#include "common/DataTypes.hpp"
#include "common/DataLayouts.hpp"
#include "finiteElement/elementFormulations/H1_Hexahedron_Lagrange1_GaussLegendre2.hpp"
#include "finiteElement/elementFormulations/H1_Pyramid_Lagrange1_Gauss5.hpp"
#include "finiteElement/elementFormulations/H1_Tetrahedron_Lagrange1_Gauss.hpp"
#include "finiteElement/elementFormulations/H1_Wedge_Lagrange1_Gauss6.hpp"
#include "LvArray/src/output.hpp"
#include "LvArray/src/tensorOps.hpp"

Namespaces
	geos

Functions
template<typename LINEDIR_TYPE , typename POINT_TYPE , typename NORMAL_TYPE , typename ORIGIN_TYPE , typename INTPOINT_TYPE >
void	geos::computationalGeometry::LinePlaneIntersection (LINEDIR_TYPE const &lineDir, POINT_TYPE const &linePoint, NORMAL_TYPE const &planeNormal, ORIGIN_TYPE const &planeOrigin, INTPOINT_TYPE &intersectionPoint)
	Calculate the intersection between a line and a plane. More...

template<typename NORMAL_TYPE >
array1d< int >	geos::computationalGeometry::orderPointsCCW (arrayView2d< real64 > const &points, NORMAL_TYPE const &normal)
	Reorder a set of points counter-clockwise. More...

template<typename NORMAL_TYPE >
real64	geos::computationalGeometry::ComputeSurfaceArea (arrayView2d< real64 const > const &points, NORMAL_TYPE const &&normal)
	Calculate the area of a polygon given the set of points in ccw order defining it. More...

template<localIndex DIMENSION, typename POINT_COORDS_TYPE >
GEOS_HOST_DEVICE GEOS_FORCE_INLINE real64	geos::computationalGeometry::computeDiameter (POINT_COORDS_TYPE points, localIndex const &numPoints)
	Calculate the diameter of a set of points in a given dimension. More...

template<typename CENTER_TYPE , typename NORMAL_TYPE >
GEOS_HOST_DEVICE GEOS_FORCE_INLINE real64	geos::computationalGeometry::centroid_3DPolygon (arraySlice1d< localIndex const > const pointsIndices, arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &points, CENTER_TYPE &&center, NORMAL_TYPE &&normal, real64 const areaTolerance=0.0)
	Calculate the centroid of a convex 3D polygon as well as the normal and the rotation matrix. More...

template<typename NORMAL_TYPE >
GEOS_HOST_DEVICE void	geos::computationalGeometry::FixNormalOrientation_3D (NORMAL_TYPE &&normal)
	Change the orientation of the input vector to be consistent in a global sense. More...

template<typename NORMAL_TYPE , typename MATRIX_TYPE >
GEOS_HOST_DEVICE void	geos::computationalGeometry::RotationMatrix_3D (NORMAL_TYPE const &normal, MATRIX_TYPE &&rotationMatrix)
	Calculate the rotation matrix for a face in the 3D space. More...

template<typename T >
GEOS_HOST_DEVICE GEOS_FORCE_INLINE int	geos::computationalGeometry::sign (T const val)
	Return the sign of a given value as an integer. More...

template<typename POINT_TYPE >
GEOS_HOST_DEVICE bool	geos::computationalGeometry::isPointInsidePolyhedron (arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &nodeCoordinates, arraySlice1d< localIndex const > const &faceIndices, ArrayOfArraysView< localIndex const > const &facesToNodes, POINT_TYPE const &elemCenter, POINT_TYPE const &point, real64 const areaTolerance=0.0)
	Check if a point is inside a convex polyhedron (3D polygon) More...

template<typename POLYGON_TYPE , typename POINT_TYPE >
bool	geos::computationalGeometry::isPointInPolygon2d (POLYGON_TYPE const &polygon, integer n, POINT_TYPE const &point, real64 const tol=1e-10)
	Check if a point is inside a polygon (2D version) More...

template<typename POLYGON_TYPE , typename POINT_TYPE >
bool	geos::computationalGeometry::isPointInPolygon3d (POLYGON_TYPE const &polygon, integer const n, POINT_TYPE const &point, real64 const tol=1e-10)
	Check if a point is inside a polygon (3D version) More...

template<typename COORD_TYPE , typename POINT_TYPE >
GEOS_HOST_DEVICE int	geos::computationalGeometry::lexicographicalCompareVertex (POINT_TYPE const ax, POINT_TYPE const ay, POINT_TYPE const az, COORD_TYPE const bx, COORD_TYPE const by, COORD_TYPE const bz)
	Method to perform lexicographic comparison of two nodes based on coordinates. More...

template<typename COORD_TYPE , typename POINT_TYPE >
GEOS_HOST_DEVICE int	geos::computationalGeometry::lexicographicalCompareEdge (POINT_TYPE const ax, POINT_TYPE const ay, POINT_TYPE const az, COORD_TYPE const e1x, COORD_TYPE const e1y, COORD_TYPE const e1z, COORD_TYPE const e2x, COORD_TYPE const e2y, COORD_TYPE const e2z)
	Method to perform lexicographic comparison of a node and an edge based on coordinates. More...

template<typename COORD_TYPE , typename POINT_TYPE >
GEOS_HOST_DEVICE int	geos::computationalGeometry::lexicographicalCompareTriangle (POINT_TYPE const ax, POINT_TYPE const ay, POINT_TYPE const az, COORD_TYPE const t1x, COORD_TYPE const t1y, COORD_TYPE const t1z, COORD_TYPE const t2x, COORD_TYPE const t2y, COORD_TYPE const t2z, COORD_TYPE const t3x, COORD_TYPE const t3y, COORD_TYPE const t3z)
	Method to perform lexicographic comparison of a node and a triangle based on coordinates. More...

template<typename ... LIST_TYPE>
GEOS_HOST_DEVICE int	geos::computationalGeometry::findVertexRefElement (arraySlice1d< localIndex const > const &nodeElements, arrayView1d< globalIndex const > const &elementGlobalIndex)
	Method to find the reference element touching a vertex. The element with the lowest global ID is chosen from the list. More...

template<typename ... LIST_TYPE>
GEOS_HOST_DEVICE int	geos::computationalGeometry::findEdgeRefElement (arraySlice1d< localIndex const > const &nodeElements1, arraySlice1d< localIndex const > const &nodeElements2, arrayView1d< globalIndex const > const &elementGlobalIndex)
	Method to find the reference element for an edge. The element with the lowest global ID is chosen from the list. More...

template<typename ... LIST_TYPE>
GEOS_HOST_DEVICE int	geos::computationalGeometry::findTriangleRefElement (arraySlice1d< localIndex const > const &nodeElements1, arraySlice1d< localIndex const > const &nodeElements2, arraySlice1d< localIndex const > const &nodeElements3, arrayView1d< globalIndex const > const &elementGlobalIndex)
	Method to find the reference element for a triangle. The element with the lowest global ID is chosen from the list. More...

template<typename COORD_TYPE , typename POINT_TYPE >
GEOS_HOST_DEVICE bool	geos::computationalGeometry::computeWindingNumber (localIndex element, arrayView2d< COORD_TYPE const, nodes::REFERENCE_POSITION_USD > const &nodeCoordinates, arrayView2d< localIndex const > const &elementsToFaces, ArrayOfArraysView< localIndex const > const &facesToNodes, ArrayOfArraysView< localIndex const > const &nodesToElements, arrayView1d< globalIndex const > const &nodeLocalToGlobal, arrayView1d< globalIndex const > const &elementLocalToGlobal, POINT_TYPE const &elemCenter, POINT_TYPE const &point)
	Computes the winding number of a point with respect to a mesh element. More...

template<typename COORD_TYPE , typename POINT_TYPE >
GEOS_HOST_DEVICE bool	geos::computationalGeometry::isPointInsideConvexPolyhedronRobust (localIndex element, arrayView2d< COORD_TYPE const, nodes::REFERENCE_POSITION_USD > const &nodeCoordinates, arrayView2d< localIndex const > const &elementsToFaces, ArrayOfArraysView< localIndex const > const &facesToNodes, ArrayOfArraysView< localIndex const > const &nodesToElements, arrayView1d< globalIndex const > const &nodeLocalToGlobal, arrayView1d< globalIndex const > const &elementLocalToGlobal, POINT_TYPE const &elemCenter, POINT_TYPE const &point)
	Check if a point is inside a convex polyhedron (3D polygon), using a robust method to avoid ambiguity when the point lies on an interface. This method is based on the following method: More...

template<typename NODE_MAP_TYPE , typename VEC_TYPE >
GEOS_HOST_DEVICE void	geos::computationalGeometry::getBoundingBox (localIndex const elemIndex, NODE_MAP_TYPE const &pointIndices, arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &pointCoordinates, VEC_TYPE &&boxDims)
	Compute the dimensions of the bounding box containing the element defined here by the coordinates of its vertices. More...

template<typename FE_TYPE >
GEOS_HOST_DEVICE real64	geos::computationalGeometry::elementVolume (real64 const (&X)[FE_TYPE::numNodes][3])
	Compute the volume of an element (tetrahedron, pyramid, wedge, hexahedron) More...

GEOS_HOST_DEVICE real64	geos::computationalGeometry::hexahedronVolume (real64 const (&X)[8][3])
	Compute the volume of an hexahedron. More...

GEOS_HOST_DEVICE real64	geos::computationalGeometry::tetrahedronVolume (real64 const (&X)[4][3])
	Compute the volume of an tetrahedron. More...

GEOS_HOST_DEVICE real64	geos::computationalGeometry::wedgeVolume (real64 const (&X)[6][3])
	Compute the volume of a wedge. More...

GEOS_HOST_DEVICE real64	geos::computationalGeometry::pyramidVolume (real64 const (&X)[5][3])
	Compute the volume of a pyramid. More...

template<integer N>
GEOS_HOST_DEVICE real64	geos::computationalGeometry::prismVolume (real64 const (&X)[2 *N][3])
	Compute the volume of a prism with N-sided polygon base. More...

Variables
constexpr real64	geos::computationalGeometry::machinePrecision = LvArray::NumericLimits< real64 >::epsilon
	Machine epsilon for double-precision calculations.

Function Documentation

◆ centroid_3DPolygon()

template<typename CENTER_TYPE , typename NORMAL_TYPE >

GEOS_HOST_DEVICE GEOS_FORCE_INLINE real64 geos::computationalGeometry::centroid_3DPolygon	(	arraySlice1d< localIndex const > const	pointsIndices,
		arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &	points,
		CENTER_TYPE &&	center,
		NORMAL_TYPE &&	normal,
		real64 const	areaTolerance = `0.0`
	)

Calculate the centroid of a convex 3D polygon as well as the normal and the rotation matrix.

Template Parameters

CENTER_TYPE	The type of `center`.
NORMAL_TYPE	The type of `normal`.

Parameters

[in]	pointsIndices	list of index references for the points array in order (CW or CCW) about the polygon loop
[in]	points	3D point list
[out]	center	3D center of the given ordered polygon point list
[out]	normal	normal to the face
[in]	areaTolerance	tolerance used in the geometric computations

Returns: area of the convex 3D polygon

if area < - areaTolerance, this function will throw an error, and if (- areaTolerance <= area <= areaTolerance), the area is set to zero

Definition at line 234 of file ComputationalGeometry.hpp.

◆ computeDiameter()

template<localIndex DIMENSION, typename POINT_COORDS_TYPE >

GEOS_HOST_DEVICE GEOS_FORCE_INLINE real64 geos::computationalGeometry::computeDiameter	(	POINT_COORDS_TYPE	points,
		localIndex const &	numPoints
	)

Calculate the diameter of a set of points in a given dimension.

Template Parameters

DIMENSION	The dimensionality of the points.
POINT_COORDS_TYPE	The type of the container holding the point coordinates.

Parameters

[in]	points	The container holding the coordinates of the points.
[in]	numPoints	The number of points in the container.

Returns: The diameter of the set of points.

Definition at line 194 of file ComputationalGeometry.hpp.

◆ ComputeSurfaceArea()

template<typename NORMAL_TYPE >

real64 geos::computationalGeometry::ComputeSurfaceArea	(	arrayView2d< real64 const > const &	points,
		NORMAL_TYPE const &&	normal
	)

Calculate the area of a polygon given the set of points in ccw order defining it.

Template Parameters

NORMAL_TYPE the type of normal

Parameters

[in]	points	coordinates of the points
[in]	normal	vector normal to the plane

Returns: the area of the polygon

Definition at line 153 of file ComputationalGeometry.hpp.

◆ computeWindingNumber()

template<typename COORD_TYPE , typename POINT_TYPE >

GEOS_HOST_DEVICE bool geos::computationalGeometry::computeWindingNumber	(	localIndex	element,
		arrayView2d< COORD_TYPE const, nodes::REFERENCE_POSITION_USD > const &	nodeCoordinates,
		arrayView2d< localIndex const > const &	elementsToFaces,
		ArrayOfArraysView< localIndex const > const &	facesToNodes,
		ArrayOfArraysView< localIndex const > const &	nodesToElements,
		arrayView1d< globalIndex const > const &	nodeLocalToGlobal,
		arrayView1d< globalIndex const > const &	elementLocalToGlobal,
		POINT_TYPE const &	elemCenter,
		POINT_TYPE const &	point
	)

Computes the winding number of a point with respect to a mesh element.

Template Parameters

POINT_TYPE type of point

Parameters

[in]	element	the element to be checked
[in]	nodeCoordinates	a global array of nodal coordinates
[in]	elementsToFaces	map from elements to faces
[in]	facesToNodes	map from faces to nodes
[in]	nodesToElements	map from nodes to elements
[in]	nodeLocalToGlobal	global indices of nodes
[in]	elementLocalToGlobal	global indices of elements
[in]	elemCenter	coordinates of the element centroid
[in]	point	coordinates of the query point

Returns: the signed winding number, which is positive if and only if the point is inside the mesh element.

Definition at line 798 of file ComputationalGeometry.hpp.

◆ elementVolume()

template<typename FE_TYPE >

GEOS_HOST_DEVICE real64 geos::computationalGeometry::elementVolume ( real64 const (&) X[FE_TYPE::numNodes][3] )

inline

Compute the volume of an element (tetrahedron, pyramid, wedge, hexahedron)

Template Parameters

FE_TYPE the type of finite element space

Parameters

[in] X vertices of the element

Returns: the volume of the element

Definition at line 1018 of file ComputationalGeometry.hpp.

◆ findEdgeRefElement()

template<typename ... LIST_TYPE>

GEOS_HOST_DEVICE int geos::computationalGeometry::findEdgeRefElement	(	arraySlice1d< localIndex const > const &	nodeElements1,
		arraySlice1d< localIndex const > const &	nodeElements2,
		arrayView1d< globalIndex const > const &	elementGlobalIndex
	)

Method to find the reference element for an edge. The element with the lowest global ID is chosen from the list.

Parameters

[in]	nodeElements1	the list of elements adjacent to the first node
[in]	nodeElements2	the list of elements adjacent to the second node
[in]	elementGlobalIndex	the global IDs for elements

Returns: the element shared by the two nodes, with the minimal global index

Definition at line 716 of file ComputationalGeometry.hpp.

◆ findTriangleRefElement()

template<typename ... LIST_TYPE>

GEOS_HOST_DEVICE int geos::computationalGeometry::findTriangleRefElement	(	arraySlice1d< localIndex const > const &	nodeElements1,
		arraySlice1d< localIndex const > const &	nodeElements2,
		arraySlice1d< localIndex const > const &	nodeElements3,
		arrayView1d< globalIndex const > const &	elementGlobalIndex
	)

Method to find the reference element for a triangle. The element with the lowest global ID is chosen from the list.

Parameters

[in]	nodeElements1	the list of elements adjacent to the first node
[in]	nodeElements2	the list of elements adjacent to the second node
[in]	nodeElements3	the list of elements adjacent to the third node
[in]	elementGlobalIndex	the global IDs for elements

Returns: the element shared by the three nodes, with the minimal global index

Definition at line 752 of file ComputationalGeometry.hpp.

◆ findVertexRefElement()

template<typename ... LIST_TYPE>

GEOS_HOST_DEVICE int geos::computationalGeometry::findVertexRefElement	(	arraySlice1d< localIndex const > const &	nodeElements,
		arrayView1d< globalIndex const > const &	elementGlobalIndex
	)

Method to find the reference element touching a vertex. The element with the lowest global ID is chosen from the list.

Parameters

[in]	nodeElements	the list of elements adjacent to the vertex
[in]	elementGlobalIndex	the global IDs for elements

Returns: element touching the vertex with the least global index

Definition at line 689 of file ComputationalGeometry.hpp.

◆ FixNormalOrientation_3D()

template<typename NORMAL_TYPE >

GEOS_HOST_DEVICE void geos::computationalGeometry::FixNormalOrientation_3D ( NORMAL_TYPE && normal )

Change the orientation of the input vector to be consistent in a global sense.

Template Parameters

NORMAL_TYPE type of normal

Parameters

[in,out] normal normal to the face

Definition at line 294 of file ComputationalGeometry.hpp.

◆ getBoundingBox()

template<typename NODE_MAP_TYPE , typename VEC_TYPE >

GEOS_HOST_DEVICE void geos::computationalGeometry::getBoundingBox	(	localIndex const	elemIndex,
		NODE_MAP_TYPE const &	pointIndices,
		arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &	pointCoordinates,
		VEC_TYPE &&	boxDims
	)

Compute the dimensions of the bounding box containing the element defined here by the coordinates of its vertices.

Template Parameters

VEC_TYPE type of boxDims

Parameters

[in]	elemIndex	index of the element in pointIndices.
[in]	pointIndices	the indices of the vertices in pointCoordinates.
[in]	pointCoordinates	the vertices coordinates.
[out]	boxDims	The dimensions of the bounding box.

Definition at line 983 of file ComputationalGeometry.hpp.

◆ hexahedronVolume()

GEOS_HOST_DEVICE real64 geos::computationalGeometry::hexahedronVolume ( real64 const (&) X[8][3] )

inline

Compute the volume of an hexahedron.

Parameters

[in] X vertices of the hexahedron

Returns: the volume of the hexahedron

Definition at line 1035 of file ComputationalGeometry.hpp.

◆ isPointInPolygon2d()

template<typename POLYGON_TYPE , typename POINT_TYPE >

bool geos::computationalGeometry::isPointInPolygon2d	(	POLYGON_TYPE const &	polygon,
		integer	n,
		POINT_TYPE const &	point,
		real64 const	tol = `1e-10`
	)

Check if a point is inside a polygon (2D version)

Template Parameters

POLYGON_TYPE	type of `polygon`
POINT_TYPE	type of `point`

Parameters

[in]	polygon	array of polygon nodes coordinates
[in]	n	number of polygon nodes
[in]	point	coordinates of the query point
[in]	tol	tolerance for coordinate comparisons

Returns: whether the point is inside

Definition at line 447 of file ComputationalGeometry.hpp.

◆ isPointInPolygon3d()

template<typename POLYGON_TYPE , typename POINT_TYPE >

bool geos::computationalGeometry::isPointInPolygon3d	(	POLYGON_TYPE const &	polygon,
		integer const	n,
		POINT_TYPE const &	point,
		real64 const	tol = `1e-10`
	)

Check if a point is inside a polygon (3D version)

Template Parameters

POLYGON_TYPE	type of `polygon`
POINT_TYPE	type of `point`

Parameters

[in]	polygon	array of polygon nodes coordinates
[in]	n	number of polygon nodes
[in]	point	coordinates of the query point
[in]	tol	tolerance for coordinate comparisons

Returns: whether the point is inside

Definition at line 504 of file ComputationalGeometry.hpp.

◆ isPointInsideConvexPolyhedronRobust()

template<typename COORD_TYPE , typename POINT_TYPE >

GEOS_HOST_DEVICE bool geos::computationalGeometry::isPointInsideConvexPolyhedronRobust	(	localIndex	element,
		arrayView2d< COORD_TYPE const, nodes::REFERENCE_POSITION_USD > const &	nodeCoordinates,
		arrayView2d< localIndex const > const &	elementsToFaces,
		ArrayOfArraysView< localIndex const > const &	facesToNodes,
		ArrayOfArraysView< localIndex const > const &	nodesToElements,
		arrayView1d< globalIndex const > const &	nodeLocalToGlobal,
		arrayView1d< globalIndex const > const &	elementLocalToGlobal,
		POINT_TYPE const &	elemCenter,
		POINT_TYPE const &	point
	)

Check if a point is inside a convex polyhedron (3D polygon), using a robust method to avoid ambiguity when the point lies on an interface. This method is based on the following method:

the winding number omega of the point with respect to the cell is used to determine if the point is inside (omega=1) or not (omega=0)
corner cases (point lying on a face, edge or vertex of the cell) are detected using a robust method based on lexicographical comparisons
these comparisons are made consistent across MPI ranks by consistently arranging items based on global indices (GIDs). In particular:
- Faces are triangulated using the vertex with the smallest GID as root;
- Edges and faces are described by vertices in increasing GID order

Finally, if the point lies on a (vertex, edge, face), it is assigned to the first shared element with the least global index

Template Parameters

POINT_TYPE type of point

Parameters

[in]	element	the element to be checked
[in]	nodeCoordinates	a global array of nodal coordinates
[in]	elementsToFaces	map from elements to faces
[in]	facesToNodes	map from faces to nodes
[in]	nodesToElements	map from nodes to elements
[in]	nodeLocalToGlobal	global indices of nodes
[in]	elementLocalToGlobal	global indices of elements
[in]	elemCenter	coordinates of the element centroid
[in]	point	coordinates of the query point

Returns: whether the point is inside

Definition at line 959 of file ComputationalGeometry.hpp.

◆ isPointInsidePolyhedron()

template<typename POINT_TYPE >

GEOS_HOST_DEVICE bool geos::computationalGeometry::isPointInsidePolyhedron	(	arrayView2d< real64 const, nodes::REFERENCE_POSITION_USD > const &	nodeCoordinates,
		arraySlice1d< localIndex const > const &	faceIndices,
		ArrayOfArraysView< localIndex const > const &	facesToNodes,
		POINT_TYPE const &	elemCenter,
		POINT_TYPE const &	point,
		real64 const	areaTolerance = `0.0`
	)

Check if a point is inside a convex polyhedron (3D polygon)

Template Parameters

POINT_TYPE type of point

Parameters

[in]	nodeCoordinates	a global array of nodal coordinates
[in]	faceIndices	global indices of the faces of the cell
[in]	facesToNodes	map from face to nodes
[in]	elemCenter	coordinates of the element center
[in]	point	coordinates of the query point
[in]	areaTolerance	same as in centroid_3DPolygon

Returns: whether the point is inside

Note: For faces with n>3 nodes that are non-planar, average normal is used

Definition at line 399 of file ComputationalGeometry.hpp.

◆ lexicographicalCompareEdge()

template<typename COORD_TYPE , typename POINT_TYPE >

GEOS_HOST_DEVICE int geos::computationalGeometry::lexicographicalCompareEdge	(	POINT_TYPE const	ax,
		POINT_TYPE const	ay,
		POINT_TYPE const	az,
		COORD_TYPE const	e1x,
		COORD_TYPE const	e1y,
		COORD_TYPE const	e1z,
		COORD_TYPE const	e2x,
		COORD_TYPE const	e2y,
		COORD_TYPE const	e2z
	)

Method to perform lexicographic comparison of a node and an edge based on coordinates.

Template Parameters

COORD_TYPE	type of coordinate
POINT_TYPE	type of point

Parameters

[in]	ax	x-coordinate of the first vertex
[in]	ay	y-coordinate of the first vertex
[in]	az	z-coordinate of the first vertex
[in]	e1x	x-coordinate of the first edge vertex
[in]	e1y	y-coordinate of the first edge vertex
[in]	e1z	z-coordinate of the first edge vertex
[in]	e2x	x-coordinate of the second edge vertex
[in]	e2y	y-coordinate of the second edge vertex
[in]	e2z	z-coordinate of the second edge vertex

Returns: 0 if the vertices lies on the edge, +1 if e > a and -1 if a > e

Definition at line 625 of file ComputationalGeometry.hpp.

◆ lexicographicalCompareTriangle()

template<typename COORD_TYPE , typename POINT_TYPE >

GEOS_HOST_DEVICE int geos::computationalGeometry::lexicographicalCompareTriangle	(	POINT_TYPE const	ax,
		POINT_TYPE const	ay,
		POINT_TYPE const	az,
		COORD_TYPE const	t1x,
		COORD_TYPE const	t1y,
		COORD_TYPE const	t1z,
		COORD_TYPE const	t2x,
		COORD_TYPE const	t2y,
		COORD_TYPE const	t2z,
		COORD_TYPE const	t3x,
		COORD_TYPE const	t3y,
		COORD_TYPE const	t3z
	)

Method to perform lexicographic comparison of a node and a triangle based on coordinates.

Template Parameters

COORD_TYPE	type of coordinate
POINT_TYPE	type of point

Parameters

[in]	ax	x-coordinate of the first vertex
[in]	ay	y-coordinate of the first vertex
[in]	az	z-coordinate of the first vertex
[in]	t1x	x-coordinate of the first triangle vertex
[in]	t1y	y-coordinate of the first triangle vertex
[in]	t1z	z-coordinate of the first triangle vertex
[in]	t2x	x-coordinate of the second triangle vertex
[in]	t2y	y-coordinate of the second triangle vertex
[in]	t2z	z-coordinate of the second triangle vertex
[in]	t3x	x-coordinate of the third triangle vertex
[in]	t3y	y-coordinate of the third triangle vertex
[in]	t3z	z-coordinate of the third triangle vertex

Returns: 0 if the vertices lies on the triangle, +1 if t > a and -1 if t > e

Definition at line 657 of file ComputationalGeometry.hpp.

◆ lexicographicalCompareVertex()

template<typename COORD_TYPE , typename POINT_TYPE >

GEOS_HOST_DEVICE int geos::computationalGeometry::lexicographicalCompareVertex	(	POINT_TYPE const	ax,
		POINT_TYPE const	ay,
		POINT_TYPE const	az,
		COORD_TYPE const	bx,
		COORD_TYPE const	by,
		COORD_TYPE const	bz
	)

Method to perform lexicographic comparison of two nodes based on coordinates.

Template Parameters

COORD_TYPE	type of coordinate
POINT_TYPE	type of point

Parameters

[in]	ax	x-coordinate of the first vertex
[in]	ay	y-coordinate of the first vertex
[in]	az	z-coordinate of the first vertex
[in]	bx	x-coordinate of the second vertex
[in]	by	y-coordinate of the second vertex
[in]	bz	z-coordinate of the second vertex

Returns: 0 if the vertices coincide, +1 if a > b and -1 if b > a

Definition at line 590 of file ComputationalGeometry.hpp.

◆ LinePlaneIntersection()

template<typename LINEDIR_TYPE , typename POINT_TYPE , typename NORMAL_TYPE , typename ORIGIN_TYPE , typename INTPOINT_TYPE >

void geos::computationalGeometry::LinePlaneIntersection	(	LINEDIR_TYPE const &	lineDir,
		POINT_TYPE const &	linePoint,
		NORMAL_TYPE const &	planeNormal,
		ORIGIN_TYPE const &	planeOrigin,
		INTPOINT_TYPE &	intersectionPoint
	)

Calculate the intersection between a line and a plane.

Template Parameters

LINEDIR_TYPE	the type of `lineDir`
POINT_TYPE	the type of `linePoint`
NORMAL_TYPE	the type of `planeNormal`
ORIGIN_TYPE	the type of `planeOrigin`
INTPOINT_TYPE	the type of `instersectionPoint`

Parameters

[in]	lineDir	vector defining direction of the line
[in]	linePoint	one point of the line
[in]	planeNormal	normal to plane
[in]	planeOrigin	plane origin
[out]	intersectionPoint	the intersection point

Definition at line 58 of file ComputationalGeometry.hpp.

◆ orderPointsCCW()

template<typename NORMAL_TYPE >

array1d< int > geos::computationalGeometry::orderPointsCCW	(	arrayView2d< real64 > const &	points,
		NORMAL_TYPE const &	normal
	)

Reorder a set of points counter-clockwise.

Template Parameters

NORMAL_TYPE the type of normal

Parameters

[in]	points	coordinates of the points
[in]	normal	vector normal to the plane

Returns: an stdVector containing the original indices of the reordered points.

Definition at line 87 of file ComputationalGeometry.hpp.

◆ prismVolume()

template<integer N>

GEOS_HOST_DEVICE real64 geos::computationalGeometry::prismVolume ( real64 const (&) X[2 *N][3] )

inline

Compute the volume of a prism with N-sided polygon base.

Template Parameters

N	the number of sides in the polygon base

Parameters

[in] X vertices of the prism

Returns: the volume of the prism

Note: The volume is computed splitting the prism into wedges. The function can be called only for N > 5. For N = 3 and N = 4 function wedgeVolume and hexahedronVolume, respectively, should be used.

Definition at line 1089 of file ComputationalGeometry.hpp.

◆ pyramidVolume()

GEOS_HOST_DEVICE real64 geos::computationalGeometry::pyramidVolume ( real64 const (&) X[5][3] )

inline

Compute the volume of a pyramid.

Parameters

[in] X vertices of the pyramid

Returns: the volume of the pyramid

Definition at line 1071 of file ComputationalGeometry.hpp.

◆ RotationMatrix_3D()

template<typename NORMAL_TYPE , typename MATRIX_TYPE >

GEOS_HOST_DEVICE void geos::computationalGeometry::RotationMatrix_3D	(	NORMAL_TYPE const &	normal,
		MATRIX_TYPE &&	rotationMatrix
	)

Calculate the rotation matrix for a face in the 3D space.

Template Parameters

NORMAL_TYPE	type of `normal`
MATRIX_TYPE	type of `rotationMatrix`

Parameters

[in]	normal	normal to the face
[out]	rotationMatrix	rotation matrix for the face

Definition at line 331 of file ComputationalGeometry.hpp.

◆ sign()

template<typename T >

GEOS_HOST_DEVICE GEOS_FORCE_INLINE int geos::computationalGeometry::sign ( T const val )

Return the sign of a given value as an integer.

Template Parameters

T	type of value

Parameters

val	the value in question

Returns: -1, 0 or 1 depending on whether the value is negative, zero or positive

Definition at line 379 of file ComputationalGeometry.hpp.

◆ tetrahedronVolume()

GEOS_HOST_DEVICE real64 geos::computationalGeometry::tetrahedronVolume ( real64 const (&) X[4][3] )

inline

Compute the volume of an tetrahedron.

Parameters

[in] X vertices of the tetrahedron

Returns: the volume of the tetrahedron

Definition at line 1047 of file ComputationalGeometry.hpp.

◆ wedgeVolume()

GEOS_HOST_DEVICE real64 geos::computationalGeometry::wedgeVolume ( real64 const (&) X[6][3] )

inline

Compute the volume of a wedge.

Parameters

[in] X vertices of the wedge

Returns: the volume of the wedge

Definition at line 1059 of file ComputationalGeometry.hpp.

Namespaces

Functions

Variables

Function Documentation

◆ centroid_3DPolygon()

◆ computeDiameter()

◆ ComputeSurfaceArea()

◆ computeWindingNumber()

◆ elementVolume()

◆ findEdgeRefElement()

◆ findTriangleRefElement()

◆ findVertexRefElement()

◆ FixNormalOrientation_3D()

◆ getBoundingBox()

◆ hexahedronVolume()

◆ isPointInPolygon2d()

◆ isPointInPolygon3d()

◆ isPointInsideConvexPolyhedronRobust()

◆ isPointInsidePolyhedron()

◆ lexicographicalCompareEdge()

◆ lexicographicalCompareTriangle()

◆ lexicographicalCompareVertex()

◆ LinePlaneIntersection()

◆ orderPointsCCW()

◆ prismVolume()

◆ pyramidVolume()

◆ RotationMatrix_3D()

◆ sign()

◆ tetrahedronVolume()

◆ wedgeVolume()