precice::math::barycenter Namespace Reference

Provides operations to calculate barycentric coordinates for a point's projection onto a primitive. More...

Functions
Eigen::Vector2d	calcBarycentricCoordsForEdge (const Eigen::VectorXd &a, const Eigen::VectorXd &b, const Eigen::VectorXd &u)
static double	crossProduct2D (const Eigen::Vector2d &u, const Eigen::Vector2d &v)
Eigen::Vector3d	calcBarycentricCoordsForTriangle (const Eigen::VectorXd &a, const Eigen::VectorXd &b, const Eigen::VectorXd &c, const Eigen::VectorXd &u)
Eigen::Vector4d	calcBarycentricCoordsForTetrahedron (const Eigen::VectorXd &a, const Eigen::VectorXd &b, const Eigen::VectorXd &c, const Eigen::VectorXd &d, const Eigen::VectorXd &u)

Detailed Description

Provides operations to calculate barycentric coordinates for a point's projection onto a primitive.

Function Documentation

calcBarycentricCoordsForEdge()

Eigen::Vector2d precice::math::barycenter::calcBarycentricCoordsForEdge	(	const Eigen::VectorXd &	a,
		const Eigen::VectorXd &	b,
		const Eigen::VectorXd &	u )

Takes the end vertices of an edge and a point in 2D or 3D space. Returns the barycentric coordinates for that point's projection onto the given edge.

Parameters

a	point A of the edge AB
b	point B of the edge AB
u	the point to compute the barycentric coordinates for

Note

Simple scalar projection approach, projected point in Cartesian coordinates is not actually calculated.

Definition at line 11 of file barycenter.cpp.

calcBarycentricCoordsForTetrahedron()

Eigen::Vector4d precice::math::barycenter::calcBarycentricCoordsForTetrahedron	(	const Eigen::VectorXd &	a,
		const Eigen::VectorXd &	b,
		const Eigen::VectorXd &	c,
		const Eigen::VectorXd &	d,
		const Eigen::VectorXd &	u )

Takes the corner vertices of a tetrahedron and a point in 3D space. Returns the barycentric coordinates for that point's projection onto the given tetrahedron.

Parameters

a	point A of the tetrahedron ABCD
b	point B of the tetrahedron ABCD
c	point C of the tetrahedron ABCD
d	point D of the tetrahedron ABCD
u	the point to compute the barycentric coordinates for

Note

This implements an efficient one-step algorithm (no separate projection) described in Boris Martin's Master's thesis

Definition at line 101 of file barycenter.cpp.

calcBarycentricCoordsForTriangle()

Eigen::Vector3d precice::math::barycenter::calcBarycentricCoordsForTriangle	(	const Eigen::VectorXd &	a,
		const Eigen::VectorXd &	b,
		const Eigen::VectorXd &	c,
		const Eigen::VectorXd &	u )

Takes the corner vertices of a triangle and a point in 3D space. Returns the barycentric coordinates for that point's projection onto the given triangle.

Parameters

a	point A of the triangle ABC
b	point B of the triangle ABC
c	point C of the triangle ABC
u	the point to compute the barycentric coordinates for

Note

This implements the efficient one-step algorithm (no separate projection) presented in Computing the barycentric coordinates of a projected point by W. Heidrich (2005)

Definition at line 45 of file barycenter.cpp.

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crossProduct2D()

static double precice::math::barycenter::crossProduct2D ( const Eigen::Vector2d & u, const Eigen::Vector2d & v )

static

Definition at line 40 of file barycenter.cpp.