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...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.10.1/src/axom/primal/geometry/Polyhedron.hpp>

Public Types
using	PointType = Point< T, NDIMS >

using	VectorType = Vector< T, NDIMS >

using	NumArrayType = NumericArray< T, NDIMS >

Public Member Functions
	Polyhedron ()=default

AXOM_HOST_DEVICE int	numVertices () const

AXOM_HOST_DEVICE int	addVertex (const PointType &pt)
	Appends a vertex to the list of vertices. More...

AXOM_HOST_DEVICE void	addNeighbors (const PointType &pt, std::initializer_list< std::int8_t > nbrs)
	Stores nbrs as the neighbors of vertex pt. If vertex pt is not in the polyhedron, neighbors are not added. More...

AXOM_HOST_DEVICE void	addNeighbors (int vtxId, std::initializer_list< std::int8_t > nbrs)
	Stores nbrs as the neighbors of vertex at a given index. More...

AXOM_HOST_DEVICE void	addNeighbors (int vtxId, int nbr)
	Adds a single nbr as the neighbor of vertex at a given index. More...

AXOM_HOST_DEVICE void	clear ()

Coords &	getVertices ()

AXOM_HOST_DEVICE PointType &	operator[] (int idx)

AXOM_HOST_DEVICE const PointType &	operator[] (int idx) const

AXOM_HOST_DEVICE Neighbors &	getNeighbors ()

AXOM_HOST_DEVICE int	getNumNeighbors (int i) const

AXOM_HOST_DEVICE Neighbors::VertexNbrs &	getNeighbors (int i)

AXOM_HOST_DEVICE const Neighbors::VertexNbrs &	getNeighbors (int i) const

AXOM_HOST_DEVICE PointType	vertexMean () const
	Computes the vertex mean as the average of the polyhedron's vertex positions. More...

AXOM_HOST_DEVICE void	getFaces (int faces, int face_size, int *face_offset, int &face_count) const
	Helper function to find the faces of the Polyhedron, assuming the vertex neighbors are in counter-clockwise ordering. More...

AXOM_HOST_DEVICE void	moments (double &volume, PointType &centroid, bool should_compute_centroid=true) const
	Computes the moments of the polyhedron. The 0th moment is the volume of the polyhedron, the 1st moment is the centroid. More...

AXOM_HOST_DEVICE double	signedVolume () const
	Computes the signed volume of the polyhedron. More...

AXOM_HOST_DEVICE double	volume () const
	Returns the absolute (unsigned) volume of the polyhedron. More...

AXOM_HOST_DEVICE PointType	centroid () const
	Computes the centroid as the center of mass of the polyhedron. More...

std::ostream &	print (std::ostream &os) const
	Simple formatted print of a polyhedron instance. More...

AXOM_HOST_DEVICE bool	isValid () const
	Simple check for validity of a polyhedron. More...

AXOM_HOST_DEVICE bool	hasDuplicateVertices (double eps=1.e-10) const
	Check if any vertices are duplicate, within a tolerance. More...

AXOM_HOST_DEVICE bool	hasNeighbors () const
	Check if vertex neighbors information is available. More...

Static Public Member Functions
static AXOM_HOST_DEVICE Polyhedron	from_primitive (const Hexahedron< T, NDIMS > &hex, bool tryFixOrientation=false)
	Creates a Polyhedron from a given Hexahedron's vertices. More...

static AXOM_HOST_DEVICE Polyhedron	from_primitive (const Octahedron< T, NDIMS > &oct, bool tryFixOrientation=false)
	Creates a Polyhedron from a given Octahedron's vertices. More...

static AXOM_HOST_DEVICE Polyhedron	from_primitive (const Tetrahedron< T, NDIMS > &tet, bool tryFixOrientation=false)
	Creates a Polyhedron from a given Tetrahedron's vertices. More...

Static Public Attributes
constexpr static int	MAX_VERTS = NeighborCollection::MAX_VERTS

Detailed Description

template<typename T, int NDIMS = 3>
class axom::primal::Polyhedron< T, NDIMS >

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)

Template Parameters

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

Note: The Polyhedron functions do not check that points defining a face are coplanar. It is the responsibility of the caller to pass a valid set of points and neighbors representing a convex polyhedron.; The polyhedron neighbors should be ordered counter clockwise as when viewing the polyhedron externally.


         3--------2          +y
        /|       /|
       / |      / |           ^
      7--------6  |           |
      |  0-----|--1           |
      | /      | /            -----> +x
      |/       |/            /
      4--------5            /
                           <
                          +z

For example, vertex 5 above should have neighbors (4,1,6).

Note: The Polyhedron functions do not check that neighbors are ordered counter clockwise. It is the responsibility of the caller to pass a valid neighbors ordering.

Member Typedef Documentation

◆ PointType

template<typename T , int NDIMS = 3>

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

◆ VectorType

template<typename T , int NDIMS = 3>

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

◆ NumArrayType

template<typename T , int NDIMS = 3>

using axom::primal::Polyhedron< T, NDIMS >::NumArrayType = NumericArray<T, NDIMS>

Constructor & Destructor Documentation

◆ Polyhedron()

template<typename T , int NDIMS = 3>

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

default

Default constructor for an empty polyhedron

Member Function Documentation

◆ numVertices()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE int axom::primal::Polyhedron< T, NDIMS >::numVertices ( ) const

inline

Return the number of vertices in the polyhedron

◆ addVertex()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE int axom::primal::Polyhedron< T, NDIMS >::addVertex ( const PointType & pt )

inline

Appends a vertex to the list of vertices.

Returns: The index where the vertex was inserted into.

References axom::primal::Polyhedron< T, NDIMS >::MAX_VERTS, and SLIC_ASSERT.

◆ addNeighbors() [1/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Polyhedron< T, NDIMS >::addNeighbors	(	const PointType &	pt,
		std::initializer_list< std::int8_t >	nbrs
	)

inline

Stores nbrs as the neighbors of vertex pt. If vertex pt is not in the polyhedron, neighbors are not added.

Note: pt should be a vertex of this polyhedron. Otherwise, pt may not be found due to floating point precision differences.

Parameters

[in]	pt	The vertex to add neighbors
[in]	nbrs	The neighbors to add to the list of neighbors

References axom::primal::NeighborCollection::addNeighbors().

◆ addNeighbors() [2/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Polyhedron< T, NDIMS >::addNeighbors	(	int	vtxId,
		std::initializer_list< std::int8_t >	nbrs
	)

inline

Stores nbrs as the neighbors of vertex at a given index.

Note: Caller is responsible for ensuring a given vertex has enough space remaining to fit the new neighbors.

Parameters

[in]	vtxId	The vertex id to add neighbors
[in]	nbrs	The neighbors to add to the list of neighbors

Precondition: vtxId < getVertices()

References axom::primal::NeighborCollection::addNeighbors().

◆ addNeighbors() [3/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Polyhedron< T, NDIMS >::addNeighbors	(	int	vtxId,
		int	nbr
	)

inline

Adds a single nbr as the neighbor of vertex at a given index.

Note: Caller is responsible for ensuring a given vertex has enough space remaining to fit the new neighbor.

Parameters

[in]	vtxId	The vertex id to add the neighbor
[in]	nbr	The neighbor to add to the list of neighbors

Precondition: vtxId < getVertices()

References axom::primal::NeighborCollection::addNeighbors().

◆ clear()

template<typename T , int NDIMS = 3>

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

inline

Clears the list of vertices and neighbors

References axom::primal::NeighborCollection::clear().

◆ getVertices()

template<typename T , int NDIMS = 3>

Coords& axom::primal::Polyhedron< T, NDIMS >::getVertices ( )

inline

Retrieves the vertices

◆ operator[]() [1/2]

template<typename T , int NDIMS = 3>

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

inline

Retrieves the vertex at index idx

◆ operator[]() [2/2]

template<typename T , int NDIMS = 3>

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

inline

Retrieves the vertex at index idx

◆ getNeighbors() [1/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE Neighbors& axom::primal::Polyhedron< T, NDIMS >::getNeighbors ( )

inline

Retrieves the neighbors

◆ getNumNeighbors()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE int axom::primal::Polyhedron< T, NDIMS >::getNumNeighbors ( int i ) const

inline

References axom::primal::NeighborCollection::getNumNeighbors().

◆ getNeighbors() [2/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE Neighbors::VertexNbrs& axom::primal::Polyhedron< T, NDIMS >::getNeighbors ( int i )

inline

Retrieves the neighbors for vertex i

◆ getNeighbors() [3/3]

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE const Neighbors::VertexNbrs& axom::primal::Polyhedron< T, NDIMS >::getNeighbors ( int i ) const

inline

Retrieves the neighbors for vertex i

◆ vertexMean()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE PointType axom::primal::Polyhedron< T, NDIMS >::vertexMean ( ) const

inline

Computes the vertex mean as the average of the polyhedron's vertex positions.

Returns: The vertex mean of the polyhedron's vertices

Precondition: polyhedron.isValid() is true

References axom::primal::Polyhedron< T, NDIMS >::isValid(), axom::primal::Polyhedron< T, NDIMS >::numVertices(), and SLIC_ASSERT.

◆ getFaces()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Polyhedron< T, NDIMS >::getFaces	(	int *	faces,
		int *	face_size,
		int *	face_offset,
		int &	face_count
	)		const

inline

Helper function to find the faces of the Polyhedron, assuming the vertex neighbors are in counter-clockwise ordering.

Parameters

[out]	faces	is the vertex indices for faces
[out]	face_offset	is the offset for each face
[out]	face_size	is the number of vertices for each face
[out]	face_count	is the number of faces

Warning: Function is experimental, input parameters and/or output may change in the future.

Note: This function does not check that the provided buffers are large enough to hold all values. It is the responsibility of the caller to know ahead of time and pass buffers with appropriate size.; Function is based off extractFaces() in Mike Owen's PolyClipper.

Precondition: polyhedron vertex neighbors are defined

References axom::primal::NeighborCollection::getNumNeighbors(), axom::primal::Polyhedron< T, NDIMS >::MAX_VERTS, and axom::primal::Polyhedron< T, NDIMS >::numVertices().

◆ moments()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE void axom::primal::Polyhedron< T, NDIMS >::moments	(	double &	volume,
		PointType &	centroid,
		bool	should_compute_centroid = `true`
	)		const

inline

Computes the moments of the polyhedron. The 0th moment is the volume of the polyhedron, the 1st moment is the centroid.

Parameters

[out]	volume	The volume of the polyhedron (0th moment)
[out]	centroid	The centroid of the polyhedron (1st moment)
[in]	should_compute_centroid	If true, computes the centroid of the polyhedron. Default is true.

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

Precondition: polyhedron vertex neighbors are defined, and polyhedron is 3D

See also: volume(); centroid()

References axom::primal::Polyhedron< T, NDIMS >::centroid(), axom::primal::Polyhedron< T, NDIMS >::getFaces(), axom::primal::Polyhedron< T, NDIMS >::hasDuplicateVertices(), axom::primal::Polyhedron< T, NDIMS >::hasNeighbors(), axom::primal::Polyhedron< T, NDIMS >::isValid(), axom::primal::Polyhedron< T, NDIMS >::MAX_VERTS, axom::primal::Vector< T, NDIMS >::scalar_triple_product(), SLIC_CHECK_MSG, and axom::primal::Polyhedron< T, NDIMS >::volume().

◆ signedVolume()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE double axom::primal::Polyhedron< T, NDIMS >::signedVolume ( ) const

inline

Computes the signed volume of the polyhedron.

Returns: The signed volume of the polyhedron

Precondition: polyhedron vertex neighbors are defined, and polyhedron is 3D

See also: volume()

References axom::primal::Polyhedron< T, NDIMS >::centroid(), axom::primal::Polyhedron< T, NDIMS >::moments(), and axom::primal::Polyhedron< T, NDIMS >::volume().

◆ volume()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE double axom::primal::Polyhedron< T, NDIMS >::volume ( ) const

inline

Returns the absolute (unsigned) volume of the polyhedron.

See also: signedVolume()

References axom::utilities::abs(), and axom::primal::Polyhedron< T, NDIMS >::signedVolume().

◆ centroid()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE PointType axom::primal::Polyhedron< T, NDIMS >::centroid ( ) const

inline

Computes the centroid as the center of mass of the polyhedron.

Returns: The centroid of the polyhedron

Precondition: polyhedron.isValid() is true

References axom::primal::Polyhedron< T, NDIMS >::moments(), and axom::primal::Polyhedron< T, NDIMS >::volume().

◆ print()

template<typename T , int NDIMS = 3>

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

inline

Simple formatted print of a polyhedron instance.

Parameters

os	The output stream to write to

Returns: A reference to the modified ostream

References axom::primal::Polyhedron< T, NDIMS >::getNeighbors(), axom::primal::NeighborCollection::getNumNeighbors(), axom::primal::Polyhedron< T, NDIMS >::hasNeighbors(), and axom::primal::Polyhedron< T, NDIMS >::numVertices().

◆ isValid()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE bool axom::primal::Polyhedron< T, NDIMS >::isValid ( ) const

inline

Simple check for validity of a polyhedron.

Initial check is that the polyhedron has four or more vertices

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

◆ hasDuplicateVertices()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE bool axom::primal::Polyhedron< T, NDIMS >::hasDuplicateVertices ( double eps = 1.e-10 ) const

inline

Check if any vertices are duplicate, within a tolerance.

Parameters

[in] eps The tolerance

Returns: True, if the polyhedron has duplicate vertices, False otherwise

References axom::utilities::isNearlyEqual().

◆ hasNeighbors()

template<typename T , int NDIMS = 3>

AXOM_HOST_DEVICE bool axom::primal::Polyhedron< T, NDIMS >::hasNeighbors ( ) const

inline

Check if vertex neighbors information is available.

Checks if neighbors is not empty

Returns: True, if the polyhedron has neighbors info for each vertex, False otherwise

References axom::primal::NeighborCollection::getNumNeighbors().

◆ from_primitive() [1/3]

template<typename T , int NDIMS = 3>

static AXOM_HOST_DEVICE Polyhedron axom::primal::Polyhedron< T, NDIMS >::from_primitive	(	const Hexahedron< T, NDIMS > &	hex,
		bool	tryFixOrientation = `false`
	)

inlinestatic

Creates a Polyhedron from a given Hexahedron's vertices.

Parameters

[in]	hex	The hexahedron
[in]	tryFixOrientation	If true, checks if the signed volume of the Polyhedron is negative and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A Polyhedron with the Hexahedron's vertices and added vertex neighbors

Note

The Hexahedron is assumed to have a specific vertex order:

*
*          4--------7          +z
*         /|       /|               +y
*        / |      / |           ^  >
*       5--------6  |           | /
*       |  0-----|--3           |/
*       | /      | /            -----> +x
*       |/       |/
*       1--------2
*
*

  The Polyhedron's vertex neighbors are created assuming this vertex
  ordering.

Warning: tryFixOrientation flag does not guarantee the Polyhedron's vertex order will be valid. It is the responsiblity of the caller to pass a Hexahedron with a valid vertex order. Otherwise, if the Hexahedron has an invalid vertex order, 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 axom::primal::Polyhedron< T, NDIMS >::addNeighbors(), axom::primal::Polyhedron< T, NDIMS >::addVertex(), and axom::primal::Polyhedron< T, NDIMS >::signedVolume().

◆ from_primitive() [2/3]

template<typename T , int NDIMS = 3>

static AXOM_HOST_DEVICE Polyhedron axom::primal::Polyhedron< T, NDIMS >::from_primitive	(	const Octahedron< T, NDIMS > &	oct,
		bool	tryFixOrientation = `false`
	)

inlinestatic

Creates a Polyhedron from a given Octahedron's vertices.

Parameters

[in]	oct	The octahedron
[in]	tryFixOrientation	If true, checks if the signed volume of the Polyhedron is negative and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A Polyhedron with the Octahedron's vertices and added vertex neighbors

Note: The Octahedron is assumed to have a specific vertex order: (view looking down from +z axis):

*
*            4                +z
*            /\                    +y
*       0 --/  \-- 2           ^  >
*         \/    \ /            | /
*         /      \             |/
*       5 -------- 3           -----> +x
*            \/
*            1
*
*

  The Polyhedron's vertex neighbors are created assuming this vertex
  ordering.

Warning: tryFixOrientation flag does not guarantee the Polyhedron's vertex order will be valid. It is the responsiblity of the caller to pass an Octahedron with a valid vertex order. Otherwise, if the Octahedron has an invalid vertex order, 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 axom::primal::Polyhedron< T, NDIMS >::addNeighbors(), axom::primal::Polyhedron< T, NDIMS >::addVertex(), and axom::primal::Polyhedron< T, NDIMS >::signedVolume().

◆ from_primitive() [3/3]

template<typename T , int NDIMS = 3>

static AXOM_HOST_DEVICE Polyhedron axom::primal::Polyhedron< T, NDIMS >::from_primitive	(	const Tetrahedron< T, NDIMS > &	tet,
		bool	tryFixOrientation = `false`
	)

inlinestatic

Creates a Polyhedron from a given Tetrahedron's vertices.

Parameters

[in]	tet	The tetrahedron
[in]	tryFixOrientation	If true, checks if the signed volume of the Polyhedron is negative and swaps the order of some vertices in that shape to try to obtain a nonnegative signed volume. Defaults to false.

Returns: A Polyhedron with the Tetrahedron's vertices and added vertex neighbors

Note

The Tetrahedron is assumed to have a specific vertex order:

*
*              3                    +z
*             / \\                       +y
*            /   \ \                 ^  >
*           /     \  \               | /
*          /       \   \             |/
*         /         \    2           -----> +x
*        /           \  /
*       /_____________\/
*      0               1
*
*

  The Polyhedron's vertex neighbors are created assuming this vertex
  ordering.

Warning: tryFixOrientation flag does not guarantee the Polyhedron's vertex order will be valid. It is the responsiblity of the caller to pass a Tetrahedron with a valid vertex order. Otherwise, if the Tetrahedron has an invalid vertex order, 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 axom::primal::Polyhedron< T, NDIMS >::addNeighbors(), axom::primal::Polyhedron< T, NDIMS >::addVertex(), and axom::primal::Tetrahedron< T, NDIMS >::signedVolume().

Member Data Documentation

◆ MAX_VERTS

template<typename T , int NDIMS = 3>

constexpr static int axom::primal::Polyhedron< T, NDIMS >::MAX_VERTS = NeighborCollection::MAX_VERTS

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/v0.10.1/src/axom/primal/geometry/Polyhedron.hpp

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Detailed Description

template<typename T, int NDIMS = 3> class axom::primal::Polyhedron< T, NDIMS >

Member Typedef Documentation

◆ PointType

◆ VectorType

◆ NumArrayType

Constructor & Destructor Documentation

◆ Polyhedron()

Member Function Documentation

◆ numVertices()

◆ addVertex()

◆ addNeighbors() [1/3]

◆ addNeighbors() [2/3]

◆ addNeighbors() [3/3]

◆ clear()

◆ getVertices()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ getNeighbors() [1/3]

◆ getNumNeighbors()

◆ getNeighbors() [2/3]

◆ getNeighbors() [3/3]

◆ vertexMean()

◆ getFaces()

◆ moments()

◆ signedVolume()

◆ volume()

◆ centroid()

◆ print()

◆ isValid()

◆ hasDuplicateVertices()

◆ hasNeighbors()

◆ from_primitive() [1/3]

◆ from_primitive() [2/3]

◆ from_primitive() [3/3]

Member Data Documentation

◆ MAX_VERTS

template<typename T, int NDIMS = 3>
class axom::primal::Polyhedron< T, NDIMS >