A class for incremental generation of a 2D or 3D Delaunay triangulation. More...

#include </home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/latest/src/axom/quest/Delaunay.hpp>

Inheritance diagram for axom::quest::Delaunay< DIM >:

Public Types
using	DataType = double

using	PointType = primal::Point< DataType, DIM >

using	ElementType = typename std::conditional< DIM==2, primal::Triangle< DataType, 2 >, primal::Tetrahedron< DataType, 3 > >::type

using	BaryCoordType = primal::Point< DataType, DIM+1 >

using	BoundingBox = primal::BoundingBox< DataType, DIM >

using	IAMeshType = slam::IAMesh< DIM, DIM, PointType >

using	IndexType = typename IAMeshType::IndexType

using	IndexArray = typename IAMeshType::IndexArray

using	IndexPairType = std::pair< IndexType, IndexType >

Public Member Functions
	AXOM_STATIC_ASSERT_MSG (DIM==2\|\|DIM==3, "The template parameter DIM can only be 2 or 3. ")

	Delaunay ()
	Default constructor. More...

void	initializeBoundary (const BoundingBox &bb)
	Defines the boundary of the triangulation. More...

void	insertPoint (const PointType &new_pt)
	Adds a new point and locally re-triangulates the mesh to ensure that it stays Delaunay. More...

template<int TDIM = DIM>
std::enable_if< TDIM==2, ElementType >::type	getElement (int element_index) const

template<int TDIM = DIM>
std::enable_if< TDIM==3, ElementType >::type	getElement (int element_index) const

void	printMesh ()
	Prints out mesh details, for debugging purpose. More...

void	writeToVTKFile (const std::string &filename)
	Write the m_mesh to a legacy VTK file. More...

void	removeBoundary ()
	Removes the vertices that defines the boundary of the mesh, and the elements attached to them. More...

const IAMeshType *	getMeshData () const
	Get the IA mesh data pointer. More...

bool	isValid (bool verboseOutput=false) const
	Checks that the underlying mesh is a valid Delaunay triangulation of the point set. More...

IndexType	findContainingElement (const PointType &query_pt, bool warnOnInvalid=true) const
	Find the index of the element that contains the query point, or the element closest to the point. More...

BaryCoordType	getBaryCoords (IndexType element_idx, const PointType &q_pt) const
	helper function to retrieve the barycentric coordinate of the query point in the element More...

Delaunay< 2 >::BaryCoordType	getBaryCoords (IndexType element_idx, const PointType &query_pt) const

Delaunay< 3 >::BaryCoordType	getBaryCoords (IndexType element_idx, const PointType &query_pt) const

Static Public Attributes
static constexpr int	VERT_PER_ELEMENT = DIM + 1

static constexpr IndexType	INVALID_INDEX = -1

Detailed Description

template<int DIM = 2>
class axom::quest::Delaunay< DIM >

A class for incremental generation of a 2D or 3D Delaunay triangulation.

Construct a Delaunay triangulation incrementally by inserting points one by one. A bounding box of the points needs to be defined first via initializeBoundary(...)

Member Typedef Documentation

◆ DataType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::DataType = double

◆ PointType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::PointType = primal::Point<DataType, DIM>

◆ ElementType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::ElementType = typename std::conditional<DIM == 2, primal::Triangle<DataType, 2>, primal::Tetrahedron<DataType, 3> >::type

◆ BaryCoordType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::BaryCoordType = primal::Point<DataType, DIM + 1>

◆ BoundingBox

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::BoundingBox = primal::BoundingBox<DataType, DIM>

◆ IAMeshType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::IAMeshType = slam::IAMesh<DIM, DIM, PointType>

◆ IndexType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::IndexType = typename IAMeshType::IndexType

◆ IndexArray

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::IndexArray = typename IAMeshType::IndexArray

◆ IndexPairType

template<int DIM = 2>

using axom::quest::Delaunay< DIM >::IndexPairType = std::pair<IndexType, IndexType>

Constructor & Destructor Documentation

◆ Delaunay()

template<int DIM = 2>

axom::quest::Delaunay< DIM >::Delaunay ( )

inline

Default constructor.

Note: User must call initializeBoundary(BoundingBox) before adding points.

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG()

template<int DIM = 2>

axom::quest::Delaunay< DIM >::AXOM_STATIC_ASSERT_MSG	(	DIM	= `=2\|\|DIM==3`,
		"The template parameter DIM can only be 2 or 3. "
	)

◆ initializeBoundary()

template<int DIM = 2>

void axom::quest::Delaunay< DIM >::initializeBoundary ( const BoundingBox & bb )

inline

Defines the boundary of the triangulation.

subsequent points added to the triangulation must not be outside of this boundary.

◆ insertPoint()

template<int DIM = 2>

void axom::quest::Delaunay< DIM >::insertPoint ( const PointType & new_pt )

inline

Adds a new point and locally re-triangulates the mesh to ensure that it stays Delaunay.

This function will traverse the mesh to find the element that contains this point, creates the Delaunay cavity, which takes out all the elements that contains the point in its sphere, and fill it with a Delaunay ball.

Precondition: The current mesh must already be Delaunay.

References axom::primal::BoundingBox< T, NDIMS >::contains(), axom::quest::Delaunay< DIM >::findContainingElement(), axom::quest::Delaunay< DIM >::INVALID_INDEX, SLIC_ASSERT_MSG, and SLIC_WARNING.

◆ getElement() [1/2]

template<int DIM = 2>

template<int TDIM = DIM>

std::enable_if<TDIM == 2, ElementType>::type axom::quest::Delaunay< DIM >::getElement ( int element_index ) const

inline

◆ getElement() [2/2]

template<int DIM = 2>

template<int TDIM = DIM>

std::enable_if<TDIM == 3, ElementType>::type axom::quest::Delaunay< DIM >::getElement ( int element_index ) const

inline

◆ printMesh()

template<int DIM = 2>

void axom::quest::Delaunay< DIM >::printMesh ( )

inline

Prints out mesh details, for debugging purpose.

◆ writeToVTKFile()

template<int DIM = 2>

void axom::quest::Delaunay< DIM >::writeToVTKFile ( const std::string & filename )

inline

Write the m_mesh to a legacy VTK file.

Parameters

filename The name of the file to write to,

Note: The suffix ".vtk" will be appended to the provided filename

This function uses mint to write the m_mesh to VTK format.

References axom::mint::UnstructuredMesh< TOPO >::appendCell(), axom::mint::UnstructuredMesh< TOPO >::appendNodes(), axom::mint::TET, axom::mint::TRIANGLE, and axom::mint::write_vtk().

◆ removeBoundary()

template<int DIM = 2>

void axom::quest::Delaunay< DIM >::removeBoundary ( )

inline

Removes the vertices that defines the boundary of the mesh, and the elements attached to them.

After this function is called, no more points can be added to the m_mesh.

◆ getMeshData()

template<int DIM = 2>

const IAMeshType* axom::quest::Delaunay< DIM >::getMeshData ( ) const

inline

Get the IA mesh data pointer.

◆ isValid()

template<int DIM = 2>

bool axom::quest::Delaunay< DIM >::isValid ( bool verboseOutput = false ) const

inline

Checks that the underlying mesh is a valid Delaunay triangulation of the point set.

A Delaunay triangulation is valid when none of the vertices are inside the circumspheres of any of the elements of the mesh

References axom::primal::BoundingBox< T, NDIMS >::addPoint(), axom::utilities::ceil(), axom::numerics::dot_product(), axom::quest::Delaunay< DIM >::getElement(), axom::primal::ON_NEGATIVE_SIDE, and SLIC_INFO.

◆ findContainingElement()

template<int DIM = 2>

IndexType axom::quest::Delaunay< DIM >::findContainingElement	(	const PointType &	query_pt,
		bool	warnOnInvalid = `true`
	)		const

inline

Find the index of the element that contains the query point, or the element closest to the point.

References axom::primal::NumericArray< T, SIZE >::argMin(), axom::primal::Point< T, NDIMS >::array(), axom::primal::BoundingBox< T, NDIMS >::contains(), axom::quest::Delaunay< DIM >::getBaryCoords(), axom::quest::Delaunay< DIM >::INVALID_INDEX, SLIC_ASSERT, SLIC_ERROR_IF, and SLIC_WARNING_IF.

◆ getBaryCoords() [1/3]

template<int DIM = 2>

BaryCoordType axom::quest::Delaunay< DIM >::getBaryCoords	(	IndexType	element_idx,
		const PointType &	q_pt
	)		const

helper function to retrieve the barycentric coordinate of the query point in the element

◆ getBaryCoords() [2/3]

Delaunay< 2 >::BaryCoordType axom::quest::Delaunay< 2 >::getBaryCoords	(	IndexType	element_idx,
		const PointType &	query_pt
	)		const

inline

◆ getBaryCoords() [3/3]

Delaunay< 3 >::BaryCoordType axom::quest::Delaunay< 3 >::getBaryCoords	(	IndexType	element_idx,
		const PointType &	query_pt
	)		const

inline

Member Data Documentation

◆ VERT_PER_ELEMENT

template<int DIM = 2>

constexpr int axom::quest::Delaunay< DIM >::VERT_PER_ELEMENT = DIM + 1

staticconstexpr

◆ INVALID_INDEX

template<int DIM>

constexpr Delaunay< DIM >::IndexType axom::quest::Delaunay< DIM >::INVALID_INDEX = -1

staticconstexpr

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

/home/docs/checkouts/readthedocs.org/user_builds/axom/checkouts/latest/src/axom/quest/Delaunay.hpp

Public Types

Public Member Functions

Static Public Attributes

Detailed Description

template<int DIM = 2> class axom::quest::Delaunay< DIM >

Member Typedef Documentation

◆ DataType

◆ PointType

◆ ElementType

◆ BaryCoordType

◆ BoundingBox

◆ IAMeshType

◆ IndexType

◆ IndexArray

◆ IndexPairType

Constructor & Destructor Documentation

◆ Delaunay()

Member Function Documentation

◆ AXOM_STATIC_ASSERT_MSG()

◆ initializeBoundary()

◆ insertPoint()

◆ getElement() [1/2]

◆ getElement() [2/2]

◆ printMesh()

◆ writeToVTKFile()

◆ removeBoundary()

◆ getMeshData()

◆ isValid()

◆ findContainingElement()

◆ getBaryCoords() [1/3]

◆ getBaryCoords() [2/3]

◆ getBaryCoords() [3/3]

Member Data Documentation

◆ VERT_PER_ELEMENT

◆ INVALID_INDEX

template<int DIM = 2>
class axom::quest::Delaunay< DIM >