Typedefs
using	Point1D = std::array< double, 1 >

using	Point2D = std::array< double, 2 >

using	Point3D = std::array< double, 3 >

Functions
std::vector< int >	assignRanks (const std::vector< double > &x, int N_ranks)
	Assign ranks to a point cloud.

std::vector< int >	assignRanks (const std::vector< Point1D > &x, int N_ranks)
	Assign ranks to a point cloud.

std::vector< int >	assignRanks (const std::vector< Point2D > &x, int N_ranks)
	Assign ranks to a point cloud.

std::vector< int >	assignRanks (const std::vector< Point3D > &x, int N_ranks)
	Assign ranks to a point cloud.

template<int NP, int NDIM>
std::array< double, NP >	barycentric (const std::array< std::array< double, NDIM >, NP > &x, const std::array< double, NDIM > &p)
	Compute the barycentric coordinates.

double	distance (const Point3D &x1, const Point3D &x2)
	Compute the distance between two points.

template<std::size_t NDIM>
double	distanceToBox (const std::array< double, NDIM > &pos, const std::array< double, NDIM > &ang, const std::array< double, NDIM > &lb, const std::array< double, NDIM > &ub)
	Compute the intersection of a ray and a box.

double	distanceToCircle (double r, const Point2D &pos, const Point2D &ang)
	Compute the intersection of a ray and circle (2D)

double	distanceToCircularFrustum (double rb, double rt, double h, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and circular frustum.

double	distanceToCone (const Point3D &V, double theta, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and cone.

double	distanceToCylinder (double r, double h, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and cylinder.

double	distanceToLine (const Point2D &pos, const Point2D &ang, const Point2D &v1, const Point2D &v2)
	Compute the intersection of a ray and a line segment.

double	distanceToLine (const Point3D &pos, const Point3D &ang, const Point3D &v1, const Point3D &v2)
	Compute the intersection of a ray and a line segment.

double	distanceToPlane (const Point3D &n, const Point3D &p0, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and an infinite plane.

double	distanceToQuadrilateral (const std::array< Point2D, 4 > &quad, const Point2D &pos, const Point2D &ang)
	Compute the intersection of a ray and quadrilateral.

double	distanceToQuadrilateral (const std::array< Point3D, 4 > &quad, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and quadrilateral.

double	distanceToSphere (double r, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and sphere.

double	distanceToTetrahedron (const std::array< Point3D, 4 > &tet, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and tetrahedron.

double	distanceToTriangle (const std::array< Point2D, 3 > &tri, const Point2D &pos, const Point2D &ang)
	Compute the intersection of a ray and triangle.

double	distanceToTriangle (const std::array< Point3D, 3 > &tri, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and triangle.

double	distanceToTube (double r1, double r2, double h, const Point3D &pos, const Point3D &ang)
	Compute the intersection of a ray and tube.

std::vector< Point2D >	get_poly_vertices (int N, double R)
	Get the Vertices of a regular polygon.

Point2D	map_circle_logical (double R, int method, double x, double y)
	Map physical coordinates to the logical coordinates.

Point2D	map_logical_circle (double R, int method, double x, double y)
	Map logical coordinates to a circle.

Point2D	map_logical_poly (int N, double R, double x, double y)
	Map logical coordinates to a regular polygon.

Point3D	map_logical_shell (double r1, double r2, double x, double y, double z)
	Map logical coordinates to a shell.

Point3D	map_logical_sphere (double R, double x, double y, double z)
	Map logical coordinates to a sphere.

Point3D	map_logical_sphere_surface (int method, double R, double x, double y)
	Map logical coordinates to the surface of a sphere.

Point2D	map_poly_logical (int N, double R, double x, double y)
	Map physical coordinates to the logical coordinates.

Point3D	map_shell_logical (double r1, double r2, double x, double y, double z)
	Map a shell to logical coordinates.

Point3D	map_sphere_logical (double R, double x, double y, double z)
	Map logical coordinates to a sphere.

Point2D	map_sphere_surface_logical (int method, double R, double x, double y, double z)
	Map coordinates from the surface of a sphere to logical.

Point2D	nearest (const Point2D &v1, const Point2D &v2, const Point2D &p)
	Find the nearest point to a line segment.

Point3D	nearest (const Point3D &v1, const Point3D &v2, const Point3D &p)
	Find the nearest point to a line segment.

Point3D	nearest (const std::array< Point3D, 3 > &v, const Point3D &p)
	Find the nearest point to a triangle.

Point3D	nearest (const std::array< Point3D, 4 > &v, const Point3D &p)
	Find the nearest point to a tetrahedron.

Point2D	normal (const Point2D &a, const Point2D &b)
	Compute the normal to a line defined by 2 points.

Point3D	normal (const Point3D &a, const Point3D &b, const Point3D &c)
	Compute the normal to a plane defined by 3 points.

Point3D	normalToQuadrilateral (const std::array< Point3D, 4 > &quad)
	Compute the normal to a quadrilateral.

std::vector< Point3D >	sampleLine (const std::array< Point3D, 2 > &v, double d0, bool interior=true)
	Sample a line.

std::vector< Point3D >	sampleQuad (const std::array< Point3D, 4 > &v, double d0, bool interior=true)
	Sample a line.

std::vector< Point3D >	sampleTet (const std::array< Point3D, 4 > &v, double d0, bool interior=true)
	Sample a line.

std::vector< Point3D >	sampleTri (const std::array< Point3D, 3 > &v, double d0, bool interior=true)
	Sample a line.

std::vector< AMP::Mesh::Point >	subdivide (const std::array< AMP::Mesh::Point, 3 > &v, double res)
	Subdivide a triangle.

Typedef Documentation

◆ Point1D

using AMP::Geometry::GeometryHelpers::Point1D = typedef std::array<double, 1>

Definition at line 17 of file GeometryHelpers.h.

◆ Point2D

using AMP::Geometry::GeometryHelpers::Point2D = typedef std::array<double, 2>

Definition at line 18 of file GeometryHelpers.h.

◆ Point3D

using AMP::Geometry::GeometryHelpers::Point3D = typedef std::array<double, 3>

Definition at line 19 of file GeometryHelpers.h.

Function Documentation

◆ assignRanks() [1/4]

std::vector< int > AMP::Geometry::GeometryHelpers::assignRanks	(	const std::vector< double > &	x,
		int	N_ranks
	)

Assign ranks to a point cloud.

This routine will divide a point cloud spatially and assign ranks to a point cloud.

Parameters

[in]	x	Points
[in]	N_ranks	Number of processors

Returns: Returns the rank of each point

◆ assignRanks() [2/4]

std::vector< int > AMP::Geometry::GeometryHelpers::assignRanks	(	const std::vector< Point1D > &	x,
		int	N_ranks
	)

Assign ranks to a point cloud.

This routine will divide a point cloud spatially and assign ranks to a point cloud.

Parameters

[in]	x	Points
[in]	N_ranks	Number of processors

Returns: Returns the rank of each point

◆ assignRanks() [3/4]

std::vector< int > AMP::Geometry::GeometryHelpers::assignRanks	(	const std::vector< Point2D > &	x,
		int	N_ranks
	)

Assign ranks to a point cloud.

This routine will divide a point cloud spatially and assign ranks to a point cloud.

Parameters

[in]	x	Points
[in]	N_ranks	Number of processors

Returns: Returns the rank of each point

◆ assignRanks() [4/4]

std::vector< int > AMP::Geometry::GeometryHelpers::assignRanks	(	const std::vector< Point3D > &	x,
		int	N_ranks
	)

Assign ranks to a point cloud.

This routine will divide a point cloud spatially and assign ranks to a point cloud.

Parameters

[in]	x	Points
[in]	N_ranks	Number of processors

Returns: Returns the rank of each point

◆ barycentric()

template<int NP, int NDIM>

std::array< double, NP > AMP::Geometry::GeometryHelpers::barycentric	(	const std::array< std::array< double, NDIM >, NP > &	x,
		const std::array< double, NDIM > &	p
	)

Compute the barycentric coordinates.

This function will compute the barycentric coordinates determine the normal.

Parameters

[in]	x	Vertices
[in]	p	Point of interest

Returns: Returns the barycentric coordinates

◆ distance()

double AMP::Geometry::GeometryHelpers::distance	(	const Point3D &	x1,
		const Point3D &	x2
	)

Compute the distance between two points.

This function will compute the distance between two points

Parameters

[in]	x1	First point
[in]	x2	Second point

Returns: Returns the distance

◆ distanceToBox()

template<std::size_t NDIM>

double AMP::Geometry::GeometryHelpers::distanceToBox	(	const std::array< double, NDIM > &	pos,
		const std::array< double, NDIM > &	ang,
		const std::array< double, NDIM > &	lb,
		const std::array< double, NDIM > &	ub
	)

Compute the intersection of a ray and a box.

This function will compute the intersection of a ray with a box. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	pos	Starting point of ray
[in]	ang	Direction of ray
[in]	lb	Lower bound of the box
[in]	ub	Upper bound of the box

Returns: Returns the distance

◆ distanceToCircle()

double AMP::Geometry::GeometryHelpers::distanceToCircle	(	double	r,
		const Point2D &	pos,
		const Point2D &	ang
	)

Compute the intersection of a ray and circle (2D)

This function will compute the intersection of a ray with a circle. It assumes a circle of radius r centered at the origin. If the ray is inside the cylinder the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	r	Radius of circle
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToCircularFrustum()

double AMP::Geometry::GeometryHelpers::distanceToCircularFrustum	(	double	rb,
		double	rt,
		double	h,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and circular frustum.

This function will compute the intersection of a ray with a circular frustum. It assumes the circular frustum is located at the origin (base radius), with the given height, oriented in the +z direction. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	rb	Base radius
[in]	rt	Top radius
[in]	h	Object height
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToCone()

double AMP::Geometry::GeometryHelpers::distanceToCone	(	const Point3D &	V,
		double	theta,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and cone.

This function will compute the intersection of a ray with a cone. It assumes a cone with the apex at the origin in the direction given by V. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	V	Direction of cone
[in]	theta	Apex angle of cone
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToCylinder()

double AMP::Geometry::GeometryHelpers::distanceToCylinder	(	double	r,
		double	h,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and cylinder.

This function will compute the intersection of a ray with a cylinder. It assumes a cylinder of radius r and height h, centered at the origin along the z axis: z=[-h/2,h/2]. If the ray is inside the cylinder the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	r	Radius of cylinder
[in]	h	Height of cylinder
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToLine() [1/2]

double AMP::Geometry::GeometryHelpers::distanceToLine	(	const Point2D &	pos,
		const Point2D &	ang,
		const Point2D &	v1,
		const Point2D &	v2
	)

Compute the intersection of a ray and a line segment.

This function will compute the intersection of a ray with a line segment. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	pos	Starting point of ray
[in]	ang	Direction of ray
[in]	v1	First vertex
[in]	v2	Second vertex

Returns: Returns the distance

◆ distanceToLine() [2/2]

double AMP::Geometry::GeometryHelpers::distanceToLine	(	const Point3D &	pos,
		const Point3D &	ang,
		const Point3D &	v1,
		const Point3D &	v2
	)

Compute the intersection of a ray and a line segment.

This function will compute the intersection of a ray with a line segment. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	pos	Starting point of ray
[in]	ang	Direction of ray
[in]	v1	First vertex
[in]	v2	Second vertex

Returns: Returns the distance

◆ distanceToPlane()

double AMP::Geometry::GeometryHelpers::distanceToPlane	(	const Point3D &	n,
		const Point3D &	p0,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and an infinite plane.

This function will compute the intersection of a ray with an infinite plane. The plane is described by the normal and a point on the plane. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	n	Normal to the plane
[in]	p0	A point on the plane
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToQuadrilateral() [1/2]

double AMP::Geometry::GeometryHelpers::distanceToQuadrilateral	(	const std::array< Point2D, 4 > &	quad,
		const Point2D &	pos,
		const Point2D &	ang
	)

Compute the intersection of a ray and quadrilateral.

This function will compute the intersection of a ray with a quadrilateral. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	quad	Triangle coordinates
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToQuadrilateral() [2/2]

double AMP::Geometry::GeometryHelpers::distanceToQuadrilateral	(	const std::array< Point3D, 4 > &	quad,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and quadrilateral.

This function will compute the intersection of a ray with a quadrilateral. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	quad	Triangle coordinates
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToSphere()

double AMP::Geometry::GeometryHelpers::distanceToSphere	(	double	r,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and sphere.

This function will compute the intersection of a ray with a cylinder. It assumes a sphere of radius r and height h, centered at the origin. If the ray is inside the cylinder the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	r	Radius of cylinder
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToTetrahedron()

double AMP::Geometry::GeometryHelpers::distanceToTetrahedron	(	const std::array< Point3D, 4 > &	tet,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and tetrahedron.

This function will compute the intersection of a ray with a tetrahedron. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	tet	Tetrahedron coordinates
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToTriangle() [1/2]

double AMP::Geometry::GeometryHelpers::distanceToTriangle	(	const std::array< Point2D, 3 > &	tri,
		const Point2D &	pos,
		const Point2D &	ang
	)

Compute the intersection of a ray and triangle.

This function will compute the intersection of a ray with a triangle. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	tri	Triangle coordinates
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToTriangle() [2/2]

double AMP::Geometry::GeometryHelpers::distanceToTriangle	(	const std::array< Point3D, 3 > &	tri,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and triangle.

This function will compute the intersection of a ray with a triangle. If the ray is inside the cone the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	tri	Triangle coordinates
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ distanceToTube()

double AMP::Geometry::GeometryHelpers::distanceToTube	(	double	r1,
		double	r2,
		double	h,
		const Point3D &	pos,
		const Point3D &	ang
	)

Compute the intersection of a ray and tube.

This function will compute the intersection of a ray with a tube. It assumes a tube ith inner radius r1, outer radius r2, and height h centered at the origin along the z axis: z=[-h/2,h/2]. If the ray is inside the cylinder the distance is negative. If the ray will never intersect the object, this distance is inf.

Parameters

[in]	r1	Inner radius of cylinder
[in]	r2	Outer radius of cylinder
[in]	h	Height of cylinder
[in]	pos	Starting point of ray
[in]	ang	Direction of ray

Returns: Returns the distance

◆ get_poly_vertices()

std::vector< Point2D > AMP::Geometry::GeometryHelpers::get_poly_vertices	(	int	N,
		double	R
	)

Get the Vertices of a regular polygon.

This function will return the Vertices of a N-sided polygon that is compatible with the functions map_logical_poly and map_poly_logical.

Parameters

[in]	N	Number of faces
[in]	R	Radius of circumcircle

Returns: Returns the Vertices clockwise (physical coordinates)

◆ map_circle_logical()

Point2D AMP::Geometry::GeometryHelpers::map_circle_logical	(	double	R,
		int	method,
		double	x,
		double	y
	)

Map physical coordinates to the logical coordinates.

This function will map physical coordinates (x,y) coordinates in a circle to [0,1] logical coordinates. It uses the inverse of the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008) There are 3 methods to choose from: 1 - D(d) = r*d/sqrt(2), R(d) = r*d 2 - D(d) = r*d/sqrt(2), R(d) = r 3 - D(d) = r*d*(2-d)/sqrt(2), R(d) = r1

Parameters

[in]	R	Radius of circle
[in]	method	Method to map
[in]	x	Physical x coordinate
[in]	y	Physical y coordinate

Returns: Returns a pair with the logical (x,y) value

◆ map_logical_circle()

Point2D AMP::Geometry::GeometryHelpers::map_logical_circle	(	double	R,
		int	method,
		double	x,
		double	y
	)

Map logical coordinates to a circle.

This function will map logical coordinates in [0,1] to (x,y) coordinates in a circle. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008) There are 3 methods to choose from: 1 - D(d) = r*d/sqrt(2), R(d) = r*d 2 - D(d) = r*d/sqrt(2), R(d) = r 3 - D(d) = r*d*(2-d)/sqrt(2), R(d) = r1

Parameters

[in]	R	Radius of circle
[in]	method	Method to map
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate

Returns: Returns a pair with the (x,y) value

◆ map_logical_poly()

Point2D AMP::Geometry::GeometryHelpers::map_logical_poly	(	int	N,
		double	R,
		double	x,
		double	y
	)

Map logical coordinates to a regular polygon.

This function will map logical coordinates in [0,1] to (x,y) coordinates in a regular polygon.

Parameters

[in]	N	Number of faces
[in]	R	Radius of circumcircle
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate

Returns: Returns a pair with the (x,y) value

◆ map_logical_shell()

Point3D AMP::Geometry::GeometryHelpers::map_logical_shell	(	double	r1,
		double	r2,
		double	x,
		double	y,
		double	z
	)

Map logical coordinates to a shell.

This function will map logical coordinates in [0,1] to (x,y,z) coordinates in a shell. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	r1	Inner radius of shell
[in]	r2	Outer radius of shell
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate
[in]	z	Logical z coordinate

Returns: Returns the physical point

◆ map_logical_sphere()

Point3D AMP::Geometry::GeometryHelpers::map_logical_sphere	(	double	R,
		double	x,
		double	y,
		double	z
	)

Map logical coordinates to a sphere.

This function will map logical coordinates in [0,1] to (x,y,z) coordinates in a sphere. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	R	Radius of sphere
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate
[in]	z	Logical z coordinate

Returns: Returns the physical point

◆ map_logical_sphere_surface()

Point3D AMP::Geometry::GeometryHelpers::map_logical_sphere_surface	(	int	method,
		double	R,
		double	x,
		double	y
	)

Map logical coordinates to the surface of a sphere.

This function will map logical coordinates in [0,1] to (x,y,z) coordinates on the surface of a sphere. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	method	Method to use: 1 - Use method in Calhoun, requires extra attention to boundary conditions 2 - Half sphere mapping 3 - Spherical coordinates
[in]	R	Radius of sphere
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate

Returns: Returns the physical point

◆ map_poly_logical()

Point2D AMP::Geometry::GeometryHelpers::map_poly_logical	(	int	N,
		double	R,
		double	x,
		double	y
	)

Map physical coordinates to the logical coordinates.

This function will map physical coordinates (x,y) coordinates in a regular polygon to [0,1] logical coordinates.

Parameters

[in]	N	Number of faces
[in]	R	Radius of circumcircle
[in]	x	Physical x coordinate
[in]	y	Physical y coordinate

Returns: Returns a pair with the logical (x,y) value

◆ map_shell_logical()

Point3D AMP::Geometry::GeometryHelpers::map_shell_logical	(	double	r1,
		double	r2,
		double	x,
		double	y,
		double	z
	)

Map a shell to logical coordinates.

This function will map (x,y,z) coordinates in a shell to logical coordinates in [0,1]. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	r1	Inner radius of shell
[in]	r2	Outer radius of shell
[in]	x	Logical x coordinate
[in]	y	Logical y coordinate
[in]	z	Logical z coordinate

Returns: Returns the physical point

◆ map_sphere_logical()

Point3D AMP::Geometry::GeometryHelpers::map_sphere_logical	(	double	R,
		double	x,
		double	y,
		double	z
	)

Map logical coordinates to a sphere.

This function will map physical coordinates in (x,y,z) to [0,1] locial coordinates in a sphere. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains",Point3D SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	R	Radius of sphere
[in]	x	Physical x coordinate
[in]	y	Physical y coordinate
[in]	z	Physical z coordinate

Returns: Returns the logical point

◆ map_sphere_surface_logical()

Point2D AMP::Geometry::GeometryHelpers::map_sphere_surface_logical	(	int	method,
		double	R,
		double	x,
		double	y,
		double	z
	)

Map coordinates from the surface of a sphere to logical.

This function will map the (x,y,z) coordinates on the surface of a sphere to logical coordinates in [0,1]. It uses the mapping by: Dona Calhoun, Christiane Helzel, Randall LeVeque, "Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains", SIAM Review, Vol. 50, No. 4, pp. 723-752 (2008)

Parameters

[in]	method	Method to use: 1 - Use method in Calhoun, requires extra attention to boundary conditions 2 - Half sphere mapping 3 - Spherical coordinates
[in]	R	Radius of sphere
[in]	x	Physical x coordinate
[in]	y	Physical y coordinate
[in]	z	Physical z coordinate

Returns: Returns a pair with the logical (x,y) values

◆ nearest() [1/4]

Point2D AMP::Geometry::GeometryHelpers::nearest	(	const Point2D &	v1,
		const Point2D &	v2,
		const Point2D &	p
	)

Find the nearest point to a line segment.

This function will compute the nearest point to a line segment in 2D.

Parameters

[in]	v1	First vertex
[in]	v2	Second vertex
[in]	p	Point of interest

Returns: Returns the normal

◆ nearest() [2/4]

Point3D AMP::Geometry::GeometryHelpers::nearest	(	const Point3D &	v1,
		const Point3D &	v2,
		const Point3D &	p
	)

Find the nearest point to a line segment.

This function will compute the nearest point to a line segment in 3D.

Parameters

[in]	v1	First vertex
[in]	v2	Second vertex
[in]	p	Point of interest

Returns: Returns the normal

◆ nearest() [3/4]

Point3D AMP::Geometry::GeometryHelpers::nearest	(	const std::array< Point3D, 3 > &	v,
		const Point3D &	p
	)

Find the nearest point to a triangle.

This function will compute the nearest point to a triangle defined by three points in 3D.

Parameters

[in]	v	Vertices
[in]	p	Point of interest

Returns: Returns the normal

◆ nearest() [4/4]

Point3D AMP::Geometry::GeometryHelpers::nearest	(	const std::array< Point3D, 4 > &	v,
		const Point3D &	p
	)

Find the nearest point to a tetrahedron.

This function will compute the nearest point to a tetrahedron defined by three points in 3D.

Parameters

[in]	v	Vertices
[in]	p	Point of interest

Returns: Returns the normal

◆ normal() [1/2]

Point2D AMP::Geometry::GeometryHelpers::normal	(	const Point2D &	a,
		const Point2D &	b
	)

Compute the normal to a line defined by 2 points.

This function will compute the normal to a line defined by two points. The order of the points will determine the normal.

Parameters

[in]	a	First point
[in]	b	Second point

Returns: Returns the normal

◆ normal() [2/2]

Point3D AMP::Geometry::GeometryHelpers::normal	(	const Point3D &	a,
		const Point3D &	b,
		const Point3D &	c
	)

Compute the normal to a plane defined by 3 points.

This function will compute the normal to a plane defined by three points. The order of the points will determine the normal.

Parameters

[in]	a	First point
[in]	b	Second point
[in]	c	Third point

Returns: Returns the normal

◆ normalToQuadrilateral()

Point3D AMP::Geometry::GeometryHelpers::normalToQuadrilateral ( const std::array< Point3D, 4 > & quad )

Compute the normal to a quadrilateral.

This function will compute the normal to a quadrilateral. Since the points within the quadrilateral may not be co-planer, this will approximate the normal by dividing the quadrilateral into 4 triangles, computing the normal to each triangle, and then averaging the normal.

Parameters

[in] quad Triangle coordinates

Returns: Returns the distance

◆ sampleLine()

std::vector< Point3D > AMP::Geometry::GeometryHelpers::sampleLine	(	const std::array< Point3D, 2 > &	v,
		double	d0,
		bool	interior = `true`
	)

Sample a line.

Compute points on a line such that no point along the line is farther than d0 from a sample point

Parameters

[in]	v	Vertices
[in]	d0	Maximum distance between points
[in]	interior	Choose interior points (default) or include the Vertices

Returns: Returns the new points

◆ sampleQuad()

std::vector< Point3D > AMP::Geometry::GeometryHelpers::sampleQuad	(	const std::array< Point3D, 4 > &	v,
		double	d0,
		bool	interior = `true`
	)

Sample a line.

Compute points on a line such that no point within a quadrilateral is farther than d0 from a sample point

Parameters

[in]	v	Vertices
[in]	d0	Maximum distance between points
[in]	interior	Choose interior points (default) or include the Vertices

Returns: Returns the new points

◆ sampleTet()

std::vector< Point3D > AMP::Geometry::GeometryHelpers::sampleTet	(	const std::array< Point3D, 4 > &	v,
		double	d0,
		bool	interior = `true`
	)

Sample a line.

Compute points on a line such that no point within a tetrahedron is farther than d0 from a sample point

Parameters

[in]	v	Vertices
[in]	d0	Maximum distance between points
[in]	interior	Choose interior points (default) or include the Vertices

Returns: Returns the new points

◆ sampleTri()

std::vector< Point3D > AMP::Geometry::GeometryHelpers::sampleTri	(	const std::array< Point3D, 3 > &	v,
		double	d0,
		bool	interior = `true`
	)

Sample a line.

Compute points on a triangle such that no point within the triangle is farther than d0 from a sample point

Parameters

[in]	v	Vertices
[in]	d0	Maximum distance between points
[in]	interior	Choose interior points (default) or include the Vertices

Returns: Returns the new points

◆ subdivide()

std::vector< AMP::Mesh::Point > AMP::Geometry::GeometryHelpers::subdivide	(	const std::array< AMP::Mesh::Point, 3 > &	v,
		double	res
	)

Subdivide a triangle.

Given the Vertices of a triangle, sub-divide the triangle recursively until it is with the resolution, returning the new set of points

Parameters

[in]	v	Vertices
[in]	res	Desired resolution

Returns: Returns the new points (excluding the Vertices)

Typedefs

Functions

Typedef Documentation

◆ Point1D

◆ Point2D

◆ Point3D

Function Documentation

◆ assignRanks() [1/4]

◆ assignRanks() [2/4]

◆ assignRanks() [3/4]

◆ assignRanks() [4/4]

◆ barycentric()

◆ distance()

◆ distanceToBox()

◆ distanceToCircle()

◆ distanceToCircularFrustum()

◆ distanceToCone()

◆ distanceToCylinder()

◆ distanceToLine() [1/2]

◆ distanceToLine() [2/2]

◆ distanceToPlane()

◆ distanceToQuadrilateral() [1/2]

◆ distanceToQuadrilateral() [2/2]

◆ distanceToSphere()

◆ distanceToTetrahedron()

◆ distanceToTriangle() [1/2]

◆ distanceToTriangle() [2/2]

◆ distanceToTube()

◆ get_poly_vertices()

◆ map_circle_logical()

◆ map_logical_circle()

◆ map_logical_poly()

◆ map_logical_shell()

◆ map_logical_sphere()

◆ map_logical_sphere_surface()

◆ map_poly_logical()

◆ map_shell_logical()

◆ map_sphere_logical()

◆ map_sphere_surface_logical()

◆ nearest() [1/4]

◆ nearest() [2/4]

◆ nearest() [3/4]

◆ nearest() [4/4]

◆ normal() [1/2]

◆ normal() [2/2]

◆ normalToQuadrilateral()

◆ sampleLine()

◆ sampleQuad()

◆ sampleTet()

◆ sampleTri()

◆ subdivide()