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...

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

Inheritance diagram for axom::primal::Plane< T, NDIMS >:

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Public Types
using	VectorType = primal::Vector< T, NDIMS >

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

Public Member Functions
AXOM_HOST_DEVICE const VectorType &	getNormal () const
	Returns a const pointer to the plane's normal vector. More...

AXOM_HOST_DEVICE T	getOffset () const
	Returns the offset of the plane from origin. More...

AXOM_HOST_DEVICE T	signedDistance (const PointType &x) const
	Computes the signed distance of the specified point to this Plane. More...

AXOM_HOST_DEVICE PointType	projectPoint (const PointType &x) const
	Computes the projection of a given point, x, onto this Plane. More...

AXOM_HOST_DEVICE PointType	reflectPoint (const PointType &x) const
	Computes the reflection of a given point, x, across this Plane. More...

AXOM_HOST_DEVICE void	flip ()
	Flips the orientation of the plane. More...

AXOM_HOST_DEVICE int	getOrientation (const PointType &x, double TOL=1.e-9) const
	Computes the orientation of the point with respect to this Plane. More...

AXOM_HOST_DEVICE bool	isValid (double TOL=PRIMAL_TINY) const
	Simple check for validity of a Plane. More...

std::ostream &	print (std::ostream &os) const
	Prints the Plane information in the given output stream. More...

Constructors
	Plane ()=default
	Constructs a Plane with a zero normal vector and zero offset. More...

AXOM_HOST_DEVICE	Plane (const VectorType &normal, const PointType &x, bool normalize=true)
	Constructs a Plane with a given normal, \( \mathcal{N} \), that passes through the specified point, \( x \). More...

AXOM_HOST_DEVICE	Plane (const VectorType &normal, T offset, bool normalize=true)
	Constructs a plane with a specified normal, \( \mathcal{N} \), located at the given offset from origin. More...

Static Public Member Functions
static constexpr AXOM_HOST_DEVICE int	getDimension ()
	Returns the dimension of the Plane. More...

Detailed Description

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

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

The Plane object defines an oriented plane in Hessian Normal form:

     \f$ \mathcal{N} \cdot x - d = 0 \f$

where, \( \mathcal{N} \) is a normal and \( d \) is the offset of the plane (in the direction of the specified normal) to the origin.

The Plane class defines a co-dimension-one plane that splits the ambient space into two halfspaces, such that, the signed distance for any point is: (a) negative below the plance, (b) positive above the plane and (c) zero on the plane.

A Plane object may be constructed in three ways:

Specifying a normal and a point that the plane passes through
Specifying a normal and an offset from the origin, or
Specifying the points that the plane passes through. A minimum of two points are required to define a plane in 2D, or, three points for 3D.

Template Parameters

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

Precondition: NDIMS==2 || NDIMS==3

Member Typedef Documentation

◆ VectorType

template<typename T , int NDIMS>

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

◆ PointType

template<typename T , int NDIMS>

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

Constructor & Destructor Documentation

◆ Plane() [1/3]

template<typename T , int NDIMS>

axom::primal::Plane< T, NDIMS >::Plane ( )

default

Constructs a Plane with a zero normal vector and zero offset.

Postcondition: isValid() == false

◆ Plane() [2/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE axom::primal::Plane< T, NDIMS >::Plane	(	const VectorType &	normal,
		const PointType &	x,
		bool	normalize = `true`
	)

Constructs a Plane with a given normal, \( \mathcal{N} \), that passes through the specified point, \( x \).

Parameters

[in]	normal	the supplied plane normal, \( \mathcal{N} \)
[in]	x	a specified point that the plane passes through, \( x \)
[in]	normalize	if true, normalize the given vector (default: true)

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

◆ Plane() [3/3]

template<typename T , int NDIMS>

AXOM_HOST_DEVICE axom::primal::Plane< T, NDIMS >::Plane	(	const VectorType &	normal,
		T	offset,
		bool	normalize = `true`
	)

Constructs a plane with a specified normal, \( \mathcal{N} \), located at the given offset from origin.

Parameters

[in]	normal	the supplied plane normal, \( \mathcal{N} \)
[in]	offset	the plane offset from origin
[in]	normalize	if true, normalize the given vector (default: true)

References axom::primal::Vector< T, NDIMS >::is_zero(), axom::numerics::normalize(), and SLIC_ASSERT_MSG.

Member Function Documentation

◆ getDimension()

template<typename T , int NDIMS>

static constexpr AXOM_HOST_DEVICE int axom::primal::Plane< T, NDIMS >::getDimension ( )

inlinestaticconstexpr

Returns the dimension of the Plane.

Returns: dim the dimension of the Plane.

Postcondition: (dim==2) || (dim==3)

◆ getNormal()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE const VectorType& axom::primal::Plane< T, NDIMS >::getNormal ( ) const

inline

Returns a const pointer to the plane's normal vector.

Returns: N the normal vector.

◆ getOffset()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE T axom::primal::Plane< T, NDIMS >::getOffset ( ) const

inline

Returns the offset of the plane from origin.

Returns: offSet the offset of the plane from origin.

◆ signedDistance()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE T axom::primal::Plane< T, NDIMS >::signedDistance ( const PointType & x ) const

inline

Computes the signed distance of the specified point to this Plane.

Parameters

[in] x buffer consisting of the query point coordinates.

Returns: d the signed distance of the point x to the plane.

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

◆ projectPoint()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Plane< T, NDIMS >::PointType axom::primal::Plane< T, NDIMS >::projectPoint ( const PointType & x ) const

Computes the projection of a given point, x, onto this Plane.

Parameters

[in] x buffer consisting of the coordinates of the point to project.

Returns: projx the coordinates of the projected point.

Postcondition: this->getOrientedSide( projx ) == ON_BOUNDARY

◆ reflectPoint()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE Plane< T, NDIMS >::PointType axom::primal::Plane< T, NDIMS >::reflectPoint ( const PointType & x ) const

Computes the reflection of a given point, x, across this Plane.

Parameters

[in] x buffer consisting of the coordinates of the point to project.

Returns: refx the coordinates of the reflected point.

Postcondition: The reflected point will be on the Plane if x is on the Plane, otherwise it will be on the opposite side of the Plane from x.

◆ flip()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE void axom::primal::Plane< T, NDIMS >::flip

Flips the orientation of the plane.

◆ getOrientation()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE int axom::primal::Plane< T, NDIMS >::getOrientation	(	const PointType &	x,
		double	TOL = `1.e-9`
	)		const

Computes the orientation of the point with respect to this Plane.

Parameters

[in]	x	buffer consisting of the query point coordinates.
[in]	TOL	user-supplied tolerance. Optional. Default is 1.e-9.

Returns: orientation the orientation of the point

Note

This method returns one of the following values:

ON_BOUNDARY : if x lies on the plane
ON_POSITIVE_SIDE : if x is above the plane
ON_NEGATIVE_SIDE : if x is below the plane

See also: OrientationResult

References axom::utilities::isNearlyEqual(), axom::primal::ON_BOUNDARY, axom::primal::ON_NEGATIVE_SIDE, and axom::primal::ON_POSITIVE_SIDE.

◆ isValid()

template<typename T , int NDIMS>

AXOM_HOST_DEVICE bool axom::primal::Plane< T, NDIMS >::isValid ( double TOL = PRIMAL_TINY ) const

Simple check for validity of a Plane.

Check that the normal is not the zero vector.

Parameters

[in] TOL user-supplied tolerance. Optional. Default is 1.0e-50.

Returns: True, if the Plane is valid, False otherwise

References axom::utilities::isNearlyEqual().

◆ print()

template<typename T , int NDIMS>

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

Prints the Plane information in the given output stream.

Parameters

[in] os The output stream to write to.

Note: This method is primarily used for debugging.

Returns: s the modified output stream object.

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/Plane.hpp

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

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

Member Typedef Documentation

◆ VectorType

◆ PointType

Constructor & Destructor Documentation

◆ Plane() [1/3]

◆ Plane() [2/3]

◆ Plane() [3/3]

Member Function Documentation

◆ getDimension()

◆ getNormal()

◆ getOffset()

◆ signedDistance()

◆ projectPoint()

◆ reflectPoint()

◆ flip()

◆ getOrientation()

◆ isValid()

◆ print()

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