polyhedrondistance.hh File Reference

#include <dune/common/dynvector.hh>
#include <dune/common/dynmatrix.hh>
#include <dune/fufem/geometry/convexpolyhedron.hh>

Go to the source code of this file.

Functions
template<class Coordinate , class Matrix >
void	populateMatrix (ConvexPolyhedron< Coordinate > const &segment, Matrix &matrix)
template<class Coordinate >
void	approximate (Coordinate const &target, Dune::DynamicMatrix< double > const &A, Dune::DynamicVector< double > const &l, ConvexPolyhedron< Coordinate > const &segment, Dune::DynamicVector< double > &sol)
template<class Coordinate >
double	distance (const Coordinate &target, const ConvexPolyhedron< Coordinate > &segment, double correctionTolerance, size_t maxIterations=1000)
template<class Coordinate >
double	distance (const ConvexPolyhedron< Coordinate > &s1, const ConvexPolyhedron< Coordinate > &s2, double valueCorrectionTolerance, size_t maxIterations=1000)
template<class Geometry >
double	distance (typename Geometry::GlobalCoordinate const &point, Geometry const &geo, double valueCorrectionTolerance)
template<class Geometry >
double	distance (ConvexPolyhedron< typename Geometry::GlobalCoordinate > const &p1, Geometry const &geo, double valueCorrectionTolerance, size_t maxIterations=1000)

Function Documentation

approximate()

template<class Coordinate >

void approximate	(	Coordinate const &	target,
		Dune::DynamicMatrix< double > const &	A,
		Dune::DynamicVector< double > const &	l,
		ConvexPolyhedron< Coordinate > const &	segment,
		Dune::DynamicVector< double > &	sol
	)

The functional to be minimized is

\[ 0.5*|\sum_i \lambda_i corner_i - target|^2 \]

where \(\lambda_i\) are barycentric coordinates, i.e.

\[ 0 \le \lambda_i \le 1 \text{ and }\sum_i \lambda_i=1 \]

The resulting quadratic minimization problem is given by

\[ 0.5 \lambda^T*A*\lambda - l^T*\lambda \]

with \(A_ij = (corner_i,corner_j)\) and \(l_i = (corner_i, target)\).

distance() [1/4]

template<class Coordinate >

double distance	(	const ConvexPolyhedron< Coordinate > &	s1,
		const ConvexPolyhedron< Coordinate > &	s2,
		double	valueCorrectionTolerance,
		size_t	maxIterations = 1000
	)

distance() [2/4]

template<class Coordinate >

double distance	(	const Coordinate &	target,
		const ConvexPolyhedron< Coordinate > &	segment,
		double	correctionTolerance,
		size_t	maxIterations = 1000
	)

distance() [3/4]

template<class Geometry >

double distance	(	ConvexPolyhedron< typename Geometry::GlobalCoordinate > const &	p1,
		Geometry const &	geo,
		double	valueCorrectionTolerance,
		size_t	maxIterations = 1000
	)

distance() [4/4]

template<class Geometry >

double distance	(	typename Geometry::GlobalCoordinate const &	point,
		Geometry const &	geo,
		double	valueCorrectionTolerance
	)

populateMatrix()

template<class Coordinate , class Matrix >

void populateMatrix	(	ConvexPolyhedron< Coordinate > const &	segment,
		Matrix &	matrix
	)