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

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/NURBSCurve.hpp>

Public Types
using	NumericType = T

using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	SegmentType = Segment< T, NDIMS >

using	WeightsVec = axom::Array< T >

using	CoordsVec = axom::Array< PointType >

using	KnotVectorType = KnotVector< T >

using	BoundingBoxType = BoundingBox< T, NDIMS >

using	OrientedBoundingBoxType = OrientedBoundingBox< T, NDIMS >

Public Member Functions
std::ostream &	print (std::ostream &os) const
	Simple formatted print of a NURBS Curve instance. More...

Query/modify curve properties (degree, rationality, ...)
void	setParameters (int npts, int degree)
	Reset the degree and resize arrays of points (and weights) More...

void	setDegree (int degree)
	Reset the knot vector. More...

int	getDegree () const
	Returns the degree of the NURBS Curve. More...

int	getOrder () const
	Returns the order of the NURBS Curve. More...

int	getNumControlPoints () const
	Returns the number of control points in the NURBS Curve. More...

void	setNumControlPoints (int npts)
	Set the number control points. More...

void	clear ()
	Clears the list of control points, make nonrational. More...

bool	isRational () const
	Use array size as flag for rationality. More...

void	makeRational ()
	Make trivially rational. If already rational, do nothing. More...

void	makeNonrational ()
	Make nonrational. If already rational, do nothing. More...

bool	isValidNURBS () const
	Function to check if the NURBS curve is valid. More...

Query/modify curve's geometry (control points, weights, bounding box, ...)
PointType &	operator[] (int idx)
	Retrieve the control point at index idx. More...

const PointType &	operator[] (int idx) const
	Retrieve the control point at index idx. More...

const PointType &	getInitPoint () const

const PointType &	getEndPoint () const

CoordsVec &	getControlPoints ()
	Returns a reference to the NURBS curve's control points. More...

const CoordsVec &	getControlPoints () const
	Returns a const reference to the NURBS curve's control points. More...

const T &	getWeight (int idx) const
	Get a specific weight. More...

void	setWeight (int idx, T weight)
	Set the weight at a specific index. More...

WeightsVec &	getWeights ()
	Returns a reference to the NURBS curve's weights. More...

const WeightsVec &	getWeights () const
	Returns a const reference to the NURBS curve's weights. More...

BoundingBoxType	boundingBox () const
	Returns an axis-aligned bounding box containing the NURBS curve. More...

OrientedBoundingBoxType	orientedBoundingBox () const
	Returns an oriented bounding box containing the NURBS curve. More...

bool	isLinear (double tol=1e-8, bool useStrictLinear=false) const
	Predicate to check if the NURBS curve is approximately linear. More...

Query/modify curve parametrization
axom::IndexType	getNumKnots () const
	Returns the number of knots in the NURBS Curve. More...

auto	getNumKnotSpans () const

void	normalize ()
	Normalize the knot vector to the span of [0, 1]. More...

void	rescale (T a, T b)
	Rescale the knot vector to the span of [a, b]. More...

const T &	getKnot (int idx) const
	Get a specific knot value. More...

void	setKnot (int idx, T knot)
	Set the knot value at a specific index. More...

void	setKnots (const axom::Array< T > &knots, int degree)
	Set the knot vector by an axom::Array. More...

void	setKnots (const KnotVectorType &knotVector)
	Set the knot vector by a KnotVector object. More...

KnotVectorType &	getKnots ()
	Return a reference to the knot vector. More...

const KnotVectorType &	getKnots () const
	Return a const reference to the knot vector. More...

T	getMinKnot () const
	Get minimum knot value. More...

T	getMaxKnot () const
	Get maximum knot value. More...

void	reverseOrientation ()
	Reverses the order of the NURBS curve's control points and weights. More...

axom::IndexType	insertKnot (T t, int target_multiplicity=1)
	Insert a knot with given multiplicity. More...

Functions to evaluate curve and its derivatives and normals
PointType	evaluate (T t) const
	Evaluate a NURBS Curve at a particular parameter value t. More...

VectorType	dt (T t) const
	Evaluate the first derivative of NURBS Curve at parameter t. More...

VectorType	dtdt (T t) const
	Evaluate the second derivative of NURBS Curve at parameter t. More...

void	evaluateFirstDerivative (T t, PointType &eval, VectorType &Dt) const
	Evaluate the curve and the first derivative at parameter t. More...

void	evaluateSecondDerivative (T t, PointType &eval, VectorType &Dt, VectorType &DtDt) const
	Evaluate the curve and the first two derivatives at parameter t. More...

void	evaluateDerivatives (T t, int d, PointType &eval, axom::Array< VectorType > &ders) const
	Evaluate the curve and the first d derivatives at parameter t. More...

Functions dealing with curve subdivision
bool	split (T t, NURBSCurve< T, NDIMS > &n1, NURBSCurve< T, NDIMS > &n2, bool normalizeParameters=false) const
	Splits a NURBS curve into two curves at a given parameter value. More...

void	bisect (NURBSCurve< T, NDIMS > &n1, NURBSCurve< T, NDIMS > &n2, bool normalizeParameters=false) const
	Splits a NURBS curve into two curves at the middle parameter value. More...

axom::Array< BezierCurve< T, NDIMS > >	extractBezier () const
	Splits a NURBS curve (at each internal knot) into several Bezier curves. More...

Friends
bool	operator== (const NURBSCurve< T, NDIMS > &lhs, const NURBSCurve< T, NDIMS > &rhs)
	Equality operator for NURBS Curves. More...

bool	operator!= (const NURBSCurve< T, NDIMS > &lhs, const NURBSCurve< T, NDIMS > &rhs)
	Inequality operator for NURBS Curves. More...

Constructors for NURBSCurve
The constructors allow for flexible initialization of NURBSCurve objects from: 1D arrays of control points, weights and knots. The control points and weight can be provided as C-style arrays with sizes, axom Arrays and axom ArrayViews. The knots can be provided as C-style arrays with sizes, axom Arrays and KnotVector instances Specified number of points and degree Rational or polynomial (nonrational) curves, depending on the presence of weights. All require: Degree >= -1. Degree -1 creates an empty/invalid curve. For valid curves, npts must be greater than the degree The weights array is optional. The curve is polynomial (non-rational) if weights are not provided When weights are provided, their size must match the number of control points The knot vector must satisfy continuity and openness conditions
	NURBSCurve (int degree=-1)
	Constructor for a simple NURBS curve that reserves space for the minimum (sensible) number of points for the given degree. More...

	NURBSCurve (int npts, int degree)
	Constructor for a NURBS curve with given number of control points and degree. More...

	NURBSCurve (axom::ArrayView< const PointType > pts, axom::ArrayView< const T > weights, const KnotVectorType &knotVector)
	Constructor for a NURBS Curve with ArrayViews of control points and weights and a KnotVector. More...

	NURBSCurve (axom::ArrayView< PointType > pts, axom::ArrayView< T > weights, const KnotVectorType &knotVector)
	Constructs a NURBSCurve from arrays of control points, weights and knots. More...

	NURBSCurve (const BezierCurve< T, NDIMS > &bezierCurve)
	Constructor for a NURBS curve from a Bezier curve. More...

	NURBSCurve (const PointType *pts, int npts, int degree)
	Constructor for a NURBS Curve with control points and degree. More...

	NURBSCurve (const PointType pts, const T weights, int npts, int degree)
	Constructor for a NURBS Curve with control points, weights, and degree. More...

	NURBSCurve (const PointType pts, int npts, const T knots, int nkts)
	Constructor for a NURBS Curve with control points and knots. More...

	NURBSCurve (const PointType pts, const T weights, int npts, const T *knots, int nkts)
	Constructor for a NURBS Curve with control points, weights, and knots. More...

	NURBSCurve (const axom::Array< PointType > &pts, int degree)
	Constructor for a NURBS Curve of the specified degree from an array of control points. More...

	NURBSCurve (const axom::Array< PointType > &pts, const axom::Array< T > &weights, int degree)
	Constructor for a NURBS Curve of the specified degree from an array of control points and weights. More...

	NURBSCurve (const axom::Array< PointType > &pts, const axom::Array< T > &knots)
	Constructor for a NURBS Curve with axom arrays of nodes and knots. More...

	NURBSCurve (const axom::Array< PointType > &pts, const axom::Array< T > &weights, const axom::Array< T > &knots)
	Constructor for a NURBS Curve with axom arrays of nodes, weights, and knots. More...

	NURBSCurve (const axom::Array< PointType > &pts, const KnotVectorType &knotVector)
	Constructor from axom array of nodes and KnotVector object. More...

	NURBSCurve (const axom::Array< PointType > &pts, const axom::Array< T > &weights, const KnotVectorType &knotVector)
	Constructor from axom array of nodes, weights, and KnotVector object. More...

static NURBSCurve	make_circular_arc_nurbs (T theta_0, T theta_1, T u, T v, T radius)
	Construct a multi-span, rational, degree 2 NURBS curve from the angles of a circular arc. More...

static NURBSCurve	make_linear_segment_nurbs (const PointType &start, const PointType &end)
	Construct a NURBS curve from the endpoints of a line segment. More...

Detailed Description

template<typename T, int NDIMS>
class axom::primal::NURBSCurve< T, NDIMS >

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

Template Parameters

T	the coordinate type, e.g., double, float, etc.
NDIMS	the number of dimensions

A NURBS curve has degree p, n+1 control points, optionally n+1 weights, and a knot vector of length k+1. A valid curve has k+1 = n+p+2 The curve must be open (clamped on each end) and continuous (unless p = 0)

Polynomial (Nonrational) NURBS curves are identified by an empty weights array.

Member Typedef Documentation

◆ NumericType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::NumericType = T

◆ PointType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::PointType = Point<T, NDIMS>

◆ VectorType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::VectorType = Vector<T, NDIMS>

◆ SegmentType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::SegmentType = Segment<T, NDIMS>

◆ WeightsVec

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::WeightsVec = axom::Array<T>

◆ CoordsVec

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::CoordsVec = axom::Array<PointType>

◆ KnotVectorType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::KnotVectorType = KnotVector<T>

◆ BoundingBoxType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::BoundingBoxType = BoundingBox<T, NDIMS>

◆ OrientedBoundingBoxType

template<typename T , int NDIMS>

using axom::primal::NURBSCurve< T, NDIMS >::OrientedBoundingBoxType = OrientedBoundingBox<T, NDIMS>

Constructor & Destructor Documentation

◆ NURBSCurve() [1/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve ( int degree = -1 )

inlineexplicit

Constructor for a simple NURBS curve that reserves space for the minimum (sensible) number of points for the given degree.

Parameters

[in] deg the degree of the resulting curve

Note: A uniform knot vector is constructed such that the curve is continuous

Precondition: degree is greater than or equal to -1

Note: When the degree is -1, no space is reserved and the NURBS curve is not valid, i.e. in this case, curve.isValid() will return false

◆ NURBSCurve() [2/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	int	npts,
		int	degree
	)

inline

Constructor for a NURBS curve with given number of control points and degree.

Parameters

[in]	npts	the number of control points
[in]	degree	the degree of the curve

Note: A uniform knot vector is constructed such that the curve is continuous; This constructor reserves space for the control points, but does not set them

Precondition: npts > degree, degree >= -1

References axom::primal::NURBSCurve< T, NDIMS >::isValidNURBS(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), and SLIC_ASSERT.

◆ NURBSCurve() [3/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	axom::ArrayView< const PointType >	pts,
		axom::ArrayView< const T >	weights,
		const KnotVectorType &	knotVector
	)

inline

Constructor for a NURBS Curve with ArrayViews of control points and weights and a KnotVector.

Parameters

[in]	pts	ArrayView of control points
[in]	weights	ArrayView of weights
[in]	knotVector	The knot vector object

For clamped and continuous curves, the control points and knot vector uniquely determine the degree

Precondition: The number of control points must be greater than the knot vector degree; If the knotVector degree is -1, pts must be empty; If the knotVector degree is higher, we assume knotVector.isValid(); weights can either be empty (yielding a non-rational spline) or its size must match that of pts

References axom::ArrayView< T, DIM, SPACE >::data(), axom::ArrayView< T, DIM, SPACE >::empty(), axom::primal::KnotVector< T >::getDegree(), axom::primal::KnotVector< T >::isValid(), axom::primal::NURBSCurve< T, NDIMS >::isValidNURBS(), axom::primal::NURBSCurve< T, NDIMS >::makeNonrational(), axom::ArrayView< T, DIM, SPACE >::size(), and SLIC_ASSERT.

◆ NURBSCurve() [4/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	axom::ArrayView< PointType >	pts,
		axom::ArrayView< T >	weights,
		const KnotVectorType &	knotVector
	)

inline

Constructs a NURBSCurve from arrays of control points, weights and knots.

Parameters

[in]	pts	ArrayView of control points
[in]	weights	ArrayView of weights
[in]	knotVector	Knot vector defining the parameterization of the curve.

◆ NURBSCurve() [5/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve ( const BezierCurve< T, NDIMS > & bezierCurve )

inlineexplicit

Constructor for a NURBS curve from a Bezier curve.

Parameters

[in] bezierCurve the Bezier curve to convert to a NURBS curve

◆ NURBSCurve() [6/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const PointType *	pts,
		int	npts,
		int	degree
	)

inline

Constructor for a NURBS Curve with control points and degree.

Parameters

[in]	pts	the control points of the curve
[in]	npts	the number of control points
[in]	degree	the degree of the curve

Precondition: Requires valid pointers, npts > degree, degree >= 0

◆ NURBSCurve() [7/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const PointType *	pts,
		const T *	weights,
		int	npts,
		int	degree
	)

inline

Constructor for a NURBS Curve with control points, weights, and degree.

Parameters

[in]	pts	the control points of the curve
[in]	weights	the weights of the control points
[in]	npts	the number of control points and weights
[in]	degree	the degree of the curve

Precondition: Requires valid pointers, npts > degree, npts == nwts, and degree >= 0

◆ NURBSCurve() [8/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const PointType *	pts,
		int	npts,
		const T *	knots,
		int	nkts
	)

inline

Constructor for a NURBS Curve with control points and knots.

Parameters

[in]	pts	the control points of the curve
[in]	npts	the number of control points and weights
[in]	knots	the weights of the control points
[in]	nkts	the length of the knot vector

Precondition: Requires valid pointers, a valid knot vector and npts > degree

◆ NURBSCurve() [9/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const PointType *	pts,
		const T *	weights,
		int	npts,
		const T *	knots,
		int	nkts
	)

inline

Constructor for a NURBS Curve with control points, weights, and knots.

Parameters

[in]	pts	the control points of the curve
[in]	weights	the weights of the control points
[in]	npts	the number of control points and weights
[in]	knots	the weights of the control points
[in]	nkts	the length of the knot vector

Precondition: Requires valid pointers, a valid knot vector, npts > degree, npts == nwts, wts > 0

◆ NURBSCurve() [10/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		int	degree
	)

inline

Constructor for a NURBS Curve of the specified degree from an array of control points.

Parameters

[in]	pts	the control points of the curve
[in]	degree	the degree of the curve

Precondition: Requires npts > degree and degree >= 0

◆ NURBSCurve() [11/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		const axom::Array< T > &	weights,
		int	degree
	)

inline

Constructor for a NURBS Curve of the specified degree from an array of control points and weights.

Parameters

[in]	pts	the control points of the curve
[in]	weights	the weights of the control points
[in]	degree	the degree of the curve

Precondition: Requires npts > degree, degree >= 0, and pts.size() == weights.size()

◆ NURBSCurve() [12/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		const axom::Array< T > &	knots
	)

inline

Constructor for a NURBS Curve with axom arrays of nodes and knots.

Parameters

[in]	pts	the control points of the curve
[in]	knots	the knot vector of the curve

Precondition: Requires a valid knot vector and npts > degree

◆ NURBSCurve() [13/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		const axom::Array< T > &	weights,
		const axom::Array< T > &	knots
	)

inline

Constructor for a NURBS Curve with axom arrays of nodes, weights, and knots.

Parameters

[in]	pts	the control points of the curve
[in]	weights	the weights of the control points
[in]	knots	the knot vector of the curve

Precondition: Requires a valid knot vector, npts > degree, npts == nwts, wts > 0

◆ NURBSCurve() [14/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		const KnotVectorType &	knotVector
	)

inline

Constructor from axom array of nodes and KnotVector object.

Parameters

[in]	pts	the control points of the curve
[in]	knotVector	A KnotVector object

Precondition: Requires a valid knot vector and npts > degree

◆ NURBSCurve() [15/15]

template<typename T , int NDIMS>

axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve	(	const axom::Array< PointType > &	pts,
		const axom::Array< T > &	weights,
		const KnotVectorType &	knotVector
	)

inline

Constructor from axom array of nodes, weights, and KnotVector object.

Parameters

[in]	pts	the control points of the curve
[in]	weights	the weights of the control points
[in]	knotVector	A KnotVector object

Precondition: Requires a valid knot vector, npts > degree, npts == nwts, wts > 0

Member Function Documentation

◆ make_circular_arc_nurbs()

template<typename T , int NDIMS>

static NURBSCurve axom::primal::NURBSCurve< T, NDIMS >::make_circular_arc_nurbs	(	T	theta_0,
		T	theta_1,
		T	u,
		T	v,
		T	radius
	)

inlinestatic

Construct a multi-span, rational, degree 2 NURBS curve from the angles of a circular arc.

Parameters

[in]	theta_0	The starting angle of the arc
[in]	theta_1	The ending angle of the arc
[in]	u,v	The center of the 2D circle
[in]	radius	The radius of the circle

Note: The curve's knots will span [0, 1], but the parameterization is not uniform with respect to the arc length; The arc is assumed to be counter-clockwise, unless theta_1 < theta_0, in which case the arc is clockwise.

Precondition: Requires a 2D NURBS curve, and the arc is less than a full circle

References axom::utilities::ceil(), axom::primal::NURBSCurve< T, NDIMS >::makeRational(), axom::utilities::min(), axom::primal::NURBSCurve< T, NDIMS >::NURBSCurve(), axom::primal::NURBSCurve< T, NDIMS >::reverseOrientation(), axom::primal::NURBSCurve< T, NDIMS >::setKnot(), axom::primal::NURBSCurve< T, NDIMS >::setWeight(), SLIC_ASSERT, and axom::utilities::swap().

◆ make_linear_segment_nurbs()

template<typename T , int NDIMS>

static NURBSCurve axom::primal::NURBSCurve< T, NDIMS >::make_linear_segment_nurbs	(	const PointType &	start,
		const PointType &	end
	)

inlinestatic

Construct a NURBS curve from the endpoints of a line segment.

Parameters

[in]	start	The starting point of the arc
[in]	end	The ending point of the arc

Precondition: Requires a 2D NURBS curve

References axom::utilities::annotations::end(), and SLIC_ASSERT.

◆ setParameters()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setParameters	(	int	npts,
		int	degree
	)

inline

Reset the degree and resize arrays of points (and weights)

Parameters

[in]	npts	The target number of control points
[in]	degree	The target degree

Warning: This method will replace existing knot vector with a uniform one.

References axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::makeUniform(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), and SLIC_ASSERT.

◆ setDegree()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setDegree ( int degree )

inline

Reset the knot vector.

Parameters

[in] degree The target degree

Warning: This method does NOT change the existing control points, i.e. does not perform degree elevation/reduction. Will replace existing knot vector with a uniform one.

Precondition: Requires target degree < npts and degree >= 0

References axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::KnotVector< T >::makeUniform(), and SLIC_ASSERT.

◆ getDegree()

template<typename T , int NDIMS>

int axom::primal::NURBSCurve< T, NDIMS >::getDegree ( ) const

inline

Returns the degree of the NURBS Curve.

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

◆ getOrder()

template<typename T , int NDIMS>

int axom::primal::NURBSCurve< T, NDIMS >::getOrder ( ) const

inline

Returns the order of the NURBS Curve.

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

◆ getNumControlPoints()

template<typename T , int NDIMS>

int axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints ( ) const

inline

Returns the number of control points in the NURBS Curve.

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

◆ setNumControlPoints()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setNumControlPoints ( int npts )

inline

Set the number control points.

Parameters

[in] npts The target number of control points

Warning: This method does NOT change the existing control points, i.e. does not perform degree elevation/reduction. Will replace existing knot vector with a uniform one.

References axom::primal::KnotVector< T >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::makeUniform(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), and SLIC_ASSERT.

◆ clear()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::clear ( )

inline

Clears the list of control points, make nonrational.

References axom::Array< T, DIM, SPACE, StoragePolicy >::clear(), axom::primal::KnotVector< T >::clear(), and axom::primal::NURBSCurve< T, NDIMS >::makeNonrational().

◆ isRational()

template<typename T , int NDIMS>

bool axom::primal::NURBSCurve< T, NDIMS >::isRational ( ) const

inline

Use array size as flag for rationality.

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

◆ makeRational()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::makeRational ( )

inline

Make trivially rational. If already rational, do nothing.

References axom::Array< T, DIM, SPACE, StoragePolicy >::fill(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), and axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ makeNonrational()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::makeNonrational ( )

inline

Make nonrational. If already rational, do nothing.

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

◆ isValidNURBS()

template<typename T , int NDIMS>

bool axom::primal::NURBSCurve< T, NDIMS >::isValidNURBS ( ) const

inline

Function to check if the NURBS curve is valid.

References axom::primal::KnotVector< T >::getDegree(), axom::primal::KnotVector< T >::getNumKnots(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::isValid(), and axom::Array< T, DIM, SPACE, StoragePolicy >::size().

◆ operator[]() [1/2]

template<typename T , int NDIMS>

PointType& axom::primal::NURBSCurve< T, NDIMS >::operator[] ( int idx )

inline

Retrieve the control point at index idx.

Parameters

[in] idx The index of the control point

Returns: A reference to the control point at index idx

◆ operator[]() [2/2]

template<typename T , int NDIMS>

const PointType& axom::primal::NURBSCurve< T, NDIMS >::operator[] ( int idx ) const

inline

Retrieve the control point at index idx.

Parameters

[in] idx The index of the control point

Returns: A const reference to the control point at index idx

◆ getInitPoint()

template<typename T , int NDIMS>

const PointType& axom::primal::NURBSCurve< T, NDIMS >::getInitPoint ( ) const

inline

◆ getEndPoint()

template<typename T , int NDIMS>

const PointType& axom::primal::NURBSCurve< T, NDIMS >::getEndPoint ( ) const

inline

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

◆ getControlPoints() [1/2]

template<typename T , int NDIMS>

CoordsVec& axom::primal::NURBSCurve< T, NDIMS >::getControlPoints ( )

inline

Returns a reference to the NURBS curve's control points.

◆ getControlPoints() [2/2]

template<typename T , int NDIMS>

const CoordsVec& axom::primal::NURBSCurve< T, NDIMS >::getControlPoints ( ) const

inline

Returns a const reference to the NURBS curve's control points.

◆ getWeight()

template<typename T , int NDIMS>

const T& axom::primal::NURBSCurve< T, NDIMS >::getWeight ( int idx ) const

inline

Get a specific weight.

Parameters

[in] idx The index of the weight

Precondition: Requires that the curve be rational

Returns: The weight at index idx

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

◆ setWeight()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setWeight	(	int	idx,
		T	weight
	)

inline

Set the weight at a specific index.

Parameters

[in]	idx	The index of the weight
[in]	weight	The updated value of the weight

Precondition: Requires that the curve be rational, and the weight be rational

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

◆ getWeights() [1/2]

template<typename T , int NDIMS>

WeightsVec& axom::primal::NURBSCurve< T, NDIMS >::getWeights ( )

inline

Returns a reference to the NURBS curve's weights.

◆ getWeights() [2/2]

template<typename T , int NDIMS>

const WeightsVec& axom::primal::NURBSCurve< T, NDIMS >::getWeights ( ) const

inline

Returns a const reference to the NURBS curve's weights.

◆ boundingBox()

template<typename T , int NDIMS>

BoundingBoxType axom::primal::NURBSCurve< T, NDIMS >::boundingBox ( ) const

inline

Returns an axis-aligned bounding box containing the NURBS curve.

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

◆ orientedBoundingBox()

template<typename T , int NDIMS>

OrientedBoundingBoxType axom::primal::NURBSCurve< T, NDIMS >::orientedBoundingBox ( ) const

inline

Returns an oriented bounding box containing the NURBS curve.

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

◆ isLinear()

template<typename T , int NDIMS>

bool axom::primal::NURBSCurve< T, NDIMS >::isLinear	(	double	tol = `1e-8`,
		bool	useStrictLinear = `false`
	)		const

inline

Predicate to check if the NURBS curve is approximately linear.

This function checks if the interior control points of the NURBSCurve are approximately on the line segment defined by its two endpoints.

Parameters

[in]	tol	Threshold for squared distance
[in]	useStrictLinear	If true, checks that the control points are evenly spaced along the endpoint segment (in addition to being near the segment). This is a stronger condition and may return false for curves that are geometrically linear but have a non-uniform control-point distribution along the segment.

Returns: True if curve is near-linear

References axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::Point< T, NDIMS >::lerp(), and axom::primal::squared_distance().

◆ getNumKnots()

template<typename T , int NDIMS>

axom::IndexType axom::primal::NURBSCurve< T, NDIMS >::getNumKnots ( ) const

inline

Returns the number of knots in the NURBS Curve.

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

◆ getNumKnotSpans()

template<typename T , int NDIMS>

auto axom::primal::NURBSCurve< T, NDIMS >::getNumKnotSpans ( ) const

inline

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

◆ normalize()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::normalize ( )

inline

Normalize the knot vector to the span of [0, 1].

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

◆ rescale()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::rescale	(	T	a,
		T	b
	)

inline

Rescale the knot vector to the span of [a, b].

Parameters

[in]	a	The lower bound of the new knot vector
[in]	b	The upper bound of the new knot vector

Precondition: Requires a < b

References axom::primal::KnotVector< T >::rescale(), and SLIC_ASSERT.

◆ getKnot()

template<typename T , int NDIMS>

const T& axom::primal::NURBSCurve< T, NDIMS >::getKnot ( int idx ) const

inline

Get a specific knot value.

Parameters

[in] idx The index of the knot

Returns: The knot value at index idx

◆ setKnot()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setKnot	(	int	idx,
		T	knot
	)

inline

Set the knot value at a specific index.

Parameters

[in]	idx	The index of the knot
[in]	knot	The updated value of the knot

◆ setKnots() [1/2]

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setKnots	(	const axom::Array< T > &	knots,
		int	degree
	)

inline

Set the knot vector by an axom::Array.

Parameters

[in] knots The new knot vector

◆ setKnots() [2/2]

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::setKnots ( const KnotVectorType & knotVector )

inline

Set the knot vector by a KnotVector object.

Parameters

[in] knotVector The new knot vector

◆ getKnots() [1/2]

template<typename T , int NDIMS>

KnotVectorType& axom::primal::NURBSCurve< T, NDIMS >::getKnots ( )

inline

Return a reference to the knot vector.

◆ getKnots() [2/2]

template<typename T , int NDIMS>

const KnotVectorType& axom::primal::NURBSCurve< T, NDIMS >::getKnots ( ) const

inline

Return a const reference to the knot vector.

◆ getMinKnot()

template<typename T , int NDIMS>

T axom::primal::NURBSCurve< T, NDIMS >::getMinKnot ( ) const

inline

Get minimum knot value.

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

◆ getMaxKnot()

template<typename T , int NDIMS>

T axom::primal::NURBSCurve< T, NDIMS >::getMaxKnot ( ) const

inline

Get maximum knot value.

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

◆ reverseOrientation()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::reverseOrientation ( )

inline

Reverses the order of the NURBS curve's control points and weights.

References axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::reverse(), and axom::utilities::swap().

◆ insertKnot()

template<typename T , int NDIMS>

axom::IndexType axom::primal::NURBSCurve< T, NDIMS >::insertKnot	(	T	t,
		int	target_multiplicity = `1`
	)

inline

Insert a knot with given multiplicity.

Parameters

[in]	t	The parameter value of the knot to insert
[in]	target_multiplicity	The multiplicity of the knot to insert

Returns: The index of the new knot

Algorithm A5.1 on p. 151 of "The NURBS Book"

Note: If the knot is already present, it will be inserted up to the given multiplicity, or the maximum permitted by the degree

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

Returns: The (maximum) index of the new knot

References axom::utilities::clampVal(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::getMaxKnot(), axom::primal::NURBSCurve< T, NDIMS >::getMinKnot(), axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::KnotVector< T >::insertKnotBySpan(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::isValidParameter(), axom::utilities::min(), axom::Array< T, DIM, SPACE, StoragePolicy >::size(), and SLIC_ASSERT.

◆ evaluate()

template<typename T , int NDIMS>

PointType axom::primal::NURBSCurve< T, NDIMS >::evaluate ( T t ) const

inline

Evaluate a NURBS Curve at a particular parameter value t.

Parameters

[in] t The parameter value at which to evaluate

Returns: p The point of the NURBS curve at t

Adapted from Algorithm A4.1 on page 124 of "The NURBS Book"

Precondition: Requires t in the span of the knots (up to a small tolerance).

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

References axom::primal::KnotVector< T >::calculateBasisFunctionsBySpan(), axom::utilities::clampVal(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::getMaxKnot(), axom::primal::NURBSCurve< T, NDIMS >::getMinKnot(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::isValidParameter(), and SLIC_ASSERT.

◆ dt()

template<typename T , int NDIMS>

VectorType axom::primal::NURBSCurve< T, NDIMS >::dt ( T t ) const

inline

Evaluate the first derivative of NURBS Curve at parameter t.

Parameters

[in] t The parameter value at which to evaluate

Returns: p The vector of NURBS curve's derivative at t

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

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

◆ dtdt()

template<typename T , int NDIMS>

VectorType axom::primal::NURBSCurve< T, NDIMS >::dtdt ( T t ) const

inline

Evaluate the second derivative of NURBS Curve at parameter t.

Parameters

[in] t The parameter value at which to evaluate

Returns: p The vector of NURBS curve's 2nd derivative at t

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

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

◆ evaluateFirstDerivative()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::evaluateFirstDerivative	(	T	t,
		PointType &	eval,
		VectorType &	Dt
	)		const

inline

Evaluate the curve and the first derivative at parameter t.

Parameters

[in]	t	The parameter value at which to evaluate
[out]	eval	The point on the curve at t
[out]	Dt	The first derivative of the curve at t

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

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

◆ evaluateSecondDerivative()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::evaluateSecondDerivative	(	T	t,
		PointType &	eval,
		VectorType &	Dt,
		VectorType &	DtDt
	)		const

inline

Evaluate the curve and the first two derivatives at parameter t.

Parameters

[in]	t	The parameter value at which to evaluate
[out]	eval	The point on the curve at t
[out]	Dt	The first derivative of the curve at t
[out]	DtDt	The second derivative of the curve at t

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

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

◆ evaluateDerivatives()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::evaluateDerivatives	(	T	t,
		int	d,
		PointType &	eval,
		axom::Array< VectorType > &	ders
	)		const

inline

Evaluate the curve and the first d derivatives at parameter t.

Parameters

[in]	t	The parameter value at which to evaluate
[in]	d	The number of derivatives to evaluate
[out]	eval	The point on the curve at t
[out]	ders	An array of the first d derivatives at t

Implementation adapted from Algorithm A3.2 on p. 93 of "The NURBS Book". Rational derivatives from Algorithm A4.2 on p. 127 of "The NURBS Book".

Precondition: Requires t in the span of the knots (up to a small tolerance)

Note: If t is outside the knot span up to this tolerance, it is clamped to the span

References axom::utilities::binomialCoefficient(), axom::utilities::clampVal(), axom::primal::KnotVector< T >::derivativeBasisFunctionsBySpan(), axom::primal::KnotVector< T >::findSpan(), axom::primal::KnotVector< T >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::getMaxKnot(), axom::primal::NURBSCurve< T, NDIMS >::getMinKnot(), axom::primal::NURBSCurve< T, NDIMS >::isRational(), axom::primal::KnotVector< T >::isValidParameter(), axom::utilities::min(), axom::Array< T, DIM, SPACE, StoragePolicy >::resize(), and SLIC_ASSERT.

◆ split()

template<typename T , int NDIMS>

bool axom::primal::NURBSCurve< T, NDIMS >::split	(	T	t,
		NURBSCurve< T, NDIMS > &	n1,
		NURBSCurve< T, NDIMS > &	n2,
		bool	normalizeParameters = `false`
	)		const

inline

Splits a NURBS curve into two curves at a given parameter value.

Parameters

[in]	t	parameter value at which to evaluate
[out]	n1	First output NURBS curve
[out]	n2	Second output NURBS curve
[in]	normalizeParameters	Whether to normalize the output curves

If t is at the knot u_0 or u_max, will return the original curve and a degenerate curve with the first or last control point

Precondition: Requires t in the strict interior of the span of the knots

Returns: True if and only if the curve was split (i.e., t is in the knot span)

◆ bisect()

template<typename T , int NDIMS>

void axom::primal::NURBSCurve< T, NDIMS >::bisect	(	NURBSCurve< T, NDIMS > &	n1,
		NURBSCurve< T, NDIMS > &	n2,
		bool	normalizeParameters = `false`
	)		const

inline

Splits a NURBS curve into two curves at the middle parameter value.

Parameters

[out]	n1	First output NURBS curve
[out]	n2	Second output NURBS curve
[in]	normalizeParameters	Whether to normalize the output curves

References axom::primal::NURBSCurve< T, NDIMS >::getMaxKnot(), axom::primal::NURBSCurve< T, NDIMS >::getMinKnot(), and axom::primal::NURBSCurve< T, NDIMS >::split().

◆ extractBezier()

template<typename T , int NDIMS>

axom::Array<BezierCurve<T, NDIMS> > axom::primal::NURBSCurve< T, NDIMS >::extractBezier ( ) const

inline

Splits a NURBS curve (at each internal knot) into several Bezier curves.

If the curve is of degree 0, will return a set of disconnected, order 0 Bezier curves

Adapted from Algorithm A5.6 on p. 173 of "The NURBS Book"

Returns: An array of Bezier curves

References axom::primal::NURBSCurve< T, NDIMS >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::KnotVector< T >::getNumKnotSpans(), axom::primal::NURBSCurve< T, NDIMS >::getWeight(), and axom::primal::NURBSCurve< T, NDIMS >::isRational().

◆ print()

template<typename T , int NDIMS>

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

inline

Simple formatted print of a NURBS Curve instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

References axom::primal::KnotVector< T >::getDegree(), axom::primal::NURBSCurve< T, NDIMS >::getNumControlPoints(), axom::primal::KnotVector< T >::getNumKnots(), and axom::primal::NURBSCurve< T, NDIMS >::isRational().

Friends And Related Function Documentation

◆ operator==

template<typename T , int NDIMS>

bool operator==	(	const NURBSCurve< T, NDIMS > &	lhs,
		const NURBSCurve< T, NDIMS > &	rhs
	)

friend

Equality operator for NURBS Curves.

Parameters

[in]	lhs	The left-hand side NURBS curve
[in]	rhs	The right-hand side NURBS curve

Returns: True if the two curves are equal, false otherwise

◆ operator!=

template<typename T , int NDIMS>

bool operator!=	(	const NURBSCurve< T, NDIMS > &	lhs,
		const NURBSCurve< T, NDIMS > &	rhs
	)

friend

Inequality operator for NURBS Curves.

Parameters

[in]	lhs	The left-hand side NURBS curve
[in]	rhs	The right-hand side NURBS curve

Returns: True if the two curves are not equal, false otherwise

The documentation for this class was generated from the following file:

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/develop/src/axom/primal/geometry/NURBSCurve.hpp

Public Types

Public Member Functions

Friends

Constructors for NURBSCurve

Detailed Description

template<typename T, int NDIMS> class axom::primal::NURBSCurve< T, NDIMS >

Member Typedef Documentation

◆ NumericType

◆ PointType

◆ VectorType

◆ SegmentType

◆ WeightsVec

◆ CoordsVec

◆ KnotVectorType

◆ BoundingBoxType

◆ OrientedBoundingBoxType

Constructor & Destructor Documentation

◆ NURBSCurve() [1/15]

◆ NURBSCurve() [2/15]

◆ NURBSCurve() [3/15]

◆ NURBSCurve() [4/15]

◆ NURBSCurve() [5/15]

◆ NURBSCurve() [6/15]

◆ NURBSCurve() [7/15]

◆ NURBSCurve() [8/15]

◆ NURBSCurve() [9/15]

◆ NURBSCurve() [10/15]

◆ NURBSCurve() [11/15]

◆ NURBSCurve() [12/15]

◆ NURBSCurve() [13/15]

◆ NURBSCurve() [14/15]

◆ NURBSCurve() [15/15]

Member Function Documentation

◆ make_circular_arc_nurbs()

◆ make_linear_segment_nurbs()

◆ setParameters()

◆ setDegree()

◆ getDegree()

◆ getOrder()

◆ getNumControlPoints()

◆ setNumControlPoints()

◆ clear()

◆ isRational()

◆ makeRational()

◆ makeNonrational()

◆ isValidNURBS()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ getInitPoint()

◆ getEndPoint()

◆ getControlPoints() [1/2]

◆ getControlPoints() [2/2]

◆ getWeight()

◆ setWeight()

◆ getWeights() [1/2]

◆ getWeights() [2/2]

◆ boundingBox()

◆ orientedBoundingBox()

◆ isLinear()

◆ getNumKnots()

◆ getNumKnotSpans()

◆ normalize()

◆ rescale()

◆ getKnot()

◆ setKnot()

◆ setKnots() [1/2]

◆ setKnots() [2/2]

◆ getKnots() [1/2]

◆ getKnots() [2/2]

◆ getMinKnot()

◆ getMaxKnot()

◆ reverseOrientation()

◆ insertKnot()

◆ evaluate()

◆ dt()

◆ dtdt()

◆ evaluateFirstDerivative()

◆ evaluateSecondDerivative()

◆ evaluateDerivatives()

◆ split()

template<typename T, int NDIMS>
class axom::primal::NURBSCurve< T, NDIMS >