IEEE International Conference on Information Visualization, 1999.

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), axom::primal::BezierCurve< T, NDIMS >::isRational(), and SLIC_ASSERT.

◆ area()

template<typename T >

T axom::primal::area	(	const primal::CurvedPolygon< BezierCurve< T, 2 >> &	poly,
		double	tol = `1e-8`
	)

Returns the area enclosed by the CurvedPolygon.

References sector_area(), SLIC_ASSERT, and SLIC_DEBUG.

◆ centroid()

template<typename T >

primal::Point<T, 2> axom::primal::centroid	(	const primal::CurvedPolygon< BezierCurve< T, 2 >> &	poly,
		double	tol = `1e-8`
	)

Returns the centroid of the CurvedPolygon.

References area(), sector_centroid(), SLIC_ASSERT, and SLIC_DEBUG.

◆ evaluate_line_integral() [1/3]

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>

LambdaRetType axom::primal::evaluate_line_integral	(	const primal::CurvedPolygon< CurveType > &	cpoly,
		Lambda &&	integrand,
		int	npts
	)

Evaluate a line integral along the boundary of a CurvedPolygon object for a function with an arbitrary return type.

The line integral is evaluated on each curve in the CurvedPolygon, and added together to represent the total integral. The curved polygon need not be connected.

Evaluate the line integral with Gauss-Legendre quadrature

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning an integrable type
LambdaRetType	A type which supports addition and scalar multiplication

Parameters

[in]	cpoly	the CurvedPolygon object
[in]	integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature points to evaluate the line integral on each edge of the CurvedPolygon

Returns: the value of the integral

References axom::primal::CurvedPolygon< CurveType >::numEdges().

◆ evaluate_line_integral() [2/3]

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>

LambdaRetType axom::primal::evaluate_line_integral	(	const CurveType &	c,
		Lambda &&	integrand,
		int	npts
	)

Evaluate a line integral along the boundary of a generic curve for a function with an arbitrary return type.

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning an integrable type
LambdaRetType	A type which supports addition and scalar multiplication

Parameters

[in]	c	the generic curve object
[in]	integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature nodes

Returns: the value of the integral

◆ evaluate_line_integral() [3/3]

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>

LambdaRetType axom::primal::evaluate_line_integral	(	const axom::Array< CurveType > &	carray,
		Lambda &&	integrand,
		int	npts
	)

Evaluate a line integral on an array of NURBS curves on a scalar field for a function with an arbitrary return type.

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning an integrable type
LambdaRetType	A type which supports addition and scalar multiplication

Parameters

[in]	carray	The array of generic curve objects
[in]	integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature nodes per curve per knot span

Note: Each NURBS curve is decomposed into Bezier segments, and the Gaussian quadrature is computed using npts on each segment

Returns: the value of the integral

References axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ evaluate_vector_line_integral() [1/3]

template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>

FuncRetType axom::primal::evaluate_vector_line_integral	(	const CurvedPolygon< CurveType > &	cpoly,
		Lambda &&	vector_integrand,
		int	npts
	)

Evaluate a vector-field line integral along the boundary of a CurvedPolygon object.

The line integral is evaluated on each curve in the CurvedPolygon, and added together to represent the total integral. The Polygon need not be connected.

Evaluate the vector field line integral with Gauss-Legendre quadrature

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning its numeric type
FuncRetType	The CurveType's numeric type

Parameters

[in]	cpoly	the CurvedPolygon object
[in]	vector_integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature points to evaluate the line integral on each edge of the CurvedPolygon

Precondition: Lambda must return the CurveTypes's vector type

Returns: the value of the integral

References axom::primal::CurvedPolygon< CurveType >::numEdges().

◆ evaluate_vector_line_integral() [2/3]

template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>

FuncRetType axom::primal::evaluate_vector_line_integral	(	const CurveType &	c,
		Lambda &&	vector_integrand,
		int	npts
	)

Evaluate a vector-field line integral on a single generic curve.

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning its numeric type
FuncRetType	The CurveType's numeric type

Parameters

[in]	c	the generic curve object
[in]	vector_integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature nodes

Precondition: Lambda must return the CurveTypes's vector type

Returns: the value of the integral

◆ evaluate_vector_line_integral() [3/3]

template<typename CurveType , typename Lambda , typename FuncRetType = typename CurveType::NumericType>

FuncRetType axom::primal::evaluate_vector_line_integral	(	const axom::Array< CurveType > &	carray,
		Lambda &&	vector_integrand,
		int	npts
	)

Evaluate a line integral on an array of generic curves on a vector field.

Template Parameters

CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve
Lambda	A callable type taking a CurveType's PointType and returning its numeric type
FuncRetType	The CurveType's numeric type

Parameters

[in]	carray	The array of generic curve objects
[in]	vector_integrand	the lambda function representing the integrand.
[in]	npts	the number of quadrature nodes per curve per knot span

Note: Each NURBS curve is decomposed into Bezier segments, and the Gaussian quadrature is computed using npts on each segment

Returns: the value of the integral

References axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ evaluate_area_integral() [1/2]

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>

LambdaRetType axom::primal::evaluate_area_integral	(	const primal::CurvedPolygon< CurveType > &	cpoly,
		Lambda &&	integrand,
		int	npts_Q,
		int	npts_P = `0`
	)

Evaluate an integral on the interior of a CurvedPolygon object.

Evaluates the integral using a Spectral Mesh-Free Quadrature derived from Green's theorem, evaluating the area integral as a line integral of the antiderivative over each component curve.

For algorithm details, see "Spectral Mesh-Free Quadrature for Planar Regions Bounded by Rational Parametric Curves" by David Gunderman et al.

Template Parameters

Lambda	A callable type taking a CurveType's PointType and returning an integrable type
CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the geometry
LambdaRetType	A type which supports addition and scalar multiplication

Parameters

[in]	cpoly	the CurvedPolygon object
[in]	integrand	the lambda function representing the integrand.
[in]	npts_Q	the number of quadrature points to evaluate the line integral
[in]	npts_P	the number of quadrature points to evaluate the antiderivative

Returns: the value of the integral

References axom::utilities::min(), and axom::primal::CurvedPolygon< CurveType >::numEdges().

◆ evaluate_area_integral() [2/2]

template<typename CurveType , typename Lambda , typename LambdaRetType = std::invoke_result_t<Lambda, typename CurveType::PointType>>

LambdaRetType axom::primal::evaluate_area_integral	(	const axom::Array< CurveType > &	carray,
		Lambda &&	integrand,
		int	npts_Q,
		int	npts_P = `0`
	)

Evaluate an integral on the interior of a region bound by 2D curves.

See above definition for details.

Template Parameters

Lambda	A callable type taking a CurveType's PointType and returning an integrable type
CurveType	The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the geometry
LambdaRetType	A type which supports addition and scalar multiplication

Parameters

[in]	carray	the array of generic curve objects that bound the region
[in]	integrand	the lambda function representing the integrand.
[in]	npts_Q	the number of quadrature points to evaluate the line integral
[in]	npts_P	the number of quadrature points to evaluate the antiderivative

Note: The numerical result is only meaningful if the curves enclose a region

Returns: the value of the integral

References axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), and axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ evaluate_surface_integral() [1/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_surface_integral	(	const primal::BezierPatch< T, 3 > &	patch,
		Lambda &&	integrand,
		int	npts
	)

Evaluate a scalar surface integral on a single Bezier patch.

Uses tensor-product Gauss-Legendre quadrature in the patch parameter space.

Parameters

[in]	patch	the Bezier patch
[in]	integrand	callable representing the integrand
[in]	npts	the number of quadrature points in each parametric direction

Precondition: The patch parameterization must be valid on its full parameter domain.

◆ evaluate_surface_integral() [2/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_surface_integral	(	const primal::NURBSPatch< T, 3 > &	patch,
		Lambda &&	integrand,
		int	npts_Q,
		int	npts_P = `0`
	)

Evaluate a scalar surface integral on a single NURBS patch.

Untrimmed patches are integrated by Bezier extraction followed by tensor-product Gauss-Legendre quadrature. Trimmed patches are integrated by reducing the parameter-space area integral to line integrals over the trimming curves.

Parameters

[in]	patch	the NURBS patch
[in]	integrand	callable representing the integrand
[in]	npts_Q	the number of quadrature points on each trimming curve or in each parametric direction for untrimmed Bezier pieces
[in]	npts_P	the number of quadrature points used for numerical antidifferentiation in parameter space

Precondition: The patch parameterization must be valid on its full parameter domain.; If the patch is trimmed, its trimming curves must bound the intended interior region in parameter space.

◆ evaluate_surface_integral() [3/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_surface_integral	(	const axom::Array< BezierPatch< T, 3 >> &	patches,
		Lambda &&	integrand,
		int	npts
	)

Evaluate a scalar surface integral on a collection of Bezier patches.

The result is the sum of the surface integrals over each patch in the array.

Parameters

[in]	patches	the patch collection
[in]	integrand	callable representing the integrand
[in]	npts	the number of quadrature points in each parametric direction

Precondition: Each patch parameterization must be valid on its full parameter domain.

◆ evaluate_surface_integral() [4/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_surface_integral	(	const axom::Array< NURBSPatch< T, 3 >> &	patches,
		Lambda &&	integrand,
		int	npts_Q,
		int	npts_P = `0`
	)

Evaluate a scalar surface integral on a collection of NURBS patches.

The result is the sum of the surface integrals over each patch in the array.

Parameters

[in]	patches	the patch collection
[in]	integrand	callable representing the integrand
[in]	npts_Q	the number of quadrature points on each trimming curve or in each parametric direction for untrimmed Bezier pieces
[in]	npts_P	the number of quadrature points used for numerical antidifferentiation in parameter space

Precondition: Each patch parameterization must be valid on its full parameter domain.; Any trimmed patch in the array must have trimming curves that bound its intended interior region in parameter space.

◆ evaluate_volume_integral() [1/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_volume_integral	(	const primal::BezierPatch< T, 3 > &	patch,
		Lambda &&	integrand,
		T	lower_bound_z,
		int	npts_uv,
		int	npts_z = `0`
	)

Evaluate a scalar volume-integral contribution from a single Bezier patch.

This applies the Stokes-based reduction used for the full volume algorithm to one patch using a z-directed numerical antiderivative.

Parameters

[in]	patch	the Bezier patch
[in]	integrand	callable representing the integrand
[in]	lower_bound_z	the shared lower integration bound used for the z-directed antiderivative across the full boundary
[in]	npts_uv	the number of quadrature points in each patch parameter direction
[in]	npts_z	the number of quadrature points used for numerical antidifferentiation in z

Precondition: The patch parameterization must be valid on its full parameter domain.; The returned value is geometrically meaningful as a volume contribution only when this patch is interpreted as part of a closed, consistently oriented boundary that uses the same lower integration bound.

◆ evaluate_volume_integral() [2/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_volume_integral	(	const primal::NURBSPatch< T, 3 > &	patch,
		Lambda &&	integrand,
		T	lower_bound_z,
		int	npts_Q,
		int	npts_P = `0`,
		int	npts_Z = `0`
	)

Evaluate a scalar volume-integral contribution from a single NURBS patch.

Trimmed patches use the same Green/Stokes reduction as the surface-integral algorithm, combined with a z-directed numerical antiderivative for the volume reduction.

Parameters

[in]	patch	the NURBS patch
[in]	integrand	callable representing the integrand
[in]	lower_bound_z	the shared lower integration bound used for the z-directed antiderivative across the full boundary
[in]	npts_Q	the number of quadrature points on each trimming curve or in each parametric direction for untrimmed Bezier pieces
[in]	npts_P	the number of quadrature points used for numerical antidifferentiation in parameter space
[in]	npts_Z	the number of quadrature points used for numerical antidifferentiation in z

Precondition: The patch parameterization must be valid on its full parameter domain.; If the patch is trimmed, its trimming curves must bound the intended interior region in parameter space.; The returned value is geometrically meaningful as a volume contribution only when this patch is interpreted as part of a closed, consistently oriented boundary that uses the same lower integration bound.

◆ evaluate_volume_integral() [3/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename BezierPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_volume_integral	(	const axom::Array< BezierPatch< T, 3 >> &	patches,
		Lambda &&	integrand,
		int	npts_uv,
		int	npts_z = `0`
	)

Evaluate a scalar volume integral over a collection of Bezier patches.

The result is obtained by summing the Stokes-based contribution from each patch in the collection.

Parameters

[in]	patches	the patch collection
[in]	integrand	callable representing the integrand
[in]	npts_uv	the number of quadrature points in each patch parameter direction
[in]	npts_z	the number of quadrature points used for numerical antidifferentiation in z

Precondition: Each patch parameterization must be valid on its full parameter domain.; The patch collection must represent a closed, consistently oriented boundary of the target volume.

References axom::utilities::min().

◆ evaluate_volume_integral() [4/4]

template<typename Lambda , typename T , typename LambdaRetType = std::invoke_result_t<Lambda, typename NURBSPatch<T, 3>::PointType>>

LambdaRetType axom::primal::evaluate_volume_integral	(	const axom::Array< NURBSPatch< T, 3 >> &	patches,
		Lambda &&	integrand,
		int	npts_Q,
		int	npts_P = `0`,
		int	npts_Z = `0`
	)

Evaluate a scalar volume integral over a collection of NURBS patches.

The result is obtained by summing the Stokes-based contribution from each patch in the collection.

Parameters

[in]	patches	the patch collection
[in]	integrand	callable representing the integrand
[in]	npts_Q	the number of quadrature points on each trimming curve or in each parametric direction for untrimmed Bezier pieces
[in]	npts_P	the number of quadrature points used for numerical antidifferentiation in parameter space
[in]	npts_Z	the number of quadrature points used for numerical antidifferentiation in z

Precondition: Each patch parameterization must be valid on its full parameter domain.; Any trimmed patch in the array must have trimming curves that bound its intended interior region in parameter space.; The patch collection must represent a closed, consistently oriented boundary of the target volume.

References axom::utilities::min().

◆ in_curved_polygon()

template<typename T , typename CurveType >

bool axom::primal::in_curved_polygon	(	const Point< T, 2 > &	query,
		const CurvedPolygon< CurveType > &	cpoly,
		bool	useNonzeroRule = `true`,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Robustly determine if query point is interior to a curved polygon.

Template Parameters

CurveType The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve

Parameters

[in]	query	The query point to test
[in]	cpoly	The CurvedPolygon object to test for containment
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Determines containment using the (rounded) winding number with respect to the given curved polygon. This algorithm is robust, as the winding number is rounded in the final in/out determination. Different protocols determine containment from the winding number differently. Nonzero Rule: If the winding number is nonzero, the point is interior. Even/Odd rule: If the winding number is odd, it is interior. Exterior otherwise.

Returns: A boolean value indicating containment.

References winding_number().

◆ in_polygon()

template<typename T >

bool axom::primal::in_polygon	(	const Point< T, 2 > &	query,
		const Polygon< T, 2 > &	poly,
		bool	includeBoundary = `false`,
		bool	useNonzeroRule = `true`,
		double	edge_tol = `1e-8`
	)

Determines containment for a point in a polygon.

Parameters

[in]	query	The query point to test
[in]	poly	The Polygon object to test for containment
[in]	includeBoundary	If true, points on the boundary are considered interior.
[in]	useNonzeroRule	If false, use even/odd protocol for inclusion
[in]	edge_tol	The distance at which a point is considered on the boundary

Determines containment using the winding number with respect to the given polygon. Different protocols determine containment from the winding number differently. Nonzero Rule: If the winding number is nonzero, the point is interior. Even/Odd rule: If the winding number is odd, it is interior. Exterior otherwise.

Returns: boolean value indicating containment.

◆ in_polyhedron()

template<typename T >

bool axom::primal::in_polyhedron	(	const Point< T, 3 > &	query,
		const Polyhedron< T, 3 > &	poly,
		bool	includeBoundary = `false`,
		bool	useNonzeroRule = `true`,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Determines containment for a point in a polygon.

Parameters

[in]	query	The query point to test
[in]	poly	The Polyhedron object to test for containment
[in]	includeBoundary	If true, points on the boundary are considered interior.
[in]	useNonzeroRule	If false, use even/odd protocol for inclusion
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	The tolerance level for collinearity

Determines containment using the winding number with respect to the given polygon. Different protocols determine containment from the winding number differently. Nonzero Rule: If the winding number is nonzero, the point is interior. Even/Odd rule: If the winding number is odd, it is interior. Exterior otherwise.

Returns: boolean value indicating containment.

References winding_number().

◆ in_sphere() [1/5]

template<typename T >

bool axom::primal::in_sphere	(	const Point< T, 2 > &	q,
		const Point< T, 2 > &	p0,
		const Point< T, 2 > &	p1,
		const Point< T, 2 > &	p2,
		double	EPS = `1e-8`
	)

inline

Tests whether a query point lies inside a 2D triangle's circumcircle.

A triangle's circumcircle is the unique circle (i.e. a 2-sphere) that passes through each of its three vertices.

Parameters

[in]	q	the query point
[in]	p0	the first vertex of the triangle
[in]	p1	the second vertex of the triangle
[in]	p2	the third vertex of the triangle
[in]	EPS	tolerance for determining if q is on the boundary. Default: 1e-8.

Returns: true if the point is inside the circumcircle, false if it is on the circle's boundary or outside the circle

References axom::numerics::determinant(), and axom::utilities::isNearlyEqual().

◆ in_sphere() [2/5]

template<typename T >

bool axom::primal::in_sphere	(	const Point< T, 2 > &	q,
		const Triangle< T, 2 > &	tri,
		double	EPS = `1e-8`
	)

inline

Tests whether a query point lies inside a 2D triangle's circumcircle.

Parameters

[in]	q	the query point
[in]	tri	the triangle
[in]	EPS	tolerance for determining if q is on the boundary. Default: 1e-8.

See also: in_sphere

References in_sphere().

◆ in_sphere() [3/5]

template<typename T >

bool axom::primal::in_sphere	(	const Point< T, 3 > &	q,
		const Point< T, 3 > &	p0,
		const Point< T, 3 > &	p1,
		const Point< T, 3 > &	p2,
		const Point< T, 3 > &	p3,
		double	EPS = `1e-8`
	)

inline

Tests whether a query point lies inside a 3D tetrahedron's circumsphere.

A tetrahedron's circumsphere is the unique sphere that passes through each of its four vertices.

Parameters

[in]	q	the query point
[in]	p0	the first vertex of the tetrahedron
[in]	p1	the second vertex of the tetrahedron
[in]	p2	the third vertex of the tetrahedron
[in]	p3	the fourth vertex of the tetrahedron
[in]	EPS	tolerance for determining if q is on the boundary. Default: 1e-8.

Returns: true if the point is inside the circumsphere, false if it is on the sphere's boundary or outside the sphere

References axom::numerics::determinant(), and axom::utilities::isNearlyEqual().

◆ in_sphere() [4/5]

template<typename T >

bool axom::primal::in_sphere	(	const Point< T, 3 > &	q,
		const Tetrahedron< T, 3 > &	tet,
		double	EPS = `1e-8`
	)

inline

Tests whether a query point lies inside a 3D tetrahedron's circumsphere.

Parameters

[in]	q	the query point
[in]	tet	the tetrahedron
[in]	EPS	tolerance for determining if q is on the boundary. Default: 1e-8.

See also: in_sphere

References in_sphere().

◆ in_sphere() [5/5]

template<typename T >

bool axom::primal::in_sphere	(	const BoundingBox< T, 2 > &	bb,
		const Sphere< T, 2 > &	circle
	)

inline

Tests whether a bounding box lies inside a 2D sphere.

Parameters

[in]	bb	the bounding box
[in]	circle	the sphere

References axom::primal::Sphere< T, NDIMS >::getCenter(), axom::primal::BoundingBox< T, NDIMS >::getMax(), axom::primal::BoundingBox< T, NDIMS >::getMin(), and axom::primal::Sphere< T, NDIMS >::getRadius().

◆ intersect() [1/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Segment< T, 3 > &	P,
		const Segment< T, 3 > &	Q,
		Point< T, 3 > &	intersection,
		const T	EPS = `static_cast<T>(1e-08)`
	)

Determines if two 3D segments intersect.

Parameters

[in]	P	A 3D line segment
[in]	Q	A 3D line segment
[out]	intersection	Intersection point of P and Q. When the segments are collinear and overlap over a nonzero interval, intersection is set to the first point of the overlap encountered when moving from P.source() to P.target().
[in]	EPS	Tolerance used in the segment-segment intersection test.

Returns: true iff P intersects with Q, otherwise, false.

Note: The value of intersection should be ignored when this function returns false.

◆ intersect() [2/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Triangle< T, 3 > &	t1,
		const Triangle< T, 3 > &	t2,
		bool	includeBoundary = `false`,
		double	EPS = `1E-08`
	)

Tests if 3D Triangles t1 and t2 intersect.

Parameters

[in]	t1	The first triangle
[in]	t2	The second triangle
[in]	includeBoundary	Indicates if boundaries should be considered when detecting intersections (default: false)
[in]	EPS	Tolerance for determining intersections (default: 1E-8)

Returns: status true iff t1 intersects with t2, otherwise, false.

If parameter includeBoundary is false (default), this function will return true if the interior of t1 intersects the interior of t2. To include triangle boundaries in intersections, specify includeBoundary as true.

◆ intersect() [3/43]

template<typename T >

bool axom::primal::intersect	(	const Triangle< T, 2 > &	t1,
		const Triangle< T, 2 > &	t2,
		bool	includeBoundary = `false`,
		double	EPS = `1E-08`
	)

Tests if 2D Triangles t1 and t2 intersect.

Parameters

[in]	t1	The first triangle
[in]	t2	The second triangle
[in]	includeBoundary	Indicates if boundaries should be considered when detecting intersections (default: false)
[in]	EPS	Tolerance for determining intersections (default: 1E-8)

Returns: status true iff t1 intersects with t2, otherwise, false.

If parameter includeBoundary is false (default), this function will return true if the interior of t1 intersects the interior of t2. To include triangle boundaries in intersections, specify includeBoundary as true.

◆ intersect() [4/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const BoundingBox< T, 3 > &	bb
	)

Determines if a triangle and a bounding box intersect.

Parameters

[in]	tri	user-supplied triangle (with three vertices).
[in]	bb	user-supplied axis aligned bounding box.

Returns: true iff tri intersects with bb, otherwise, false.

◆ intersect() [5/43]

template<typename T >

bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Ray< T, 3 > &	ray
	)

Determines if a 3D triangle intersects a 3D ray.

Parameters

[in]	tri	A 3D triangle
[in]	ray	A 3D ray

Returns: true iff tri intersects with ray, otherwise, false.

◆ intersect() [6/43]

template<typename T >

bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Ray< T, 3 > &	ray,
		T &	t
	)

Determines if a 3D triangle intersects a 3D ray.

Parameters

[in]	tri	A 3D triangle
[in]	ray	A 3D ray
[out]	t	Intersection point of tri and R, w.r.t. parametrization of R

Note: If there is an intersection, the intersection point is: R.at(t)

Returns: true iff tri intersects with ray, otherwise, false.

◆ intersect() [7/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Ray< T, 3 > &	ray,
		T &	t,
		Point< double, 3 > &	p
	)

Determines if a 3D triangle intersects a 3D ray.

Parameters

[in]	tri	A 3D triangle
[in]	ray	A 3D ray
[out]	t	Intersection point of tri and R, w.r.t. parametrization of R
[out]	p	Intersection point of tri and R, in barycentric coordinates relative to tri.

Note: If there is an intersection, the intersection point is: R.at(t)

Returns: true iff tri intersects with ray, otherwise, false.

Note: t and p only valid when function returns true

References axom::primal::Point< T, NDIMS >::array().

◆ intersect() [8/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Segment< T, 3 > &	seg
	)

Determines if a 3D triangle intersects a 3D segment.

Parameters

[in]	tri	A 3D triangle
[in]	seg	A 3D line segment

Returns: true iff tri intersects with seg, otherwise, false.

◆ intersect() [9/43]

template<typename T >

bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Segment< T, 3 > &	seg,
		T &	t
	)

Determines if a 3D triangle intersects a 3D segment.

Parameters

[in]	tri	A 3D triangle
[in]	seg	A 3D line segment
[out]	t	Intersection point of tri and seg, w.r.t. seg's parametrization

Returns: true iff tri intersects with seg, otherwise, false.

◆ intersect() [10/43]

template<typename T >

bool axom::primal::intersect	(	const Triangle< T, 3 > &	tri,
		const Segment< T, 3 > &	seg,
		T &	t,
		Point< double, 3 > &	p
	)

Determines if a 3D triangle intersects a 3D segment.

Parameters

[in]	tri	A 3D triangle
[in]	seg	A 3D line segment
[out]	t	Intersection point of tri and seg, w.r.t. seg's parametrization
[out]	p	Intersection point of tri and R, in barycentric coordinates relative to tri.

Note: If there is an intersection, the intersection point pt is: pt = seg.source() + t * ( seg.dest() - seg.target() )

Returns: true iff tri intersects with seg, otherwise, false.

Note: t and p only valid when function returns true

References axom::primal::Point< T, NDIMS >::array().

◆ intersect() [11/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Ray< T, 2 > &	R,
		const Segment< T, 2 > &	S,
		T &	ray_param,
		T &	seg_param,
		const T	EPS = `1e-8`
	)

Computes the intersection of the given ray, R, with the segment, S.

Parameters

[in]	R	the specified ray
[in]	S	the segment to check
[out]	ray_param	parametric coordinate of intersection along R, valid only if status=true.
[out]	seg_param	parametric coordinate of intersection along S, valid only if status=true.
[in]	EPS	tolerance for intersection tests

Returns: status true iff R intersects with S, otherwise, false.

See also: primal::Ray; primal::Segment

◆ intersect() [12/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 2 > &	R,
		const Segment< T, 2 > &	S,
		T &	ray_param
	)

Computes the intersection of the given ray, R, with the segment, S.

Parameters

[in]	R	the specified ray
[in]	S	the segment to check
[out]	ray_param	parametric coordinate of intersection along R, valid only if status=true

Note: If you need to specify a tolerance for the intersection tests, please use the overload of this function with two [OUT] parameters (ray_param and seg_param)

Returns: status true iff R intersects with S, otherwise, false.

See also: primal::Ray; primal::Segment

References intersect().

◆ intersect() [13/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Ray< T, 2 > &	R,
		const Segment< T, 2 > &	S
	)

Computes the intersection of the given ray, R, with the segment, S.

Parameters

[in]	R	the specified ray
[in]	S	the segment to check

Note: If you need to specify a tolerance for the intersection tests, please use the overload of this function with two [OUT] parameters (ray_param and seg_param)

Returns: status true iff R intersects with S, otherwise, false.

See also: primal::Ray; primal::Segment

References intersect().

◆ intersect() [14/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 2 > &	R,
		const Segment< T, 2 > &	S,
		Point< T, 2 > &	ip,
		const T	EPS = `1e-8`
	)

Computes the intersection of the given ray, R, with the segment, S.

Parameters

[in]	R	the specified ray
[in]	S	the segment to check
[out]	ip	the intersection point on S, valid only if status=true.
[in]	EPS	tolerance for intersection tests

Returns: status true iff R intersects with S, otherwise, false.

See also: primal::Ray; primal::Segment; primal::Point

References axom::primal::Ray< T, NDIMS >::at().

◆ intersect() [15/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Ray< T, DIM > &	R,
		const BoundingBox< T, DIM > &	bb,
		Point< T, DIM > &	ip
	)

Computes the intersection of the given ray, R, with the Box, bb.

Parameters

[in]	R	the specified ray
[in]	bb	the user-supplied axis-aligned bounding box
[out]	ip	the intersection point with minimum parameter value where R intersects bb.

Returns: status true iff bb intersects with R, otherwise, false.

See also: primal::Ray; primal::Segment; primal::BoundingBox

Note: Computes Ray Box intersection using the slab method from pg 180 of Real Time Collision Detection by Christer Ericson.

◆ intersect() [16/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Ray< T, DIM > &	R,
		const BoundingBox< T, DIM > &	bb
	)

Computes the intersection of the given ray, R, with the Box, bb.

Parameters

[in]	R	the specified ray
[in]	bb	the user-supplied axis-aligned bounding box

Returns: status true iff bb intersects with R, otherwise, false.

See also: primal::Ray; primal::Segment; primal::BoundingBox

Note: Computes Ray Box intersection using the slab method from pg 180 of Real Time Collision Detection by Christer Ericson.

References AXOM_STATIC_ASSERT, axom::utilities::max(), and axom::utilities::min().

◆ intersect() [17/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Line< T, DIM > &	L,
		const BoundingBox< T, DIM > &	bb,
		Point< T, DIM > &	ip
	)

Computes the intersection of the given line, L, with the Box, bb.

Parameters

[in]	L	the specified line (two-sided ray)
[in]	bb	the user-supplied axis-aligned bounding box
[out]	ip	the intersection point with minimum parameter value where L intersects bb.

Returns: status true iff bb intersects with R, otherwise, false.

See also: primal::Line; primal::Segment; primal::BoundingBox

Note: Computes Ray Box intersection using the slab method from pg 180 of Real Time Collision Detection by Christer Ericson.

◆ intersect() [18/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Line< T, DIM > &	L,
		const BoundingBox< T, DIM > &	bb
	)

Computes the intersection of the given line, L, with the Box, bb.

Parameters

[in]	L	the specified line (two-sided ray)
[in]	bb	the user-supplied axis-aligned bounding box

Returns: status true iff bb intersects with R, otherwise, false.

See also: primal::Line; primal::BoundingBox

Note: Computes Ray Box intersection using the slab method from pg 180 of Real Time Collision Detection by Christer Ericson.

References AXOM_STATIC_ASSERT, axom::primal::Line< T, NDIMS >::direction(), axom::utilities::max(), and axom::primal::Line< T, NDIMS >::origin().

◆ intersect() [19/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Segment< T, DIM > &	S,
		const BoundingBox< T, DIM > &	bb,
		T &	tmin,
		T &	tmax,
		const double &	EPS = `1e-8`
	)

Computes the intersection of the given segment, S, with the Box, bb. If an intersection is found, output parameter ip contains an intersection point.

Returns: status true iff bb intersects with S, otherwise, false.

Note: The intersection between segment S and box bb intersect, will, in general, be a along a (1D) subset of segment S. One variant of this function returns the two parametric coordinates of the intersections along S found while determining if there is a valid intersection. Another variant returns an intersection point along S Specifically, it is the point of smallest parametric coordinate that is contained in bb (i.e. with parameter tmin). These are only valid when the function returns true

Computes Segment-Box intersection using the slab method from pg 180 of Real Time Collision Detection by Christer Ericson. This variant returns the two parametric coordinates of the intersection segment as OUT parameters

References axom::primal::Segment< T, NDIMS >::length().

◆ intersect() [20/43]

template<typename T , int DIM>

bool axom::primal::intersect	(	const Segment< T, DIM > &	S,
		const BoundingBox< T, DIM > &	bb,
		Point< T, DIM > &	ip,
		const double &	EPS = `1e-8`
	)

This variant returns a point within the intersection as an OUT parameters.

References axom::primal::Segment< T, NDIMS >::at(), and intersect().

◆ intersect() [21/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Segment< T, DIM > &	S,
		const BoundingBox< T, DIM > &	bb
	)

References intersect().

◆ intersect() [22/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const BoundingBox< T, DIM > &	bb1,
		const BoundingBox< T, DIM > &	bb2
	)

Determines if two axis aligned bounding boxes intersect.

Parameters

[in]	bb1	user-supplied axis aligned bounding box.
[in]	bb2	user-supplied axis aligned bounding box.

Returns: true iff bb1 intersects with bb2, otherwise, false.

References axom::primal::BoundingBox< T, NDIMS >::intersectsWith().

◆ intersect() [23/43]

template<typename T , int DIM>

bool axom::primal::intersect	(	const Sphere< T, DIM > &	s1,
		const Sphere< T, DIM > &	s2,
		double	TOL = `1.e-9`
	)

Determines if two spheres intersect.

Parameters

[in]	s1	user-supplied sphere object to check for intersection.
[in]	s2	user-supplied sphere object to check for intersection.
[in]	TOL	tolerance used for intersection check (optional)

Note: If TOL is not supplied, the default is 1.e-9.

Returns: status true iff s1 intersects with s2, otherwise, false.

References axom::primal::Sphere< T, NDIMS >::intersectsWith().

◆ intersect() [24/43]

template<typename T >

bool axom::primal::intersect	(	const Sphere< T, 2 > &	circle,
		const BoundingBox< T, 2 > &	bb
	)

Determines if a 2D sphere intersects (overlaps with) a bounding box.

Parameters

[in]	circle	The sphere to check for intersection
[in]	bb	The bounding box to check for intersection

◆ intersect() [25/43]

template<typename T >

bool axom::primal::intersect	(	const Sphere< T, 2 > &	circle,
		const NURBSCurve< T, 2 > &	curve,
		axom::Array< T > &	circle_params,
		axom::Array< T > &	curve_params,
		double	tol = `1e-8`,
		double	EPS = `1e-8`
	)

Determines if a 2D sphere intersects a NURBS Curve.

Parameters

[in]	circle	The sphere to check for intersection
[in]	curve	The NURBS curve to check for intersection
[out]	circle_params	The parameter values of the sphere at the intersection points
[out]	curve_params	The parameter values of the curve at the intersection points
[in]	tol	Tolerance parameter for physical distances
[in]	EPS	Tolerance parameter for parameter-space distances

Returns: True if the sphere intersects the curve, false otherwise

References axom::primal::NURBSCurve< T, NDIMS >::extractBezier(), axom::primal::NURBSCurve< T, NDIMS >::getKnots(), axom::primal::KnotVector< T >::getUniqueKnots(), axom::Array< T, DIM, SPACE, StoragePolicy >::push_back(), and axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ intersect() [26/43]

template<typename T >

bool axom::primal::intersect	(	const OrientedBoundingBox< T, 1 > &	b1,
		const OrientedBoundingBox< T, 1 > &	b2
	)

◆ intersect() [27/43]

template<typename T >

bool axom::primal::intersect	(	const OrientedBoundingBox< T, 2 > &	b1,
		const OrientedBoundingBox< T, 2 > &	b2
	)

Determines if a 2D OBB intersects a 2D OBB.

Parameters

[in]	b1	A 2D OrientedBoundingBox
[in]	b2	A 2D OrientedBoundingBox

Returns: true iff b1 intersects with b2, otherwise, false.

◆ intersect() [28/43]

template<typename T >

bool axom::primal::intersect	(	const OrientedBoundingBox< T, 3 > &	b1,
		const OrientedBoundingBox< T, 3 > &	b2,
		double	EPS = `1E-4`
	)

Determines if a 3D OBB intersects a 3D OBB.

Parameters

[in]	b1	A 3D OrientedBoundingBox
[in]	b2	A 3D OrientedBoundingBox
[in]	EPS	error tolerance for intersection

Returns: true iff b1 intersects with b2, otherwise, false.

◆ intersect() [29/43]

template<typename T >

bool axom::primal::intersect	(	const BezierCurve< T, 2 > &	c1,
		const BezierCurve< T, 2 > &	c2,
		axom::Array< T > &	sp,
		axom::Array< T > &	tp,
		double	tol = `1E-8`
	)

Tests if two Bezier Curves c1 and c2 intersect.

Returns: status true iff c1 intersects c2, otherwise false.

Parameters

[in]	c1	the first BezierCurve, parametrized in [0,1)
[in]	c2	the second BezierCurve, parametrized in [0,1)
[out]	sp	vector of parameter space intersection points for c1
[out]	tp	vector of parameter space intersection points for c2
[in]	tol	tolerance parameter for determining if a curve can be approximated by a line segment.

Returns: True if the curves intersect, false otherwise. Intersection parameters are stored in sp and tp

Finds all intersection points between the two curves.

Note: This function assumes two dimensional curves in a plane.; This function assumes that the curves are in general position. Specifically, we assume that all intersections are at points and that the curves don't overlap.; This function assumes the all intersections have multiplicity one, i.e. there are no points at which the curves and their derivatives both intersect. Thus, the function does not find tangencies.; This function assumes that the curves are half-open, i.e. they contain their first endpoint, but not their last endpoint. Thus, the curves do not intersect at \( s==1 \) or at \( t==1 \).

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), and axom::numerics::transforms::scale().

◆ intersect() [30/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 2 > &	r,
		const BezierCurve< T, 2 > &	c,
		axom::Array< T > &	rp,
		axom::Array< T > &	cp,
		double	tol = `1E-8`,
		double	EPS = `1E-8`
	)

Function to find intersections between a ray and a Bezier curve.

Parameters

[in]	r	The input ray
[in]	c	The input curve
[out]	rp	Parametric coordinates of intersections in r [0, inf)
[out]	cp	Parametric coordinates of intersections in c [0, 1)
[in]	tol	Tolerance parameter for physical distances
[in]	EPS	Tolerance parameter for parameter-space distances

Note: A BezierCurve is parametrized in [0,1). This function assumes the all intersections have multiplicity one, i.e. the function does not find tangencies.

Returns: True if the ray intersects the Bezier curve, False otherwise

References axom::primal::BezierCurve< T, NDIMS >::getOrder(), and axom::numerics::transforms::scale().

◆ intersect() [31/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 2 > &	r,
		const NURBSCurve< T, 2 > &	n,
		axom::Array< T > &	rp,
		axom::Array< T > &	np,
		double	tol = `1E-8`,
		double	EPS = `1E-8`
	)

Function to find intersections between a ray and a NURBS curve.

Parameters

[in]	r	The input ray
[in]	n	The input curve
[out]	rp	Parametric coordinates of intersections in r [0, inf)
[out]	cp	Parametric coordinates of intersections in the knot span of n
[in]	tol	Tolerance parameter for physical distances
[in]	EPS	Tolerance parameter for parameter-space distances

Note: Assumes the NURBS curve is parameterized on a half-open interval [a, b), and assumes the all intersections have multiplicity one, i.e. the function does not find tangencies.

Returns: True if the ray intersects the NURBS curve, False otherwise

References axom::primal::NURBSCurve< T, NDIMS >::boundingBox(), axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), axom::primal::NURBSCurve< T, NDIMS >::extractBezier(), axom::primal::NURBSCurve< T, NDIMS >::getKnots(), axom::primal::KnotVector< T >::getUniqueKnots(), intersect(), axom::utilities::lerp(), axom::Array< T, DIM, SPACE, StoragePolicy >::push_back(), and axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ intersect() [32/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Plane< T, 3 > &	p,
		const BoundingBox< T, 3 > &	bb,
		bool	checkOverlaps = `false`,
		double	EPS = `1E-08`
	)

Determines if a 3D plane intersects a 3D bounding box. By default (checkOverlaps is false), checks if |s| <= r, where "s" is the distance of the bounding box center to the plane, and "r" is the projected radius of the bounding box along the line parallel to the plane normal and going through the box center. If checkOverlaps is true, checks if |s| < r, where the bounding box overlaps both half spaces of the plane.

Parameters

[in]	p	A 3D plane
[in]	bb	A 3D bounding box
[in]	checkOverlaps	If true, checks if bounding box overlaps both halfspaces of the plane. Otherwise, overlap of both halfspaces is not guaranteed. Default is false.
[in]	EPS	tolerance parameter for determining if "s" is just within min/max of "r".

Returns: true iff plane intersects with bounding box, otherwise, false.

Note: Uses method from pg 164 of Real Time Collision Detection by Christer Ericson.

◆ intersect() [33/43]

template<typename T , int DIM>

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Plane< T, DIM > &	plane,
		const Segment< T, DIM > &	seg,
		T &	t,
		const double &	EPS = `1e-12`
	)

Determines if a plane intersects a segment.

Parameters

[in]	plane	A plane
[in]	seg	A line segment
[out]	t	Intersection point of plane and seg, w.r.t. seg's parametrization
[in]	EPS	tolerance parameter for determining if 0.0 <= t <= 1.0

Note: If there is an intersection, the intersection point pt is: pt = seg.at(t)

Returns: true iff plane intersects with seg, otherwise, false.

Note: t is only valid when function returns true; Uses method from pg 176 of Real Time Collision Detection by Christer Ericson.

◆ intersect() [34/43]

template<typename T >

AXOM_HOST_DEVICE bool axom::primal::intersect	(	const Plane< T, 3 > &	p,
		const Tetrahedron< T, 3 > &	tet,
		Polygon< T, 3 > &	intersection
	)

Determines if a 3D plane intersects a tetrahedron.

Parameters

[in]	p	A 3D plane
[in]	tet	A 3D tetrahedron
[out]	intersection	A polygon containing the intersection.

Returns: true if plane intersects with tetrahedron, otherwise, false.

Note: If no intersection is found, the output polygon will be empty. If the plane intersects at a tetrahedron vertex, the polygon will contain duplicated points.

◆ intersect() [35/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 3 > &	ray,
		const BezierPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol,
		double	EPS,
		bool	isHalfOpen,
		bool &	success
	)

Determines if a ray intersects a Bezier patch.

Parameters

[in]	ray	The ray to intersect with the patch.
[in]	patch	The Bezier patch to intersect with the ray.
[out]	t	The t parameter(s) of intersection point(s).
[out]	u	The u parameter(s) of intersection point(s).
[out]	v	The v parameter(s) of intersection point(s).
[in]	tol	The tolerance for intersection (for physical distances).
[in]	EPS	The tolerance for intersection (for parameter distances).
[in]	isHalfOpen	True if the patch is parameterized in [0,1)^2.
[out]	success	False if an early return occured.

For bilinear patches, implements GARP algorithm from Chapter 8 of Ray Tracing Gems (2019) For higher order patches, intersections are found through recursive subdivison until the subpatch is approximated by a bilinear patch. Assumes that the ray is not tangent to the patch, and that the intersection is not at a point of degeneracy for which there are infinitely many intersections.

Note: This method clears the input vectors t, u, v

Warning: This function returns early if we record excessive intersections. This implies the patch is degenerate at the point of intersection.

Returns: True if an intersection is found, false otherwise

References axom::Array< T, DIM, SPACE, StoragePolicy >::clear(), axom::primal::Ray< T, NDIMS >::direction(), axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), axom::primal::BezierPatch< T, NDIMS >::getOrder_u(), axom::primal::BezierPatch< T, NDIMS >::getOrder_v(), and axom::primal::Ray< T, NDIMS >::origin().

◆ intersect() [36/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 3 > &	ray,
		const BezierPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol = `1e-8`,
		double	EPS = `1e-8`,
		bool	isHalfOpen = `false`
	)

!

Determines if a ray intersects a Bezier patch with fewer exposed parameters.

References intersect().

◆ intersect() [37/43]

template<typename T >

bool axom::primal::intersect	(	const Line< T, 3 > &	line,
		const BezierPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol,
		double	EPS,
		bool	isHalfOpen,
		bool &	success
	)

Determines if a line (two-sided ray) intersects a Bezier patch.

Parameters

[in]	line	The line to intersect with the patch.
[in]	patch	The Bezier patch to intersect with the ray.
[out]	t	The t parameter(s) of intersection point(s).
[out]	u	The u parameter(s) of intersection point(s).
[out]	v	The v parameter(s) of intersection point(s).
[in]	tol	The tolerance for intersection (for physical distances).
[in]	EPS	The tolerance for intersection (for parameter distances).
[in]	isHalfOpen	True if the patch is parameterized in [0,1)^2.
[out]	success	False if an early return occured.

For bilinear patches, implements GARP algorithm from Chapter 8 of Ray Tracing Gems (2019) For higher order patches, intersections are found through recursive subdivison until the subpatch is approximated by a bilinear patch. Assumes that the line is not tangent to the patch, and that the intersection is not at a point of degeneracy for which there are infinitely many intersections.

Note: This method clears the input vectors t, u, v

Warning: This function returns early if we record excessive intersections. This implies the patch is degenerate at the point of intersection.

Returns: True if an intersection is found, false otherwise

References axom::Array< T, DIM, SPACE, StoragePolicy >::clear(), axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), axom::primal::BezierPatch< T, NDIMS >::getOrder_u(), and axom::primal::BezierPatch< T, NDIMS >::getOrder_v().

◆ intersect() [38/43]

template<typename T >

bool axom::primal::intersect	(	const Line< T, 3 > &	line,
		const BezierPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol = `1e-8`,
		double	EPS = `1e-8`,
		bool	isHalfOpen = `false`
	)

!

Determines if a line intersects a Bezier patch with fewer exposed parameters.

References intersect().

◆ intersect() [39/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 3 > &	ray,
		const NURBSPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol,
		double	EPS,
		bool	countUntrimmed,
		bool	isHalfOpen,
		bool &	success
	)

Determines if a ray intersects a NURBS patch.

Parameters

[in]	ray	The ray to intersect with the patch.
[in]	patch	The NURBS patch to intersect with the ray.
[out]	t	The t parameter(s) of intersection point(s).
[out]	u	The u parameter(s) of intersection point(s).
[out]	v	The v parameter(s) of intersection point(s).
[in]	tol	The tolerance for intersection (for physical distances).
[in]	EPS	The tolerance for intersection (for parameter distances).
[in]	countUntrimmed	True if intersections with the untrimmed patch should also be recorded.
[in]	isHalfOpen	True if the patch is parameterized in [0,1)^2.
[out]	success	False if an early return occured.

Perform Bezier extraction and record intersections with each patch. After intersections are recorded, parameter points located outside the trimming curves are pruned from the list (unless specified by countUntrimmed).

Note: This method clears the input vectors t, u, v

Warning: This function returns early if we record excessive intersections. This implies the patch is degenerate at the point of intersection.

Returns: True if an intersection is found, false otherwise

References axom::primal::NURBSPatch< T, NDIMS >::boundingBox(), axom::Array< T, DIM, SPACE, StoragePolicy >::clear(), axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), axom::primal::NURBSPatch< T, NDIMS >::extractBezier(), axom::primal::NURBSPatch< T, NDIMS >::getKnots_u(), axom::primal::NURBSPatch< T, NDIMS >::getKnots_v(), axom::primal::KnotVector< T >::getNumKnots(), axom::primal::KnotVector< T >::getUniqueKnots(), intersect(), axom::primal::NURBSPatch< T, NDIMS >::isVisible(), axom::utilities::lerp(), axom::Array< T, DIM, SPACE, StoragePolicy >::push_back(), axom::Array< T, DIM, SPACE, StoragePolicy >::size(), and squared_distance().

◆ intersect() [40/43]

template<typename T >

bool axom::primal::intersect	(	const Ray< T, 3 > &	ray,
		const NURBSPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol = `1e-8`,
		double	EPS = `1e-8`,
		bool	countUntrimmed = `true`,
		bool	isHalfOpen = `false`
	)

!

Determines if a ray intersects a NURBS patch with fewer exposed parameters.

References intersect().

◆ intersect() [41/43]

template<typename T >

bool axom::primal::intersect	(	const Line< T, 3 > &	line,
		const NURBSPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol,
		double	EPS,
		bool	countUntrimmed,
		bool	isHalfOpen,
		bool &	success
	)

Determines if a line (two-sided ray) intersects a NURBS patch.

Parameters

[in]	line	The line to intersect with the patch.
[in]	patch	The NURBS patch to intersect with the line.
[out]	t	The t parameter(s) of intersection point(s).
[out]	u	The u parameter(s) of intersection point(s).
[out]	v	The v parameter(s) of intersection point(s).
[in]	tol	The tolerance for intersection (for physical distances).
[in]	EPS	The tolerance for intersection (for parameter distances).
[in]	countUntrimmed	True if intersections with the untrimmed patch should also be recorded.
[in]	isHalfOpen	True if the patch is parameterized in [0,1)^2.
[out]	success	False if an early return occured.

Perform Bezier extraction and record intersections with each patch. After intersections are recorded, parameter points located outside the trimming curves are pruned from the list (unless specified by countUntrimmed).

Note: This method clears the input vectors t, u, v

Warning: This function returns early if we record excessive intersections. This implies the patch is degenerate at the point of intersection.

Returns: True if an intersection is found, false otherwise

References axom::primal::NURBSPatch< T, NDIMS >::boundingBox(), axom::Array< T, DIM, SPACE, StoragePolicy >::clear(), axom::Array< T, DIM, SPACE, StoragePolicy >::empty(), axom::primal::BoundingBox< T, NDIMS >::expand(), axom::primal::NURBSPatch< T, NDIMS >::extractBezier(), axom::primal::NURBSPatch< T, NDIMS >::getKnots_u(), axom::primal::NURBSPatch< T, NDIMS >::getKnots_v(), axom::primal::KnotVector< T >::getNumKnots(), axom::primal::KnotVector< T >::getUniqueKnots(), intersect(), axom::primal::NURBSPatch< T, NDIMS >::isVisible(), axom::utilities::lerp(), axom::Array< T, DIM, SPACE, StoragePolicy >::push_back(), axom::Array< T, DIM, SPACE, StoragePolicy >::size(), and squared_distance().

◆ intersect() [42/43]

template<typename T >

bool axom::primal::intersect	(	const Line< T, 3 > &	line,
		const NURBSPatch< T, 3 > &	patch,
		axom::Array< T > &	t,
		axom::Array< T > &	u,
		axom::Array< T > &	v,
		double	tol = `1e-8`,
		double	EPS = `1e-8`,
		bool	countUntrimmed = `true`,
		bool	isHalfOpen = `false`
	)

!

Determines if a line intersects a NURBS patch with fewer exposed parameters.

References intersect().

◆ intersect() [43/43]

template<typename T >

bool axom::primal::intersect	(	const NURBSCurve< T, 2 > &	n1,
		const NURBSCurve< T, 2 > &	n2,
		axom::Array< T > &	p1,
		axom::Array< T > &	p2,
		double	tol = `1.0E-8`
	)

Finds the intersection points for two NURBS curves in 2D.

Parameters

[in]	n1	A 2D NURBSCurve.
[in]	n2	A 2D NURBSCurve.
[out]	p1	The array of parameters for intersection points in n1.
[out]	p2	The array of parameters for intersection points in n2.
[in]	tol	Tolerance used in the segment pair intersection test.

Returns: true iff n1 intersects with n2, otherwise, false.

Note: The number of new entries added to p1 and p2 is the number of intersections, and corresponding entries in p1 and p2 are for the same intersection. This function checks for intersections of Bezier segments of the two NURBS curves. It does not perform simple bounding-box checks to quickly determine no intersection, which could be done before calling this function for better efficiency in some applications.

◆ intersection_volume() [1/5]

template<typename T >

AXOM_HOST_DEVICE T axom::primal::intersection_volume	(	const Hexahedron< T, 3 > &	hex,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Finds the absolute (unsigned) intersection volume between a hexahedron and a tetrahedron.

Parameters

[in]	hex	The hexahedron
[in]	tet	The tetrahedron
[in]	eps	The tolerance for determining the intersection
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: Intersection volume between the hexahedron and tetrahedron

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned volume may be zero and/or unexpected.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned volume of intersection may be zero and/or unexpected.

References clip().

◆ intersection_volume() [2/5]

template<typename T >

AXOM_HOST_DEVICE T axom::primal::intersection_volume	(	const Tetrahedron< T, 3 > &	tet,
		const Hexahedron< T, 3 > &	hex,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Finds the absolute (unsigned) intersection volume between a tetrahedron and a hexahedron.

Parameters

[in]	hex	The tetrahedron
[in]	tet	The hexahedron
[in]	eps	The tolerance for determining the intersection
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: Intersection volume between the tetrahedron and hexahedron

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned volume may be zero and/or unexpected.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned volume of intersection may be zero and/or unexpected.

References intersection_volume().

◆ intersection_volume() [3/5]

template<typename T >

AXOM_HOST_DEVICE T axom::primal::intersection_volume	(	const Octahedron< T, 3 > &	oct,
		const Tetrahedron< T, 3 > &	tet,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Finds the absolute (unsigned) intersection volume between a octahedron and a tetrahedron.

Parameters

[in]	oct	The octahedron
[in]	tet	The tetrahedron
[in]	eps	The tolerance for determining the intersection
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: Intersection volume between the octahedron and tetrahedron

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned volume may be zero and/or unexpected.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned volume of intersection may be zero and/or unexpected.

References clip().

◆ intersection_volume() [4/5]

template<typename T >

AXOM_HOST_DEVICE T axom::primal::intersection_volume	(	const Tetrahedron< T, 3 > &	tet,
		const Octahedron< T, 3 > &	oct,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Finds the absolute (unsigned) intersection volume between a tetrahedron and a octahedron.

Parameters

[in]	oct	The tetrahedron
[in]	tet	The octahedron
[in]	eps	The tolerance for determining the intersection
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: Intersection volume between the tetrahedron and octahedron

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned volume may be zero and/or unexpected.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned volume of intersection may be zero and/or unexpected.

References intersection_volume().

◆ intersection_volume() [5/5]

template<typename T >

AXOM_HOST_DEVICE T axom::primal::intersection_volume	(	const Tetrahedron< T, 3 > &	tet1,
		const Tetrahedron< T, 3 > &	tet2,
		double	eps = `1.e-10`,
		bool	tryFixOrientation = `false`
	)

Finds the absolute (unsigned) intersection volume between a tetrahedron and another tetrahedron.

Parameters

[in]	tet1	The tetrahedron
[in]	tet2	The other tetrahedron
[in]	eps	The tolerance for determining the intersection
[in]	tryFixOrientation	If true, takes each shape with a negative signed volume and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: Intersection volume between the tetrahedra

Warning: tryFixOrientation flag does not guarantee the shapes' vertex orders will be valid. It is the responsiblity of the caller to pass shapes with a valid vertex order. Otherwise, if the shapes have invalid vertex orders, the returned volume may be zero and/or unexpected.; If tryFixOrientation flag is false and some of the shapes have a negative signed volume, the returned volume of intersection may be zero and/or unexpected.

References clip().

◆ is_convex()

template<typename T >

bool axom::primal::is_convex	(	const Polygon< T, 2 > &	poly,
		double	EPS = `1e-8`
	)

Determines if a polygon defined by ordered vertices is convex.

Parameters

[in] poly The polygon

A 2D polygon is convex when every line that does not contain an edge intersects the shape at most twice. Checks whether for each pair of vertices P[i-1]P[i+1], the point P[i] and (P[0] or P[n]) lie on the same side of the line connecting them.

Algorithm adapted from: Y. L. Ma, W.T. Hewitt. "Point inversion and projection for NURBS curve and surface: Control polygon approach" Computer Aided Geometric Design 20(2):79-99, May 2003.

Note: Only defined in 2D

Returns: A boolean value indicating convexity

References axom::primal::Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >::numVertices(), ON_BOUNDARY, and orientation().

◆ orientation() [1/2]

template<typename T >

int axom::primal::orientation	(	const Point< T, 3 > &	p,
		const Triangle< T, 3 > &	tri,
		double	EPS = `1e-9`
	)

inline

Computes the orientation of a point p with respect to an oriented triangle tri.

Parameters

[in]	p	the query point
[in]	tri	an oriented triangle
[in]	EPS	a tolerance for determining if p and tri are coplanar

Returns: The orientation of p with respect to tri

Note

The triangle lies in a plane that divides space into the positive half-space and the negative half-space. The triangle's normal vector points in the positive half-space. The return value of this routine can be one of the following:

ON_BOUNDARY, when p is coplanar with tri (within tolerance EPS)
ON_POSITIVE_SIDE, when p lies in the positive half-space
ON_NEGATIVE_SIDE, when p lies in the negative half-space

See also: OrientationResult

References axom::numerics::determinant(), axom::utilities::isNearlyEqual(), ON_BOUNDARY, ON_NEGATIVE_SIDE, and ON_POSITIVE_SIDE.

◆ orientation() [2/2]

template<typename T >

int axom::primal::orientation	(	const Point< T, 2 > &	p,
		const Segment< T, 2 > &	seg,
		double	EPS = `1e-9`
	)

inline

Computes the orientation of a point p with respect to an oriented segment.

Parameters

[in]	p	the query point
[in]	seg	an oriented segment
[in]	EPS	a tolerance for determining if p and seg are coplanar

Returns: The orientation of p with respect to seg

Note

The segment lies in a plane that divides space into the positive half-space and the negative half-space. The segment's normal vector points in the positive half-space. The return value can be one of the following:

ON_BOUNDARY, when p is coplanar with seg (within tolerance EPS)
ON_POSITIVE_SIDE, when p lies in the positive half-space
ON_NEGATIVE_SIDE, when p lies in the negative half-space

See also: OrientationResult

References axom::numerics::determinant(), axom::utilities::isNearlyEqual(), ON_BOUNDARY, ON_NEGATIVE_SIDE, and ON_POSITIVE_SIDE.

◆ slice()

template<typename T , PolygonArray ARRAY_TYPE = PolygonArray::Dynamic, int MAX_VERTS = DEFAULT_MAX_NUM_VERTICES>

AXOM_HOST_DEVICE primal::Polygon<T, 3, ARRAY_TYPE, MAX_VERTS> axom::primal::slice	(	const primal::Tetrahedron< T, 3 > &	tet,
		const primal::Plane< T, 3 > &	plane
	)

Slices a 3D tetrahedron with a plane and returns the resulting polygon.

Parameters

[in]	tet	The tetrahedron to slice
[in]	plane	The slicing plane

Returns: The polygon obtained from slicing a tetrahedron with a plane. When the plane intersects the tetrahedron in a nondegenerate cross section, the return value is a triangle or quadrilateral. Degenerate intersections are also represented as polygons: a plane that touches the tetrahedron at a single vertex returns a one-vertex polygon, and a plane that intersects the tetrahedron only along one edge returns a two-vertex polygon.

Note: For nondegenerate intersections, the polygon vertices are intended to be ordered so that the polygon normal is aligned with the plane normal.

◆ split() [1/2]

template<typename Tp >

void axom::primal::split	(	const Octahedron< Tp, 3 > &	oct,
		axom::Array< Tetrahedron< Tp, 3 >> &	out
	)

Splits an Octahedron into eight Tetrahedrons.

Template Parameters

Tp	the coordinate type, such double or float

Parameters

[in]	oct	The Octahedron to split
[out]	out	The axom::Array of Tetrahedron objects; the fragments of oct are appended to out.

The tets are produced by putting a vertex at the centroid of the oct and drawing an edge from each vertex to the centroid.

◆ split() [2/2]

template<typename Tp >

AXOM_HOST_DEVICE void axom::primal::split	(	const Octahedron< Tp, 3 > &	oct,
		Tetrahedron< Tp, 3 > *	outPtr
	)

Splits an Octahedron into eight Tetrahedrons.

Template Parameters

Tp	the coordinate type, such as double or float

Parameters

[in]	oct	The Octahedron to split
[out]	outPtr	C-style array of 8 Tetrahedron objects.

The tets are produced by putting a vertex at the centroid of the oct and drawing an edge from each vertex to the centroid.

◆ squared_distance() [1/6]

double axom::primal::squared_distance	(	const double *	A,
		const double *	B,
		int	N
	)

inline

Computes the squared distance from point A to point B, represented by arrays of length N.

Parameters

[in]	A	source point
[in]	B	end point.
[in]	N	length of A and B.

Returns: the squared distance from point A to point B. If N < 1, return 0.

Precondition: A and B are arrays of at least length N.

◆ squared_distance() [2/6]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::squared_distance	(	const Point< T, NDIMS > &	A,
		const Point< T, NDIMS > &	B
	)

inline

Computes the squared distance from point A to point B.

Parameters

[in]	A	source point
[in]	B	end point.

Returns: the squared distance from point A to point B.

References axom::primal::Vector< T, NDIMS >::squared_norm().

◆ squared_distance() [3/6]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::squared_distance	(	const Point< T, NDIMS > &	P,
		const BoundingBox< T, NDIMS > &	B
	)

inline

Computes the minimum squared distance from a query point, P, to a given axis-aligned bounding box B.

Parameters

[in]	P	the query point.
[in]	B	the axis-aligned bounding box.

Returns: the squared distance from P to the closest point on box B or axom::numerics::floating_point_limits<T>::max() if B is invalid.

References axom::utilities::clampVal(), axom::primal::BoundingBox< T, NDIMS >::contains(), axom::primal::BoundingBox< T, NDIMS >::getMax(), axom::primal::BoundingBox< T, NDIMS >::getMin(), axom::primal::BoundingBox< T, NDIMS >::isValid(), axom::utilities::max(), and squared_distance().

◆ squared_distance() [4/6]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::squared_distance	(	const BoundingBox< T, NDIMS > &	A,
		const BoundingBox< T, NDIMS > &	B
	)

inline

Computes the minimum squared distance between 2 axis-aligned boxes.

Parameters

[in]	A	the first axis-aligned bounding box.
[in]	B	the second axis-aligned bounding box. If the boxes overlap, the minimum distance is zero.

Returns: the squared distance between the closest points on A and B or axom::numerics::floating_point_limits<T>::max() if either box is invalid.

References axom::primal::BoundingBox< T, NDIMS >::getMax(), axom::primal::BoundingBox< T, NDIMS >::getMin(), axom::primal::BoundingBox< T, NDIMS >::isValid(), axom::utilities::max(), and axom::primal::Vector< T, NDIMS >::squared_norm().

◆ squared_distance() [5/6]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::squared_distance	(	const Point< T, NDIMS > &	P,
		const Segment< T, NDIMS > &	S
	)

inline

Computes the minimum squared distance from a query point, P, to the given segment, S.

Parameters

[in]	P	the query point.
[in]	S	the input segment.

Returns: the minimum squared-distance from P to the segment S.

References squared_distance().

◆ squared_distance() [6/6]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE double axom::primal::squared_distance	(	const Point< T, NDIMS > &	P,
		const Triangle< T, NDIMS > &	tri
	)

inline

Computes the minimum squared distance from a query point, P, to the closest point on the given triangle.

Parameters

[in]	P	the query point.
[in]	tri	the supplied triangle.

Returns: the squared distance from P to the closest point on the triangle T.

References squared_distance().

◆ winding_number() [1/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const Segment< T, 2 > &	s,
		double	edge_tol = `1e-8`
	)

Compute the GWN for a 2D point wrt a 2D line segment.

Parameters

[in]	q	The query point to test
[in]	s	The line segment
[in]	edge_tol	The tolerance at which a point is on the line

Returns: The GWN

◆ winding_number() [2/28]

template<typename T >

int axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const Triangle< T, 2 > &	tri,
		bool	includeBoundary = `false`,
		double	edge_tol = `1e-8`
	)

Compute the winding number for a 2D point wrt a 2D triangle.

Parameters

[in]	q	The query point to test
[in]	tri	The triangle
[in]	includeBoundary	If true, points on the boundary are considered interior.
[in]	edge_tol	The tolerance at which a point is on the line

The triangle is assumed to be closed, so the winding number is an integer

Returns: The integer winding number

References winding_number().

◆ winding_number() [3/28]

template<typename T >

int axom::primal::winding_number	(	const Point< T, 2 > &	R,
		const Polygon< T, 2 > &	P,
		bool &	isOnEdge,
		bool	includeBoundary = `false`,
		double	edge_tol = `1e-8`
	)

Computes the winding number for a 2D point wrt a 2D polygon.

Parameters

[in]	R	The query point to test
[in]	P	The Polygon object to test for containment
[out]	isOnEdge	An optional return parameter if the point is on the boundary
[in]	includeBoundary	If true, points on the boundary are considered interior
[in]	edge_tol	The distance at which a point is considered on the boundary

Returns: The integer winding number

◆ winding_number() [4/28]

template<typename T >

int axom::primal::winding_number	(	const Point< T, 2 > &	R,
		const Polygon< T, 2 > &	P,
		bool	includeBoundary = `false`,
		double	edge_tol = `1e-8`
	)

Computes the winding number for a 2D point wrt a 2D polygon.

Parameters

[in]	R	The query point to test
[in]	P	The Polygon object to test for containment
[in]	includeBoundary	If true, points on the boundary are considered interior
[in]	edge_tol	The distance at which a point is considered on the boundary

Computes the integer winding number for a polygon without an additional return parameter for whether the point is on the boundary.

Returns: The integer winding number

◆ winding_number() [5/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const NURBSCurve< T, 2 > &	n,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt a 2D NURBS curve.

Parameters

[in]	q	The query point to test
[in]	n	The NURBS curve object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Returns: The GWN.

◆ winding_number() [6/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const BezierCurve< T, 2 > &	bezier,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt a 2D NURBS curve.

Parameters

[in]	q	The query point to test
[in]	bezier	The Bezier curve object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Returns: The GWN.

◆ winding_number() [7/28]

template<typename T , typename CurveType >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const CurvedPolygon< CurveType > &	cpoly,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt to a 2D curved polygon.

Template Parameters

CurveType The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve

Parameters

[in]	q	The query point to test
[in]	cpoly	The CurvedPolygon object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the GWN for the curved polygon by summing the GWN for each curved edge

Returns: The GWN.

References axom::primal::CurvedPolygon< CurveType >::numEdges(), and winding_number().

◆ winding_number() [8/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const axom::Array< BezierCurve< T, 2 >> &	carray,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt to a collection of 2D Bezier curves.

Parameters

[in]	q	The query point to test
[in]	carray	The array of Bezier curves
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Sums the GWN at q for each curved edge

Returns: The GWN.

◆ winding_number() [9/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const axom::Array< NURBSCurve< T, 2 >> &	narray,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt to a collection of 2D NURBS curves.

Parameters

[in]	q	The query point to test
[in]	narray	The array of NURBS curves
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Sums the GWN at q for each curved edge

Returns: The GWN.

◆ winding_number() [10/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	query,
		const detail::NURBSCurveGWNCache< T > &	nurbs_cache,
		bool &	isOnCurve,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt memoized data for a 2D NURBS curve.

Parameters

[in]	query	The query point to test
[in]	nurbs_cache	The NURBS curve cache data object containing memoized values
[out]	isOnCurve	Set to true is the query point is on the curve
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Returns: The GWN.

◆ winding_number() [11/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	q,
		const detail::NURBSCurveGWNCache< T > &	nurbs_cache,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Overload without optional return parameter.

References winding_number().

◆ winding_number() [12/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	query,
		const axom::Array< detail::NURBSCurveGWNCache< T >> &	nurbs_cache_arr,
		bool &	isOnCurve,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for a 2D point wrt an array of memoized data for 2D NURBS curves.

Parameters

[in]	query	The query point to test
[in]	nurbs_cache_arr	The array of memoized curve objects
[out]	isOnCurve	Set to true is the query point is on the curve
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Returns: The GWN.

References winding_number().

◆ winding_number() [13/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	query,
		const axom::ArrayView< const detail::NURBSCurveGWNCache< T >> &	nurbs_curve_arr,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Overload for views.

References winding_number().

◆ winding_number() [14/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 2 > &	query,
		const axom::Array< detail::NURBSCurveGWNCache< T >> &	nurbs_curve_arr,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Overload without optional return parameter.

References winding_number().

◆ winding_number() [15/28]

template<typename T >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 2 >> &	query_arr,
		const axom::Array< detail::NURBSCurveGWNCache< T >> &	nurbs_cache_arr,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for an array of 2D points wrt an array of cached data for 2D NURBS curves.

Parameters

[in]	query_arr	The array of query points to test
[in]	nurbs_curve_arr	The array of memoized curve objects
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Note: This method is accelerated via memoization, i.e. dynamically caching and reusing intermediate values for each curve across query points

Returns: The array of GWN values.

◆ winding_number() [16/28]

template<typename T , typename CurveType >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 2 >> &	query_arr,
		const axom::Array< CurveType > &	curve_arr,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for an array of 2D points wrt an array of generic 2D curves.

Template Parameters

CurveType The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve

Parameters

[in]	query_arr	The array of query point to test
[in]	curve_arr	The array of curve objects
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Note: This method is accelerated via memoization, i.e. dynamically caching and reusing intermediate values for each curve across query points

Returns: The array of GWN values.

References axom::Array< T, DIM, SPACE, StoragePolicy >::emplace_back(), axom::Array< T, DIM, SPACE, StoragePolicy >::size(), and winding_number().

◆ winding_number() [17/28]

template<typename T , typename CurveType >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 2 >> &	q_arr,
		const CurvedPolygon< CurveType > &	cpoly,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for an array of 2D points wrt to a 2D curved polygon.

Template Parameters

CurveType The BezierCurve, NURBSCurve, or NURBSCurveGWNCache which represents the curve

Parameters

[in]	q_arr	The array of query points to test
[in]	cpoly	The CurvedPolygon object of generic curves
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the GWN for the curved polygon by summing the GWN for each curved edge

Note: This method is accelerated via memoization, i.e. dynamically caching and reusing intermediate values for each curve across query points

Returns: The GWN.

References axom::Array< T, DIM, SPACE, StoragePolicy >::emplace_back(), axom::primal::CurvedPolygon< CurveType >::numEdges(), and winding_number().

◆ winding_number() [18/28]

template<typename T >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 2 >> &	q_arr,
		const CurvedPolygon< detail::NURBSCurveGWNCache< T >> &	cpoly,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the GWN for an array of 2D points wrt to a 2D curved polygon.

Parameters

[in]	q_arr	The array of query points to test
[in]	cpoly	The CurvedPolygon object of NURBS curves with cached GWN data
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the GWN for the curved polygon by summing the GWN for each curved edge

Warning: Because the cache isKdiscarded immediately after computation, this method is not accelerated by memoization

Returns: The GWN.

References winding_number().

◆ winding_number() [19/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	q,
		const Triangle< T, 3 > &	tri,
		bool &	isOnFace,
		const double	edge_tol = `1e-8`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a 3D triangle.

Parameters

[in]	q	The query point to test
[in]	tri	The 3D Triangle object
[out]	isOnFace	An optional return parameter if the point is on the triangle
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the GWN as the solid angle modulo 4pi using the formula from Oosterom, Strackee, "The Solid Angle of a Plane Triangle" IEEE Transactions on Biomedical Engineering, Vol BME-30, No. 2, February 1983 with extra adjustments if the triangle takes up a full octant

Returns: The GWN.

References axom::primal::Triangle< T, NDIMS >::area(), axom::numerics::cross_product(), axom::numerics::dot_product(), and axom::utilities::isNearlyEqual().

◆ winding_number() [20/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	q,
		const Triangle< T, 3 > &	tri,
		const double	edge_tol = `1e-8`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a 3D triangle.

Parameters

[in]	q	The query point to test
[in]	tri	The 3D Triangle object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the GWN for the triangle without an additional return parameter

Returns: The GWN.

References winding_number().

◆ winding_number() [21/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	q,
		const Polygon< T, 3 > &	poly,
		bool &	isOnFace,
		const double	edge_tol = `1e-8`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a 3D planar polygon.

Parameters

[in]	q	The query point to test
[in]	poly	The Polygon object
[out]	isOnFace	Return variable to show if the point is on the polygon
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Precondition: Assumes the polygon is planar. Otherwise, a meaningless value is returned.

Triangulates the polygon and computes the triangular GWN for each component

Returns: The GWN.

References axom::primal::Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >::numVertices(), and winding_number().

◆ winding_number() [22/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	q,
		const Polygon< T, 3 > &	poly,
		const double	edge_tol = `1e-8`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a 3D planar polygon.

Parameters

[in]	q	The query point to test
[in]	poly	The Polygon object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Precondition: Assumes the polygon is planar. Otherwise, a meaningless value is returned.

Computes the GWN for the polygon without an additional return parameter

Returns: The GWN.

References winding_number().

◆ winding_number() [23/28]

template<typename T >

int axom::primal::winding_number	(	const Point< T, 3 > &	q,
		const Polyhedron< T, 3 > &	poly,
		bool	includeBoundary = `false`,
		double	edge_tol = `1e-8`,
		double	EPS = `1e-8`
	)

Computes the winding number for a 3D point wrt a 3D convex polyhedron.

Parameters

[in]	q	The query point to test
[in]	poly	The Polyhedron object
[in]	includeBoundary	If true, points on the boundary are considered interior.
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Precondition: Expects the polyhedron to be convex and closed so that the returned value is an integer.

Computes the faces of the polyhedron and computes the GWN for each. The sum is then rounded to the nearest integer, as the shape is assumed to be closed.

Returns: The integer winding number.

References axom::primal::Polygon< T, NDIMS, ARRAY_TYPE, MAX_VERTS >::addVertex(), axom::Array< T, DIM, SPACE, StoragePolicy >::data(), axom::primal::Polyhedron< T, NDIMS >::getFaces(), axom::primal::Polyhedron< T, NDIMS >::hasNeighbors(), axom::primal::Polyhedron< T, NDIMS >::numVertices(), SLIC_ASSERT, and winding_number().

◆ winding_number() [24/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	query,
		const detail::NURBSPatchGWNCache< T > &	nurbs,
		const double	edge_tol = `1e-8`,
		const double	ls_tol = `1e-8`,
		const double	quad_tol = `1e-8`,
		const double	disk_size = `0.01`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a 3D NURBS patch with precomputed data.

Parameters

[in]	query	The query point to test
[in]	nurbs	The NURBS patch object with data
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	ls_tol	The tolerance for the line-surface intersection routine
[in]	quad_tol	The maximum relative error allowed in the quadrature
[in]	disk_size	The size of extracted disks as a percent of parameter bbox diagonal
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the generalized winding number for a NURBS patch using Stokes theorem.

Returns: The GWN.

◆ winding_number() [25/28]

template<typename T >

double axom::primal::winding_number	(	const Point< T, 3 > &	query,
		const axom::ArrayView< const detail::NURBSPatchGWNCache< T >> &	nurbs_arr,
		const double	edge_tol = `1e-8`,
		const double	ls_tol = `1e-8`,
		const double	quad_tol = `1e-8`,
		const double	disk_size = `0.01`,
		const double	EPS = `1e-8`
	)

Overload for a single query and an ArrayView.

◆ winding_number() [26/28]

template<typename T , typename SurfaceType >

double axom::primal::winding_number	(	const Point< T, 3 > &	query,
		const SurfaceType &	surf,
		const double	edge_tol = `1e-8`,
		const double	ls_tol = `1e-8`,
		const double	quad_tol = `1e-8`,
		const double	disk_size = `0.01`,
		const double	EPS = `1e-8`
	)

Computes the GWN for a 3D point wrt a generic 3D surface object.

Template Parameters

SurfaceType The BezierPatch or NURBSPatch which represents the surface

Parameters

[in]	query	The query point to test
[in]	surf	The BezierPatch or NURBSPatch object
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	ls_tol	The tolerance for the line-surface intersection routine
[in]	quad_tol	The maximum relative error allowed in the quadrature
[in]	disk_size	The size of extracted disks as a percent of parameter bbox diagonal
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Warning: Because the constructed cache object is discarded after gwn evaluation, this method is not accelerated via memoization

Returns: The GWN.

References winding_number().

◆ winding_number() [27/28]

template<typename T >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 3 >> &	query_arr,
		const axom::Array< detail::NURBSPatchGWNCache< T >> &	nurbs_arr,
		const double	edge_tol = `1e-8`,
		const double	ls_tol = `1e-8`,
		const double	quad_tol = `1e-8`,
		const double	disk_size = `0.01`,
		const double	EPS = `1e-8`
	)

Computes the GWN for an array of 3D point wrt an array of NURBS patch cache data.

Parameters

[in]	query_arr	The query point to test
[in]	nurbs_arr	Array of NURBSPatchGWNCache object containing intermediate values
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	ls_tol	The tolerance for the line-surface intersection routine
[in]	quad_tol	The maximum relative error allowed in the quadrature
[in]	disk_size	The size of extracted disks as a percent of parameter bbox diagonal
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the generalized winding number for a NURBS patch using Stokes theorem.

Note: This method is accelerated via memoization, i.e. dynamically caching and reusing intermediate values for each curve across query points

Returns: The array of GWN values.

◆ winding_number() [28/28]

template<typename T , typename SurfaceType >

axom::Array<double> axom::primal::winding_number	(	const axom::Array< Point< T, 3 >> &	query_arr,
		const axom::Array< SurfaceType > &	surf_arr,
		const double	edge_tol = `1e-8`,
		const double	ls_tol = `1e-8`,
		const double	quad_tol = `1e-8`,
		const double	disk_size = `0.01`,
		const double	EPS = `1e-8`
	)

Computes the GWN for an array an array of 3D points wrt an array of generic surfaces.

Template Parameters

SurfaceType The BezierPatch or NURBSPatch which represents the surface

Parameters

[in]	query_arr	The query point to test
[in]	surf_arr	Array of NURBSPatch or BezierPatch objects
[in]	edge_tol	The physical distance level at which objects are considered indistinguishable
[in]	ls_tol	The tolerance for the line-surface intersection routine
[in]	quad_tol	The maximum relative error allowed in the quadrature
[in]	disk_size	The size of extracted disks as a percent of parameter bbox diagonal
[in]	EPS	Miscellaneous numerical tolerance level for nonphysical distances

Computes the generalized winding number for a NURBS patch using Stokes theorem.

Note: This method is accelerated via memoization, i.e. dynamically caching and reusing intermediate values for each curve across query points

Returns: The array of GWN values.

References axom::Array< T, DIM, SPACE, StoragePolicy >::emplace_back(), axom::Array< T, DIM, SPACE, StoragePolicy >::size(), and winding_number().

Namespaces

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ Point2D

◆ Point3D

◆ Vector2D

◆ Vector3D

Enumeration Type Documentation

◆ OrientationResult

◆ PolygonArray

Function Documentation

◆ operator<<() [1/23]

◆ operator<<() [2/23]

◆ operator==() [1/4]

◆ operator!=() [1/4]

◆ operator<<() [3/23]

◆ operator<<() [4/23]

◆ regular_polygon()

◆ regular_prism()

◆ operator<<() [5/23]

◆ operator<<() [6/23]

◆ operator<<() [7/23]

◆ operator<<() [8/23]

◆ operator<<() [9/23]

◆ operator<<() [10/23]

◆ operator<<() [11/23]

◆ operator==() [2/4]

◆ operator!=() [2/4]

◆ operator<<() [12/23]

◆ compute_oriented_bounding_box()

◆ operator<<() [13/23]

◆ make_plane() [1/2]

◆ make_plane() [2/2]

◆ operator==() [3/4]

◆ operator!=() [3/4]

◆ operator<<() [14/23]

◆ transform_point()

◆ operator<<() [15/23]

◆ operator<<() [16/23]

◆ operator<<() [17/23]

◆ operator<<() [18/23]

◆ operator==() [4/4]

◆ operator!=() [4/4]

◆ operator<<() [19/23]

◆ operator<<() [20/23]

◆ operator<<() [21/23]

◆ operator<<() [22/23]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator/()

◆ operator<<() [23/23]

◆ clip() [1/19]

◆ clip() [2/19]

◆ clip() [3/19]

◆ clip() [4/19]

◆ clip() [5/19]

◆ clip() [6/19]

◆ clip() [7/19]

◆ clip() [8/19]

◆ clip() [9/19]

◆ clip() [10/19]

◆ clip() [11/19]

◆ clip() [12/19]

◆ clip() [13/19]

◆ clip() [14/19]

◆ clip() [15/19]

◆ clip() [16/19]

◆ clip() [17/19]

◆ clip() [18/19]

◆ clip() [19/19]