Collaboration diagram for Elementary Computational Geometry (CGElem):

const double	bitpit::CGElem::DEFAULT_DISTANCE_TOLERANCE = 1.e-12

const double	bitpit::CGElem::DEFAULT_COPLANARITY_TOLERANCE = 1.e-12

const std::array< std::array< int, 2 >, 12 >	bitpit::CGElem::boxEdgeVertexConnectivity

const std::array< std::array< int, 4 >, 6 >	bitpit::CGElem::boxFaceVertexConnectivity

bool	bitpit::CGElem::validSegment (array3D const &, array3D const &)

bool	bitpit::CGElem::validLine (array3D const &, array3D const &)

bool	bitpit::CGElem::validPlane (array3D const &, array3D const &)

bool	bitpit::CGElem::validTriangle (array3D const &, array3D const &, array3D const &)

bool	bitpit::CGElem::validBarycentric (double const *, int)

int	bitpit::CGElem::convertBarycentricToFlagSegment (std::array< double, 2 > const &, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

int	bitpit::CGElem::convertBarycentricToFlagSegment (const double *lambda, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

int	bitpit::CGElem::convertBarycentricToFlagTriangle (std::array< double, 3 > const &, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

int	bitpit::CGElem::convertBarycentricToFlagTriangle (const double *lambda, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

int	bitpit::CGElem::convertBarycentricToFlagPolygon (std::vector< double > const &, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

int	bitpit::CGElem::convertBarycentricToFlagPolygon (std::size_t, double const *, double tolerance=DEFAULT_DISTANCE_TOLERANCE)

void	bitpit::CGElem::computeGeneralizedBarycentric (array3D const &, std::vector< array3D > const &, std::vector< double > &)

void	bitpit::CGElem::computeGeneralizedBarycentric (array3D const &, std::size_t, array3D const *, std::vector< double > &)

void	bitpit::CGElem::computeGeneralizedBarycentric (array3D const &, std::size_t, array3D const , double )

array3D	bitpit::CGElem::reconstructPointFromBarycentricSegment (array3D const &, array3D const &, std::array< double, 2 > const &)

array3D	bitpit::CGElem::reconstructPointFromBarycentricSegment (array3D const &, array3D const &, double const *)

array3D	bitpit::CGElem::reconstructPointFromBarycentricTriangle (array3D const &, array3D const &, array3D const &, std::array< double, 3 > const &)

array3D	bitpit::CGElem::reconstructPointFromBarycentricTriangle (array3D const &, array3D const &, array3D const &, double const *)

array3D	bitpit::CGElem::rotatePoint (const array3D &P, const array3D &n0, const array3D &n1, double angle)

array3D	bitpit::CGElem::reconstructPointFromBarycentricPolygon (std::vector< array3D > const &, std::vector< double > const &)

array3D	bitpit::CGElem::reconstructPointFromBarycentricPolygon (std::size_t, array3D const *, std::vector< double > const &)

array3D	bitpit::CGElem::reconstructPointFromBarycentricPolygon (std::size_t, array3D const , double const )

array3D	bitpit::CGElem::projectPointLine (array3D const &, array3D const &, array3D const &)

array3D	bitpit::CGElem::projectPointPlane (array3D const &, array3D const &, array3D const &)

array3D	bitpit::CGElem::projectPointSegment (array3D const &, array3D const &, array3D const &)

array3D	bitpit::CGElem::projectPointSegment (array3D const &, array3D const &, array3D const &, std::array< double, 2 > &)

array3D	bitpit::CGElem::projectPointSegment (array3D const &, array3D const &, array3D const &, double *)

array3D	bitpit::CGElem::projectPointTriangle (array3D const &, array3D const &, array3D const &, array3D const &)

array3D	bitpit::CGElem::projectPointTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D &)

array3D	bitpit::CGElem::projectPointTriangle (array3D const &P, array3D const &Q0, array3D const &Q1, array3D const &Q2, double *lambda)

array3D	bitpit::CGElem::restrictPointTriangle (array3D const &, array3D const &, array3D const &, array3D &)

array3D	bitpit::CGElem::restrictPointTriangle (array3D const &, array3D const &, array3D const &, double *)

std::vector< array3D >	bitpit::CGElem::projectCloudTriangle (std::vector< array3D > const &, array3D const &, array3D const &, array3D const &, std::vector< array3D > &)

array3D	bitpit::CGElem::projectPointPolygon (array3D const &, std::vector< array3D > const &)

array3D	bitpit::CGElem::projectPointPolygon (array3D const &, std::size_t, array3D const *)

array3D	bitpit::CGElem::projectPointPolygon (array3D const &, std::vector< array3D > const &, std::vector< double > &)

array3D	bitpit::CGElem::projectPointPolygon (array3D const &, std::size_t, array3D const *, std::vector< double > &)

array3D	bitpit::CGElem::projectPointPolygon (array3D const &, std::size_t, array3D const , double )

array3D	bitpit::CGElem::projectPointCone (array3D const &, array3D const &, array3D const &, double)

double	bitpit::CGElem::distancePointLine (array3D const &, array3D const &, array3D const &, array3D &)

double	bitpit::CGElem::distancePointPlane (array3D const &, array3D const &, array3D const &, array3D &)

double	bitpit::CGElem::distancePointSegment (array3D const &, array3D const &, array3D const &)

double	bitpit::CGElem::distancePointSegment (array3D const &, array3D const &, array3D const &, std::array< double, 2 > &)

double	bitpit::CGElem::distancePointTriangle (array3D const &, array3D const &, array3D const &, array3D const &)

double	bitpit::CGElem::distancePointTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D &)

double	bitpit::CGElem::distancePointCone (array3D const &, array3D const &, array3D const &, double)

std::vector< double >	bitpit::CGElem::distanceCloudTriangle (std::vector< array3D > const &, array3D const &, array3D const &, array3D const &)

std::vector< double >	bitpit::CGElem::distanceCloudTriangle (std::vector< array3D > const &, array3D const &, array3D const &, array3D const &, std::vector< array3D > &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::vector< array3D > const &, array3D &, int &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::size_t, array3D const *, array3D &, int &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::vector< array3D > const &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::size_t, array3D const *)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::vector< array3D > const &, std::vector< double > &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::size_t, array3D const *, std::vector< double > &)

double	bitpit::CGElem::distancePointPolygon (array3D const &, std::size_t, array3D const , double )

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::vector< array3D > const &, std::vector< array3D > &, std::vector< int > &)

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::size_t, array3D const *, std::vector< array3D > &, std::vector< int > &)

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::vector< array3D > const &)

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::size_t, array3D const *)

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::vector< array3D > const &, std::vector< std::vector< double > > &)

std::vector< double >	bitpit::CGElem::distanceCloudPolygon (std::vector< array3D > const &, std::size_t, array3D const *, std::vector< std::vector< double > > &)

double	bitpit::CGElem::distanceLineLine (array3D const &, array3D const &, array3D const &, array3D const &)

double	bitpit::CGElem::distanceLineLine (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &)

bool	bitpit::CGElem::intersectLineLine (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentSegment (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectLinePlane (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double coplanarityTolerance=DEFAULT_COPLANARITY_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentPlane (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPlanePlane (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &, const double coplanarityTolerance=DEFAULT_COPLANARITY_TOLERANCE)

bool	bitpit::CGElem::intersectPlaneBox (array3D const &, array3D const &, array3D const &, array3D const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPlaneBox (array3D const &, array3D const &, array3D const &, array3D const &, std::vector< array3D > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectLineTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectLinePolygon (array3D const &, array3D const &, std::vector< array3D > const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectLinePolygon (array3D const &, array3D const &, std::size_t, array3D const *, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentPolygon (array3D const &, array3D const &, std::vector< array3D > const &, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentPolygon (array3D const &, array3D const &, std::size_t, array3D const *, array3D &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxBox (array3D const &, array3D const &, array3D const &, array3D const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxBox (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D const &, bool, bool, bool, std::vector< array3D > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxTriangle (array3D const &, array3D const &, array3D const &, array3D const &, array3D const &, bool, bool, bool, std::vector< array3D > &, std::vector< int > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentBox (array3D const &, array3D const &, array3D const &, array3D const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentBox (array3D const &, array3D const &, array3D const &, array3D const &, bool, bool, std::vector< array3D > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectSegmentBox (array3D const &, array3D const &, array3D const &, array3D const &, bool, bool, std::vector< array3D > &, std::vector< int > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::vector< array3D > const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::size_t, array3D const *, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::vector< array3D > const &, bool, bool, bool, std::vector< array3D > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::size_t, array3D const *, bool, bool, bool, std::vector< array3D > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::vector< array3D > const &, bool, bool, bool, std::vector< array3D > &, std::vector< int > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxPolygon (array3D const &, array3D const &, std::size_t, array3D const *, bool, bool, bool, std::vector< array3D > &, std::vector< int > &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxCircle (array3D const &A0, array3D const &A1, array3D const &centre, double radius, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectBoxSphere (array3D const &A0, array3D const &A1, array3D const &centre, double radius, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPointLine (array3D const &, array3D const &, array3D const &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPointSegment (array3D const &, array3D const &, array3D const &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPointTriangle (array3D const &, array3D const &, array3D const &, array3D const &, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

bool	bitpit::CGElem::intersectPointBox (array3D const &, array3D const &, array3D const &, int dim=3, const double distanceTolerance=DEFAULT_DISTANCE_TOLERANCE)

void	bitpit::CGElem::computeAABBSegment (array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::computeAABBTriangle (array3D const &, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::computeAABBPolygon (std::vector< array3D > const &, array3D &, array3D &)

void	bitpit::CGElem::computeAABBPolygon (std::size_t, array3D const *, array3D &, array3D &)

void	bitpit::CGElem::unionAABB (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::unionAABB (std::vector< array3D > const &, std::vector< array3D > const &, array3D &, array3D &)

void	bitpit::CGElem::intersectionAABB (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::subtractionAABB (array3D const &, array3D const &, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::vertexOfSegment (int, array3D const &, array3D const &, array3D &)

void	bitpit::CGElem::vertexOfTriangle (int, array3D const &, array3D const &, array3D const &, array3D &)

void	bitpit::CGElem::edgeOfTriangle (int, array3D const &, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::faceOfBox (int, array3D const &, array3D const &, array3D &, array3D &, array3D &, array3D &)

void	bitpit::CGElem::edgeOfBox (int, array3D const &, array3D const &, array3D &, array3D &)

void	bitpit::CGElem::vertexOfBox (int, array3D const &, array3D const &, array3D &)

array3D	bitpit::CGElem::rotateVector (array3D const &, array3D const &, double)

double	bitpit::CGElem::areaTriangle (array3D const &, array3D const &, array3D const &)

int	bitpit::CGElem::polygonEdgesCount (std::vector< array3D > const &)

int	bitpit::CGElem::polygonEdgesCount (std::size_t, array3D const *)

int	bitpit::CGElem::polygonSubtriangleCount (std::vector< array3D > const &)

int	bitpit::CGElem::polygonSubtriangleCount (std::size_t, array3D const *)

void	bitpit::CGElem::edgeOfPolygon (int, std::vector< array3D > const &, array3D &, array3D &)

void	bitpit::CGElem::edgeOfPolygon (int, std::size_t, array3D const *, array3D &, array3D &)

void	bitpit::CGElem::subtriangleOfPolygon (int, std::vector< array3D > const &, array3D &, array3D &, array3D &)

void	bitpit::CGElem::subtriangleOfPolygon (int, std::size_t, array3D const *, array3D &, array3D &, array3D &)

Detailed Description

Function Documentation

◆ areaTriangle()

double bitpit::CGElem::areaTriangle	(	array3D const &	a,
		array3D const &	b,
		array3D const &	c )

computes the area of an triangle

Parameters

[in]	a	first vertex coordinates
[in]	b	second vertex coordinates
[in]	c	third vertex coordinates

Definition at line 2987 of file CG_elem.cpp.

◆ computeAABBPolygon() [1/2]

void bitpit::CGElem::computeAABBPolygon	(	std::size_t	nVS,
		array3D const *	VS,
		array3D &	P0,
		array3D &	P1 )

computes axis aligned boundig box of a polygon

Parameters

[in]	nVS	number of polygon vertices
[in]	VS	polygon vertices coordinates
[out]	P0	min point of bounding box
[out]	P1	max point of bounding box

Definition at line 2643 of file CG_elem.cpp.

◆ computeAABBPolygon() [2/2]

void bitpit::CGElem::computeAABBPolygon	(	std::vector< array3D > const &	VS,
		array3D &	P0,
		array3D &	P1 )

computes axis aligned boundig box of a polygon

Parameters

[in]	VS	polygon vertices coordinates
[out]	P0	min point of bounding box
[out]	P1	max point of bounding box

Definition at line 2631 of file CG_elem.cpp.

◆ computeAABBSegment()

void bitpit::CGElem::computeAABBSegment	(	array3D const &	A,
		array3D const &	B,
		array3D &	P0,
		array3D &	P1 )

computes axis aligned boundig box of a segment

Parameters

[in]	A	start point of segment
[in]	B	end point of segment
[out]	P0	min point of bounding box
[out]	P1	max point of bounding box

Definition at line 2587 of file CG_elem.cpp.

◆ computeAABBTriangle()

void bitpit::CGElem::computeAABBTriangle	(	array3D const &	A,
		array3D const &	B,
		array3D const &	C,
		array3D &	P0,
		array3D &	P1 )

computes axis aligned boundig box of a triangle

Parameters

[in]	A	first vertex of triangle
[in]	B	second vertex of triangle
[in]	C	third vertex of triangle
[out]	P0	min point of bounding box
[out]	P1	max point of bounding box

Definition at line 2609 of file CG_elem.cpp.

◆ computeGeneralizedBarycentric() [1/3]

void bitpit::CGElem::computeGeneralizedBarycentric	(	array3D const &	p,
		std::size_t	nVertices,
		array3D const *	vertex,
		double *	lambda )

Computes Generalized Barycentric Coordinates of a point in convex polygons or polyedra. No check is performed to check convexity. Formula [6] of this paper is implemented. This formula actually refers to the method of Eugene Wachpress in the manuscript A Rational Finite Elment Basis. Generalized Barycentric Coordinates cannot be evaluated for degenerate polygons (i.e. polygons with consecutive collinear edges). No checks are performed to find out if the specified polygon is degenerate.

Parameters

[in]	p	point
[in]	nVertices	number of polygon vertices
[in]	vertex	vertex coordinates of polygon
[out]	lambda	generalized barycentric coordinates of p

Definition at line 788 of file CG_elem.cpp.

◆ computeGeneralizedBarycentric() [2/3]

void bitpit::CGElem::computeGeneralizedBarycentric	(	array3D const &	p,
		std::size_t	nVertices,
		array3D const *	vertex,
		std::vector< double > &	lambda )

Computes Generalized Barycentric Coordinates of a point in convex polygons or polyedra. No check is performed to check convexity. Formula [6] of this paper is implemented. This formula actually refers to the method of Eugene Wachpress in the manuscript A Rational Finite Elment Basis. Generalized Barycentric Coordinates cannot be evaluated for degenerate polygons (i.e. polygons with consecutive collinear edges). No checks are performed to find out if the specified polygon is degenerate.

Parameters

[in]	p	point
[in]	nVertices	number of polygon vertices
[in]	vertex	vertex coordinates of polygon
[out]	lambda	generalized barycentric coordinates of p

Definition at line 768 of file CG_elem.cpp.

◆ computeGeneralizedBarycentric() [3/3]

void bitpit::CGElem::computeGeneralizedBarycentric	(	array3D const &	p,
		std::vector< array3D > const &	vertex,
		std::vector< double > &	lambda )

Computes Generalized Barycentric Coordinates of a point in convex polygons or polyedra. No check is performed to check convexity. Formula [6] of this paper is implemented. This formula actually refers to the method of Eugene Wachpress in the manuscript A Rational Finite Elment Basis. Generalized Barycentric Coordinates cannot be evaluated for degenerate polygons (i.e. polygons with consecutive collinear edges). No checks are performed to find out if the specified polygon is degenerate.

Parameters

[in]	p	point
[in]	vertex	vertex coordinates of polygon
[out]	lambda	generalized barycentric coordinates of p

Definition at line 750 of file CG_elem.cpp.

◆ convertBarycentricToFlagPolygon() [1/2]

int bitpit::CGElem::convertBarycentricToFlagPolygon	(	std::size_t	nLambda,
		double const *	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a convex polygon to a flag that indicates where the point lies. Flag = 0 Point lies within the simplex Flag = i Point coincides with the (ith - 1) vertex of simplex or lies within the area spanned by the edges incident in the (ith - 1) vertex Flag = -i Point lies on the edge starting from the (ith - 1) vertex and connecting the following vertex in counter-clockwise direction or in its shaddowed area

Parameters

[in]	nLambda	number of barycentric coordinates of point
[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 701 of file CG_elem.cpp.

◆ convertBarycentricToFlagPolygon() [2/2]

int bitpit::CGElem::convertBarycentricToFlagPolygon	(	std::vector< double > const &	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a convex polygon to a flag that indicates where the point lies. Flag = 0 Point lies within the simplex Flag = i Point coincides with the (ith - 1) vertex of simplex or lies within the area spanned by the edges incident in the (ith - 1) vertex Flag = -i Point lies on the edge starting from the (ith - 1) vertex and connecting the following vertex in counter-clockwise direction or in its shaddowed area

Parameters

[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 686 of file CG_elem.cpp.

◆ convertBarycentricToFlagSegment() [1/2]

int bitpit::CGElem::convertBarycentricToFlagSegment	(	const double *	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a segment to a flag that indicates where the point lies. Flag = 0 Point lies within the segment Flag = 1 Point coincides with the first vertex or is positioned befor the line Flag = 2 Point coincides with the second vertex or is positioned after the line

Parameters

[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 633 of file CG_elem.cpp.

◆ convertBarycentricToFlagSegment() [2/2]

int bitpit::CGElem::convertBarycentricToFlagSegment	(	std::array< double, 2 > const &	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a segment to a flag that indicates where the point lies. Flag = 0 Point lies within the segment Flag = 1 Point coincides with the first vertex or is positioned befor the line Flag = 2 Point coincides with the second vertex or is positioned after the line

Parameters

[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 618 of file CG_elem.cpp.

◆ convertBarycentricToFlagTriangle() [1/2]

int bitpit::CGElem::convertBarycentricToFlagTriangle	(	const double *	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a triangle to a flag that indicates where the point lies. Flag = 0 Point lies within the triangle Flag = i Point coincides with the (ith - 1) vertex of triangle or lies within the area spanned by the edges incident in the (ith - 1) vertex Flag = -i Point lies on the edge starting from the (ith - 1) vertex and connecting the following vertex in clockwise direction or in its shaddowed area

Parameters

[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 672 of file CG_elem.cpp.

◆ convertBarycentricToFlagTriangle() [2/2]

int bitpit::CGElem::convertBarycentricToFlagTriangle	(	array3D const &	lambda,
		double	tolerance )

Converts barycentric coordinates of a point on a triangle to a flag that indicates where the point lies. Flag = 0 Point lies within the triangle Flag = i Point coincides with the (ith - 1) vertex of triangle or lies within the area spanned by the edges incident in the (ith - 1) vertex Flag = -i Point lies on the edge starting from the (ith - 1) vertex and connecting the following vertex in clockwise direction or in its shaddowed area

Parameters

[in]	lambda	barycentric coordinates of point
[in]	tolerance	tolerance used for comparisons

Returns: flag

Definition at line 658 of file CG_elem.cpp.

◆ distanceCloudPolygon() [1/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	P,
		std::size_t	nV,
		array3D const *	V )

Computes distances of point cloud to a convex polygon

Parameters

[in]	P	point cloud coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates

Returns: distance

Definition at line 1653 of file CG_elem.cpp.

◆ distanceCloudPolygon() [2/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	cloud,
		std::size_t	nV,
		array3D const *	V,
		std::vector< array3D > &	xP,
		std::vector< int > &	flag )

Computes distances of point cloud to a convex polygon

Parameters

[in]	cloud	point cloud coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	xP	closest points on simplex
[out]	flag	point projecting onto polygon's interior (flag = 0), polygon's vertices (flag = 1, 2, ...) or polygon's edges (flag = -1, -2, -...)

Returns: distance

Definition at line 1611 of file CG_elem.cpp.

◆ distanceCloudPolygon() [3/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	cloud,
		std::size_t	nV,
		array3D const *	V,
		std::vector< std::vector< double > > &	lambda )

Computes distances of point cloud to a convex polygon

Parameters

[in]	cloud	point cloud coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	lambda	barycentric coordinates of the projection points

Returns: distance

Definition at line 1692 of file CG_elem.cpp.

◆ distanceCloudPolygon() [4/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	P,
		std::vector< array3D > const &	V )

Computes distances of point cloud to a convex polygon

Parameters

[in]	P	point cloud coordinates
[in]	V	polygon vertices coordinates

Returns: distance

Definition at line 1641 of file CG_elem.cpp.

◆ distanceCloudPolygon() [5/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	cloud,
		std::vector< array3D > const &	V,
		std::vector< array3D > &	xP,
		std::vector< int > &	flag )

Computes distances of point cloud to a convex polygon

Parameters

[in]	cloud	point cloud coordinates
[in]	V	polygon vertices coordinates
[out]	xP	closest points on simplex
[out]	flag	point projecting onto polygon's interior (flag = 0), polygon's vertices (flag = 1, 2, ...) or polygon's edges (flag = -1, -2, -...)

Returns: distance

Definition at line 1597 of file CG_elem.cpp.

◆ distanceCloudPolygon() [6/6]

std::vector< double > bitpit::CGElem::distanceCloudPolygon	(	std::vector< array3D > const &	cloud,
		std::vector< array3D > const &	V,
		std::vector< std::vector< double > > &	lambda )

Computes distances of point cloud to a convex polygon

Parameters

[in]	cloud	point cloud coordinates
[in]	V	polygon vertices coordinates
[out]	lambda	barycentric coordinates of the projection points

Returns: distance

Definition at line 1679 of file CG_elem.cpp.

◆ distanceCloudTriangle() [1/2]

std::vector< double > bitpit::CGElem::distanceCloudTriangle	(	std::vector< array3D > const &	cloud,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2 )

Computes distances of point cloud to triangle

Parameters

[in]	cloud	point cloud coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex

Returns: distances

Definition at line 1452 of file CG_elem.cpp.

◆ distanceCloudTriangle() [2/2]

std::vector< double > bitpit::CGElem::distanceCloudTriangle	(	std::vector< array3D > const &	cloud,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		std::vector< array3D > &	lambda )

Computes distances of point cloud to triangle

Parameters

[in]	cloud	point cloud coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[out]	lambda	barycentric coordinates of projection points

Returns: distances

Definition at line 1467 of file CG_elem.cpp.

◆ distanceLineLine() [1/2]

double bitpit::CGElem::distanceLineLine	(	array3D const &	P0,
		array3D const &	n0,
		array3D const &	P1,
		array3D const &	n1 )

Computes distance between two lines in 3D

Parameters

[in]	n0	direction of first line
[in]	P0	point on first line
[in]	n1	direction of second line
[in]	P1	point on second line

Returns: distance

Definition at line 1727 of file CG_elem.cpp.

◆ distanceLineLine() [2/2]

double bitpit::CGElem::distanceLineLine	(	array3D const &	P0,
		array3D const &	n0,
		array3D const &	P1,
		array3D const &	n1,
		array3D &	xP0,
		array3D &	xP1 )

Computes distance between two lines in 3D

Parameters

[in]	n0	direction of first line
[in]	P0	point on first line
[in]	n1	direction of second line
[in]	P1	point on second line
[out]	xP0	projection of line1 on line0
[out]	xP1	projection of line0 on line1

Returns: distance

Definition at line 1743 of file CG_elem.cpp.

◆ distancePointCone()

double bitpit::CGElem::distancePointCone	(	array3D const &	point,
		array3D const &	apex,
		array3D const &	axis,
		double	alpha )

Computes distance point to semi-infinite cone surface

Parameters

[in]	point	point coordinates
[in]	apex	cone apex
[in]	axis	cone axis
[in]	alpha	cone half angle

Returns: distance

Definition at line 1438 of file CG_elem.cpp.

◆ distancePointLine()

double bitpit::CGElem::distancePointLine	(	array3D const &	P,
		array3D const &	Q,
		array3D const &	n,
		array3D &	xP )

Computes distance point to line in 3D

Parameters

[in]	P	point coordinates
[in]	Q	point on line
[in]	n	line direction
[out]	xP	closest point on line

Returns: distance

Definition at line 1354 of file CG_elem.cpp.

◆ distancePointPlane()

double bitpit::CGElem::distancePointPlane	(	array3D const &	P,
		array3D const &	Q,
		array3D const &	n,
		array3D &	xP )

Computes distance point to plane

Parameters

[in]	P	point coordinates
[in]	Q	point on plane
[in]	n	plane normal
[out]	xP	closest point on line

Returns: distance

Definition at line 1368 of file CG_elem.cpp.

◆ distancePointPolygon() [1/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	simplex vertices coordinates

Returns: distance

Definition at line 1542 of file CG_elem.cpp.

◆ distancePointPolygon() [2/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V,
		array3D &	xP,
		int &	flag )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	xP	closest points on polygon
[out]	flag	point projecting onto polygon's interior (flag = 0), polygon's vertices (flag = 1, 2, ...) or polygon's edges (flag = -1, -2, -...)

Returns: distance

Definition at line 1512 of file CG_elem.cpp.

◆ distancePointPolygon() [3/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V,
		double *	lambda )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	lambda	barycentric coordinates

Returns: distance

Definition at line 1583 of file CG_elem.cpp.

◆ distancePointPolygon() [4/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V,
		std::vector< double > &	lambda )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	lambda	barycentric coordinates

Returns: distance

Definition at line 1568 of file CG_elem.cpp.

◆ distancePointPolygon() [5/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::vector< array3D > const &	V )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	V	simplex vertices coordinates

Returns: distance

Definition at line 1530 of file CG_elem.cpp.

◆ distancePointPolygon() [6/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::vector< array3D > const &	V,
		array3D &	xP,
		int &	flag )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	V	polygon vertices coordinates
[out]	xP	closest points on polygon
[out]	flag	point projecting onto polygon's interior (flag = 0), polygon's vertices (flag = 1, 2, ...) or polygon's edges (flag = -1, -2, -...)

Returns: distance

Definition at line 1498 of file CG_elem.cpp.

◆ distancePointPolygon() [7/7]

double bitpit::CGElem::distancePointPolygon	(	array3D const &	P,
		std::vector< array3D > const &	V,
		std::vector< double > &	lambda )

Computes distances of point to a convex polygon

Parameters

[in]	P	point coordinates
[in]	V	polygon vertices coordinates
[out]	lambda	barycentric coordinates

Returns: distance

Definition at line 1555 of file CG_elem.cpp.

◆ distancePointSegment() [1/2]

double bitpit::CGElem::distancePointSegment	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1 )

Computes distance point to segment

Parameters

[in]	P	point coordinates
[in]	Q0	segment starting point
[in]	Q1	segment ending point

Returns: distance

Definition at line 1381 of file CG_elem.cpp.

◆ distancePointSegment() [2/2]

double bitpit::CGElem::distancePointSegment	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		std::array< double, 2 > &	lambda )

Computes distance point to segment in 3D using barycentric coordinates

Parameters

[in]	P	point coordinates
[in]	Q0	segment starting point
[in]	Q1	segment ending point
[out]	lambda	barycentric coordinates

Returns: distance

Definition at line 1395 of file CG_elem.cpp.

◆ distancePointTriangle() [1/2]

double bitpit::CGElem::distancePointTriangle	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2 )

Computes distance point to triangle

Parameters

[in]	P	point coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex

Returns: distance

Definition at line 1409 of file CG_elem.cpp.

◆ distancePointTriangle() [2/2]

double bitpit::CGElem::distancePointTriangle	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		array3D &	lambda )

Computes distance point to triangle

Parameters

[in]	P	point coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[out]	lambda	barycentric coordinates of projection point

Returns: distance

Definition at line 1424 of file CG_elem.cpp.

◆ edgeOfBox()

void bitpit::CGElem::edgeOfBox	(	int	i,
		array3D const &	A0,
		array3D const &	A1,
		array3D &	P0,
		array3D &	P1 )

computes the edge coordiantes of a box

Parameters

[in]	i	edge index
[in]	A0	min point of bounding box
[in]	A1	max point of bounding box
[out]	P0	first vertex of edge
[out]	P1	first vertex of edge

Definition at line 2879 of file CG_elem.cpp.

◆ edgeOfPolygon() [1/2]

void bitpit::CGElem::edgeOfPolygon	(	int	edge,
		std::size_t	nV,
		array3D const *	V,
		array3D &	V0,
		array3D &	V1 )

Gets the edge coordinates of a convex polygon

Parameters

[in]	edge	index
[in]	nV	number of polygon vertices
[in]	V	polgon vertices
[in]	V0	first vertice coordinates of edge
[in]	V1	second vertice coordinates of edge

Definition at line 3064 of file CG_elem.cpp.

◆ edgeOfPolygon() [2/2]

void bitpit::CGElem::edgeOfPolygon	(	int	edge,
		std::vector< array3D > const &	V,
		array3D &	V0,
		array3D &	V1 )

Gets the edge coordinates of a convex polygon

Parameters

[in]	edge	index
[in]	V	polgon vertices
[in]	V0	first vertice coordinates of edge
[in]	V1	second vertice coordinates of edge

Definition at line 3051 of file CG_elem.cpp.

◆ edgeOfTriangle()

void bitpit::CGElem::edgeOfTriangle	(	int	i,
		array3D const &	V0,
		array3D const &	V1,
		array3D const &	V2,
		array3D &	P0,
		array3D &	P1 )

computes the edge coordiantes of a triangle

Parameters

[in]	i	edge index
[in]	V0	first vertex of triangle
[in]	V1	second vertex of triangle
[in]	V2	third vertex of triangle
[out]	P0	first vertex of edge
[out]	P1	first vertex of edge

Definition at line 2816 of file CG_elem.cpp.

◆ faceOfBox()

void bitpit::CGElem::faceOfBox	(	int	i,
		array3D const &	A0,
		array3D const &	A1,
		array3D &	P0,
		array3D &	P1,
		array3D &	P2,
		array3D &	P3 )

computes the face coordiantes of a box

Parameters

[in]	i	face index
[in]	A0	min point of bounding box
[in]	A1	max point of bounding box
[out]	P0	first vertex of face
[out]	P1	first vertex of face
[out]	P2	first vertex of face
[out]	P3	first vertex of face

Definition at line 2853 of file CG_elem.cpp.

◆ intersectBoxBox() [1/2]

bool bitpit::CGElem::intersectBoxBox	(	array3D const &	A1,
		array3D const &	A2,
		array3D const &	B1,
		array3D const &	B2,
		array3D &	I1,
		array3D &	I2,
		int	dim,
		const double	distanceTolerance )

Computes intersection between two axis aligned bounding boxes

Parameters

[in]	A1	min point of first box
[in]	A2	max point of first box
[in]	B1	min point of second box
[in]	B2	max point of second box
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	I1	min point of intersection box
[out]	I2	max point of intersection box
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2148 of file CG_elem.cpp.

◆ intersectBoxBox() [2/2]

bool bitpit::CGElem::intersectBoxBox	(	array3D const &	A1,
		array3D const &	A2,
		array3D const &	B1,
		array3D const &	B2,
		int	dim,
		const double	distanceTolerance )

Computes intersection between two axis aligned bounding boxes

Parameters

[in]	A1	min point of first box
[in]	A2	max point of first box
[in]	B1	min point of second box
[in]	B2	max point of second box
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 2125 of file CG_elem.cpp.

◆ intersectBoxCircle()

bool bitpit::CGElem::intersectBoxCircle	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	centre,
		double	radius,
		const double	distanceTolerance )

Checks it the axis aligned bounding box intersects the circle.

Parameters

[in]	A0	min point of box
[in]	A1	max point of box
[in]	centre	is the centre of the circle
[in]	radius	is the radius of the circle
[in]	distanceTolerance	is the tolerance used to checking the intersection

Returns: Returns true if the box intersects the circle, false otherwise.

Definition at line 2390 of file CG_elem.cpp.

◆ intersectBoxPolygon() [1/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::size_t	nVS,
		array3D const *	VS,
		bool	innerPolygonPoints,
		bool	polygonEdgeBoxFaceIntersections,
		bool	polygonBoxEdgeIntersections,
		std::vector< array3D > &	P,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a convex polygon

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	nVS	number of polygon vertices
[in]	VS	polygon vertices coordinates
[in]	innerPolygonPoints	simplex vertices within the box should be added to the intersection list
[in]	polygonEdgeBoxFaceIntersections	intersection between the edges of the polygon and the hull of the box should be added to the intersection list
[in]	polygonBoxEdgeIntersections	intersection between the polygon and the edges of the box should be added to the intersection list
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2336 of file CG_elem.cpp.

◆ intersectBoxPolygon() [2/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::size_t	nVS,
		array3D const *	VS,
		bool	innerPolygonPoints,
		bool	polygonEdgeBoxFaceIntersections,
		bool	polygonBoxEdgeIntersections,
		std::vector< array3D > &	P,
		std::vector< int > &	flag,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a simplex

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	nVS	number of polygon vertices
[in]	VS	simplex vertices coordinates
[in]	innerPolygonPoints	simplex vertices within the box should be added to the intersection list
[in]	polygonEdgeBoxFaceIntersections	intersection between the edges of the polygon and the hull of the box should be added to the intersection list
[in]	polygonBoxEdgeIntersections	intersection between the polygon and the edges of the box should be added to the intersection list
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[out]	flag	has the same size of P. If the ith flag=0, the intersection is due to innerPolygonPoints. If the ith flag=1, the intersection is due to polygonEdgeBoxFaceIntersections. If the ith flag=2, the intersection is due to polygonBoxEdgeIntersections.
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2375 of file CG_elem.cpp.

◆ intersectBoxPolygon() [3/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::size_t	nVS,
		array3D const *	VS,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a simplex

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	nVS	number of polygon vertices
[in]	VS	simplex vertices coordinates
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 2298 of file CG_elem.cpp.

◆ intersectBoxPolygon() [4/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::vector< array3D > const &	VS,
		bool	innerPolygonPoints,
		bool	polygonEdgeBoxFaceIntersections,
		bool	polygonBoxEdgeIntersections,
		std::vector< array3D > &	P,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a convex polygon

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	VS	polygon vertices coordinates
[in]	innerPolygonPoints	simplex vertices within the box should be added to the intersection list
[in]	polygonEdgeBoxFaceIntersections	intersection between the edges of the polygon and the hull of the box should be added to the intersection list
[in]	polygonBoxEdgeIntersections	intersection between the polygon and the edges of the box should be added to the intersection list
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2316 of file CG_elem.cpp.

◆ intersectBoxPolygon() [5/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::vector< array3D > const &	VS,
		bool	innerPolygonPoints,
		bool	polygonEdgeBoxFaceIntersections,
		bool	polygonBoxEdgeIntersections,
		std::vector< array3D > &	P,
		std::vector< int > &	flag,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a simplex

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	VS	simplex vertices coordinates
[in]	innerPolygonPoints	simplex vertices within the box should be added to the intersection list
[in]	polygonEdgeBoxFaceIntersections	intersection between the edges of the polygon and the hull of the box should be added to the intersection list
[in]	polygonBoxEdgeIntersections	intersection between the polygon and the edges of the box should be added to the intersection list
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[out]	flag	has the same size of P. If the ith flag=0, the intersection is due to innerPolygonPoints. If the ith flag=1, the intersection is due to polygonEdgeBoxFaceIntersections. If the ith flag=2, the intersection is due to polygonBoxEdgeIntersections.
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2355 of file CG_elem.cpp.

◆ intersectBoxPolygon() [6/6]

bool bitpit::CGElem::intersectBoxPolygon	(	array3D const &	A0,
		array3D const &	A1,
		std::vector< array3D > const &	VS,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a simplex

Parameters

[in]	A0	min point of first box
[in]	A1	max point of first box
[in]	VS	simplex vertices coordinates
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 2284 of file CG_elem.cpp.

◆ intersectBoxSphere()

bool bitpit::CGElem::intersectBoxSphere	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	centre,
		double	radius,
		const double	distanceTolerance )

Checks it the axis aligned bounding box intersects the sphere.

Parameters

[in]	A0	min point of box
[in]	A1	max point of box
[in]	centre	is the centre of the sphere
[in]	radius	is the radius of the sphere
[in]	distanceTolerance	is the tolerance used to checking the intersection

Returns: Returns true if the box intersects the sphere, false otherwise.

Definition at line 2416 of file CG_elem.cpp.

◆ intersectBoxTriangle() [1/3]

bool bitpit::CGElem::intersectBoxTriangle	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	V0,
		array3D const &	V1,
		array3D const &	V2,
		bool	interiorTriangleVertices,
		bool	triangleEdgeBoxFaceIntersections,
		bool	triangleBoxEdgeIntersections,
		std::vector< array3D > &	P,
		int	dim,
		const double	distanceTolerance )

Checks if an axis aligned bounding box and a triangle intersect

Parameters

[in]	A0	min point of box
[in]	A1	max point of box
[in]	V0	first vertex of triangle
[in]	V1	second vertex of triangle
[in]	V2	third vertex of triangle
[in]	interiorTriangleVertices	if true, all triangle vertices within the box will be added to the intersection points P
[in]	triangleEdgeBoxFaceIntersections	if true, the intersections between the edges of the triangle and the hull of the box will be added to the intersection points P
[in]	triangleBoxEdgeIntersections	if true, the intersections between the edges (dim=3) or vertices (dim=2) of the box and the triangle will be added to the intersection points P
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2197 of file CG_elem.cpp.

◆ intersectBoxTriangle() [2/3]

bool bitpit::CGElem::intersectBoxTriangle	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	V0,
		array3D const &	V1,
		array3D const &	V2,
		bool	interiorTriangleVertices,
		bool	triangleEdgeBoxHullIntersections,
		bool	triangleBoxEdgeIntersections,
		std::vector< array3D > &	P,
		std::vector< int > &	flag,
		int	dim,
		const double	distanceTolerance )

Checks if an axis aligned bounding box and a triangle intersect

Parameters

[in]	A0	min point of box
[in]	A1	max point of box
[in]	V0	first vertex of triangle
[in]	V1	second vertex of triangle
[in]	V2	third vertex of triangle
[in]	interiorTriangleVertices	if true, all triangle vertices within the box will be added to the intersection points P
[in]	triangleEdgeBoxHullIntersections	if true, the intersections between the edges of the triangle and the outer hull of the box will be added to the intersection points P
[in]	triangleBoxEdgeIntersections	if true, the intersections between the edges (dim=3) or vertices (dim=2) of the box and the triangle will be added to the intersection points P
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	calculated intersection points
[out]	flag	has the same size of P. If the ith flag=0, the intersection is due to interiorTriangleVertices. If the ith flag=1, the intersection is due to triangleEdgeBoxHullIntersection. If the ith flag=2, the intersection is due to triangleBoxEdgeIntersections.
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2218 of file CG_elem.cpp.

◆ intersectBoxTriangle() [3/3]

bool bitpit::CGElem::intersectBoxTriangle	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	V0,
		array3D const &	V1,
		array3D const &	V2,
		int	dim,
		const double	distanceTolerance )

Checks if an axis aligned bounding box and a triangle intersect

Parameters

[in]	A0	min point of box
[in]	A1	max point of box
[in]	V0	first vertex of triangle
[in]	V1	second vertex of triangle
[in]	V2	third vertex of triangle
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 2177 of file CG_elem.cpp.

◆ intersectionAABB()

void bitpit::CGElem::intersectionAABB	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	B0,
		array3D const &	B1,
		array3D &	C0,
		array3D &	C1 )

computes the bounding box of the intersection of two axis aligned bounding boxes

Parameters

[in]	A0	min point of first bounding box
[in]	A1	max point of first bounding box
[in]	B0	min point of second bounding box
[in]	B1	max point of second bounding box
[out]	C0	min point of intersection of boxes
[out]	C1	max point of intersection of boxes

Definition at line 2710 of file CG_elem.cpp.

◆ intersectLineLine()

bool bitpit::CGElem::intersectLineLine	(	array3D const &	P1,
		array3D const &	n1,
		array3D const &	P2,
		array3D const &	n2,
		array3D &	P,
		double	distanceTolerance )

Computes intersection between two lines in 3D

Parameters

[in]	n1	direction of first line
[in]	P1	point on first line
[in]	n2	direction of second line
[in]	P2	point on second line
[out]	P	intersection point if intersect, else unaltered
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 1785 of file CG_elem.cpp.

◆ intersectLinePlane()

bool bitpit::CGElem::intersectLinePlane	(	array3D const &	P1,
		array3D const &	n1,
		array3D const &	P2,
		array3D const &	n2,
		array3D &	P,
		const double	coplanarityTolerance )

Computes intersection between line and plane

Parameters

[in]	P1	point on line
[in]	n1	direction of line
[in]	P2	point on plane
[in]	n2	normal to plane
[in]	coplanarityTolerance	if angle between the line and plane is less than this value, they are considered as coplanar and not intersecting
[out]	P	intersection point if intersect, else unaltered

Returns: if intersect

Definition at line 1837 of file CG_elem.cpp.

◆ intersectLinePolygon() [1/2]

bool bitpit::CGElem::intersectLinePolygon	(	array3D const &	P,
		array3D const &	n,
		std::size_t	nV,
		array3D const *	V,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between triangle and a convex polygon

Parameters

[in]	P	point on line
[in]	n	direction of line
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 2055 of file CG_elem.cpp.

◆ intersectLinePolygon() [2/2]

bool bitpit::CGElem::intersectLinePolygon	(	array3D const &	P,
		array3D const &	n,
		std::vector< array3D > const &	V,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between triangle and a convex polygon

Parameters

[in]	P	point on line
[in]	n	direction of line
[in]	V	polygon vertices coordinates
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 2040 of file CG_elem.cpp.

◆ intersectLineTriangle()

bool bitpit::CGElem::intersectLineTriangle	(	array3D const &	P,
		array3D const &	n,
		array3D const &	A,
		array3D const &	B,
		array3D const &	C,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between triangle and a line

Parameters

[in]	P	point on plane
[in]	n	normal to plane
[in]	A	first vertex of triangle
[in]	B	second vertex of triangle
[in]	C	third vertex of triangle
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 1986 of file CG_elem.cpp.

◆ intersectPlaneBox() [1/2]

bool bitpit::CGElem::intersectPlaneBox	(	array3D const &	P1,
		array3D const &	n1,
		array3D const &	A0,
		array3D const &	A1,
		int	dim,
		const double	distanceTolerance )

Computes if plane a box intersect

Parameters

[in]	P1	point on first plane
[in]	n1	normal to first plane
[in]	A0	min point of box
[in]	A1	max point of box
[in]	dim	number of dimensions
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 1952 of file CG_elem.cpp.

◆ intersectPlaneBox() [2/2]

bool bitpit::CGElem::intersectPlaneBox	(	array3D const &	P1,
		array3D const &	n1,
		array3D const &	A0,
		array3D const &	A1,
		std::vector< array3D > &	intersects,
		int	dim,
		const double	distanceTolerance )

Computes if plane a box intersect and intersection points between plane and edges of box

Parameters

[in]	P1	point on first plane
[in]	n1	normal to first plane
[in]	A0	min point of box
[in]	A1	max point of box
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	intersects	intersection points
[in]	dim	number of dimensions

Returns: if intersect

Definition at line 1969 of file CG_elem.cpp.

◆ intersectPlanePlane()

bool bitpit::CGElem::intersectPlanePlane	(	array3D const &	P1,
		array3D const &	n1,
		array3D const &	P2,
		array3D const &	n2,
		array3D &	Pl,
		array3D &	nl,
		const double	coplanarityTolerance )

Computes intersection between two planes

Parameters

[in]	P1	point on first plane
[in]	n1	normal to first plane
[in]	P2	point on second plane
[in]	n2	normal to second plane
[out]	Pl	point on intersection line
[out]	nl	direction of intersection line
[in]	coplanarityTolerance	if angle between planes is less than this value, they are considered as coplanar and not intersecting

Returns: if intersect

Definition at line 1900 of file CG_elem.cpp.

◆ intersectPointBox()

bool bitpit::CGElem::intersectPointBox	(	array3D const &	P,
		array3D const &	B1,
		array3D const &	B2,
		int	dim,
		const double	distanceTolerance )

checks if points lies within axis aligned box

Parameters

[in]	P	point coordinates
[in]	B1	min coodinates of box
[in]	B2	max coodinates of box
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if point in box

Definition at line 2568 of file CG_elem.cpp.

◆ intersectPointLine()

bool bitpit::CGElem::intersectPointLine	(	array3D const &	P,
		array3D const &	Q,
		array3D const &	n,
		const double	distanceTolerance )

checks if points lies on line defined by two given points in 3D

Parameters

[in]	P	point coordinates
[in]	Q	point on line
[in]	n	line direction
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if point lies on segment

Definition at line 2510 of file CG_elem.cpp.

◆ intersectPointSegment()

bool bitpit::CGElem::intersectPointSegment	(	array3D const &	P,
		array3D const &	P1,
		array3D const &	P2,
		const double	distanceTolerance )

checks if points lies on segment in 3D

Parameters

[in]	P	point coordinates
[in]	P1	start point of segment
[in]	P2	end point of segment
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if point lies on segment

Definition at line 2530 of file CG_elem.cpp.

◆ intersectPointTriangle()

bool bitpit::CGElem::intersectPointTriangle	(	array3D const &	P,
		array3D const &	A,
		array3D const &	B,
		array3D const &	C,
		const double	distanceTolerance )

checks if points lies on triangle

Parameters

[in]	P	point coordinates
[in]	A	first vertex of triangle
[in]	B	second vertex of triangle
[in]	C	third vertex of triangle
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if point lies on triangle

Definition at line 2549 of file CG_elem.cpp.

◆ intersectSegmentBox() [1/3]

bool bitpit::CGElem::intersectSegmentBox	(	array3D const &	V0,
		array3D const &	V1,
		array3D const &	A0,
		array3D const &	A1,
		bool	interiorSegmentVertice,
		bool	segmentBoxHullIntersection,
		std::vector< array3D > &	P,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a segment

Parameters

[in]	V0	start point of segment
[in]	V1	end point of segment
[in]	A0	min point of box
[in]	A1	max point of box
[in]	interiorSegmentVertice	if the segment vertices within the box should be added to the list of intersection points
[in]	segmentBoxHullIntersection	if the intersections between the segment and the outer hull of the box should be added to the list of intersection points
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	list of intersection points. If no intersetion points should be calculated nullptr can be passed as argument
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2251 of file CG_elem.cpp.

◆ intersectSegmentBox() [2/3]

bool bitpit::CGElem::intersectSegmentBox	(	array3D const &	V0,
		array3D const &	V1,
		array3D const &	A0,
		array3D const &	A1,
		bool	interiorSegmentVertice,
		bool	segmentBoxHullIntersection,
		std::vector< array3D > &	P,
		std::vector< int > &	flag,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a segment

Parameters

[in]	V0	start point of segment
[in]	V1	end point of segment
[in]	A0	min point of box
[in]	A1	max point of box
[in]	interiorSegmentVertice	if the segment vertices within the box should be added to the list of intersection points
[in]	segmentBoxHullIntersection	if the intersections between the segment and the outer hull of the box should be added to the list of intersection points
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	list of intersection points. If no intersetion points should be calculated nullptr can be passed as argument
[out]	flag	indicates for each intersection if it belongs to interiorSegmentVertice (flag=0) or segmentHullIntersection (flag=1)
[in]	dim	number of dimensions to be checked

Returns: if intersect

Definition at line 2270 of file CG_elem.cpp.

◆ intersectSegmentBox() [3/3]

bool bitpit::CGElem::intersectSegmentBox	(	array3D const &	V0,
		array3D const &	V1,
		array3D const &	A0,
		array3D const &	A1,
		int	dim,
		const double	distanceTolerance )

Computes intersection between an axis aligned bounding box and a segment

Parameters

[in]	V0	start point of segment
[in]	V1	end point of segment
[in]	A0	min point of box
[in]	A1	max point of box
[in]	dim	number of dimensions to be checked
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting

Returns: if intersect

Definition at line 2233 of file CG_elem.cpp.

◆ intersectSegmentPlane()

bool bitpit::CGElem::intersectSegmentPlane	(	array3D const &	Q1,
		array3D const &	Q2,
		array3D const &	P2,
		array3D const &	n2,
		array3D &	P,
		const double	distanceTolerance )

Computes intersection between segment and plane

Parameters

[in]	Q1	start point of segment
[in]	Q2	end point of segment
[in]	P2	point on plane
[in]	n2	normal to plane
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	P	intersection point if intersect, else unaltered

Returns: if intersect

Definition at line 1870 of file CG_elem.cpp.

◆ intersectSegmentPolygon() [1/2]

bool bitpit::CGElem::intersectSegmentPolygon	(	array3D const &	P0,
		array3D const &	P1,
		std::size_t	nV,
		array3D const *	V,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between a segment and a polygon

Parameters

[in]	P0	start point of segment
[in]	P1	end point of segment
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 2097 of file CG_elem.cpp.

◆ intersectSegmentPolygon() [2/2]

bool bitpit::CGElem::intersectSegmentPolygon	(	array3D const &	P0,
		array3D const &	P1,
		std::vector< array3D > const &	V,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between a segment and a polygon

Parameters

[in]	P0	start point of segment
[in]	P1	end point of segment
[in]	V	polygon vertices coordinates
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 2082 of file CG_elem.cpp.

◆ intersectSegmentSegment()

bool bitpit::CGElem::intersectSegmentSegment	(	array3D const &	P1,
		array3D const &	P2,
		array3D const &	Q1,
		array3D const &	Q2,
		array3D &	x,
		double	distanceTolerance )

Computes intersection between two segments in 3D

Parameters

[in]	P1	start point of first segment
[in]	P2	end point of first segment
[in]	Q1	start point of second segment
[in]	Q2	end point of second segment
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	x	intersection point if intersect, else unaltered

Returns: if intersect

Definition at line 1806 of file CG_elem.cpp.

◆ intersectSegmentTriangle()

bool bitpit::CGElem::intersectSegmentTriangle	(	array3D const &	P0,
		array3D const &	P1,
		array3D const &	A,
		array3D const &	B,
		array3D const &	C,
		array3D &	Q,
		const double	distanceTolerance )

Computes intersection between triangle and a segment

Parameters

[in]	P0	start point of segment
[in]	P1	end point of segment
[in]	A	first vertex of triangle
[in]	B	second vertex of triangle
[in]	C	third vertex of triangle
[in]	distanceTolerance	if distance among features exceed this value they are considered as not intersecting
[out]	Q	intersection point

Returns: if intersect

Definition at line 2014 of file CG_elem.cpp.

◆ polygonEdgesCount() [1/2]

int bitpit::CGElem::polygonEdgesCount	(	std::size_t	nV,
		array3D const *	V )

Gets the number of edges of a polygon

Parameters

[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates

Returns: number of edges

Definition at line 3007 of file CG_elem.cpp.

◆ polygonEdgesCount() [2/2]

int bitpit::CGElem::polygonEdgesCount ( std::vector< array3D > const & V )

Gets the number of edges of a polygon

Returns: number of edges

Definition at line 2996 of file CG_elem.cpp.

◆ polygonSubtriangleCount() [1/2]

int bitpit::CGElem::polygonSubtriangleCount	(	std::size_t	nV,
		array3D const *	V )

Gets the number of subtriangles of a polygon

See subtriangleOfPolygon(int triangle, std::size_t nV, array3D const *V, array3D &V0, array3D &V1, array3D &V2) for an explanation of how a polygon is divided in triangles.

Parameters

[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates

Returns: number of subtriangles

Definition at line 3037 of file CG_elem.cpp.

◆ polygonSubtriangleCount() [2/2]

int bitpit::CGElem::polygonSubtriangleCount ( std::vector< array3D > const & V )

Gets the number of subtriangles of a polygon

See subtriangleOfPolygon(int triangle, std::vector<array3D> const &V, array3D &V0, array3D &V1, array3D &V2) for an explanation of how a polygon is divided in triangles.

Returns: number of subtriangles

Definition at line 3022 of file CG_elem.cpp.

◆ projectCloudTriangle()

std::vector< array3D > bitpit::CGElem::projectCloudTriangle	(	std::vector< array3D > const &	cloud,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		std::vector< array3D > &	lambda )

Projects a point cloud onto a triangle. Projection points are the closest points to the original points within the triangle.

Parameters

[in]	cloud	point cloud coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[in,out]	lambda	barycentric coordinates of projection points

Returns: distances

Definition at line 1193 of file CG_elem.cpp.

◆ projectPointCone()

array3D bitpit::CGElem::projectPointCone	(	array3D const &	point,
		array3D const &	apex,
		array3D const &	axis,
		double	alpha )

Computes projection point on semi-infinite cone surface

Parameters

[in]	point	point coordinates
[in]	apex	cone apex
[in]	axis	cone axis
[in]	alpha	cone half angle

Returns: projection point

Definition at line 1313 of file CG_elem.cpp.

◆ projectPointLine()

array3D bitpit::CGElem::projectPointLine	(	array3D const &	P,
		array3D const &	Q,
		array3D const &	n )

Computes projection of point on line in 3D

Parameters

[in]	P	point coordinates
[in]	Q	point on line
[in]	n	line direction

Returns: projection point

Definition at line 970 of file CG_elem.cpp.

◆ projectPointPlane()

array3D bitpit::CGElem::projectPointPlane	(	array3D const &	P,
		array3D const &	Q,
		array3D const &	n )

Computes projection of point on line in 3D

Parameters

[in]	P	point coordinates
[in]	Q	point on plane
[in]	n	plane normal

Returns: projection point

Definition at line 983 of file CG_elem.cpp.

◆ projectPointPolygon() [1/5]

array3D bitpit::CGElem::projectPointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V )

Computes projection of point onto a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates

Returns: coordinates of projection point

Definition at line 1226 of file CG_elem.cpp.

◆ projectPointPolygon() [2/5]

array3D bitpit::CGElem::projectPointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V,
		double *	lambda )

Computes projection of point onto a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	lambda	baycentric coordinates of projection point

Returns: coordinates of projection point

Definition at line 1267 of file CG_elem.cpp.

◆ projectPointPolygon() [3/5]

array3D bitpit::CGElem::projectPointPolygon	(	array3D const &	P,
		std::size_t	nV,
		array3D const *	V,
		std::vector< double > &	lambda )

Computes projection of point onto a convex polygon

Parameters

[in]	P	point coordinates
[in]	nV	number of polygon vertices
[in]	V	polygon vertices coordinates
[out]	lambda	baycentric coordinates of projection point

Returns: coordinates of projection point

Definition at line 1252 of file CG_elem.cpp.

◆ projectPointPolygon() [4/5]

array3D bitpit::CGElem::projectPointPolygon	(	array3D const &	P,
		std::vector< array3D > const &	V )

Computes projection of point onto a convex polygon

Parameters

[in]	P	point coordinates
[in]	V	polygon vertices coordinates

Returns: coordinates of projection point

Definition at line 1214 of file CG_elem.cpp.

◆ projectPointPolygon() [5/5]

array3D bitpit::CGElem::projectPointPolygon	(	array3D const &	P,
		std::vector< array3D > const &	V,
		std::vector< double > &	lambda )

Computes projection of point onto a convex polygon

Parameters

[in]	P	point coordinates
[in]	V	polygon vertices coordinates
[out]	lambda	baycentric coordinates of projection point

Returns: coordinates of projection point

Definition at line 1239 of file CG_elem.cpp.

◆ projectPointSegment() [1/3]

array3D bitpit::CGElem::projectPointSegment	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1 )

Computes projection of point on line in 3D

Parameters

[in]	P	point coordinates
[in]	Q0	first line vertex
[in]	Q1	second line vertex

Returns: projection point

Definition at line 996 of file CG_elem.cpp.

◆ projectPointSegment() [2/3]

array3D bitpit::CGElem::projectPointSegment	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		double *	lambda )

Computes projection of point on line in 3D

Parameters

[in]	P	point coordinates
[in]	Q0	first line vertex
[in]	Q1	second line vertex
[out]	lambda	barycentric coordinates of projection point

Returns: projection point

Definition at line 1024 of file CG_elem.cpp.

◆ projectPointSegment() [3/3]

array3D bitpit::CGElem::projectPointSegment	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		std::array< double, 2 > &	lambda )

Computes projection of point on line in 3D

Parameters

[in]	P	point coordinates
[in]	Q0	first line vertex
[in]	Q1	second line vertex
[out]	lambda	barycentric coordinates of projection point

Returns: projection point

Definition at line 1011 of file CG_elem.cpp.

◆ projectPointTriangle() [1/3]

array3D bitpit::CGElem::projectPointTriangle	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2 )

Computes projection of point on triangle

Parameters

[in]	P	point coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex

Returns: coordinates of projection point

Definition at line 1049 of file CG_elem.cpp.

◆ projectPointTriangle() [2/3]

array3D bitpit::CGElem::projectPointTriangle	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		array3D &	lambda )

Computes projection of point on triangle

Parameters

[in]	P	point coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[out]	lambda	barycentric coordinates of projection point

Returns: coordinates of projection point

Definition at line 1066 of file CG_elem.cpp.

◆ projectPointTriangle() [3/3]

array3D bitpit::CGElem::projectPointTriangle	(	array3D const &	P,
		array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		double *	lambda )

Computes projection of point on triangle

Parameters

[in]	P	point coordinates
[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[out]	lambda	barycentric coordinates of projection point

Returns: coordinates of projection point

Definition at line 1080 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricPolygon() [1/3]

array3D bitpit::CGElem::reconstructPointFromBarycentricPolygon	(	std::size_t	nV,
		array3D const *	V,
		double const *	lambda )

Reconstructs a point from barycentric coordinates of a polygon

Parameters

[in]	nV	number of polygon vertices
[in]	V	vertices of simplex
[in]	lambda	barycentric coordinates

Returns: reconstructed Point

Definition at line 951 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricPolygon() [2/3]

array3D bitpit::CGElem::reconstructPointFromBarycentricPolygon	(	std::size_t	nV,
		array3D const *	V,
		std::vector< double > const &	lambda )

Reconstructs a point from barycentric coordinates of a polygon

Parameters

[in]	nV	number of polygon vertices
[in]	V	vertices of simplex
[in]	lambda	barycentric coordinates

Returns: reconstructed Point

Definition at line 939 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricPolygon() [3/3]

array3D bitpit::CGElem::reconstructPointFromBarycentricPolygon	(	std::vector< array3D > const &	V,
		std::vector< double > const &	lambda )

Reconstructs a point from barycentric coordinates of a polygon

Parameters

[in]	V	vertices of simplex
[in]	lambda	barycentric coordinates

Returns: reconstructed Point

Definition at line 927 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricSegment() [1/2]

array3D bitpit::CGElem::reconstructPointFromBarycentricSegment	(	array3D const &	Q0,
		array3D const &	Q1,
		double const *	lambda )

Reconstructs a point from barycentric coordinates of a segment

Parameters

[in]	Q0	first vertex of segment
[in]	Q1	second vertex of segment
[in]	lambda	barycentric coordinates

Returns: The reconstructed point

Definition at line 842 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricSegment() [2/2]

array3D bitpit::CGElem::reconstructPointFromBarycentricSegment	(	array3D const &	Q0,
		array3D const &	Q1,
		std::array< double, 2 > const &	lambda )

Reconstructs a point from barycentric coordinates of a segment

Parameters

[in]	Q0	first vertex of segment
[in]	Q1	second vertex of segment
[in]	lambda	barycentric coordinates

Returns: The reconstructed point

Definition at line 828 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricTriangle() [1/2]

array3D bitpit::CGElem::reconstructPointFromBarycentricTriangle	(	array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		double const *	lambda )

Reconstructs a point from barycentric coordinates of a triangle

Parameters

[in]	Q0	first vertex of triangle
[in]	Q1	second vertex of triangle
[in]	Q2	third vertex of triangle
[in]	lambda	barycentric coordinates

Returns: The reconstructed point

Definition at line 872 of file CG_elem.cpp.

◆ reconstructPointFromBarycentricTriangle() [2/2]

array3D bitpit::CGElem::reconstructPointFromBarycentricTriangle	(	array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		array3D const &	lambda )

Reconstructs a point from barycentric coordinates of a triangle

Parameters

[in]	Q0	first vertex of triangle
[in]	Q1	second vertex of triangle
[in]	Q2	third vertex of triangle
[in]	lambda	barycentric coordinates

Returns: The reconstructed point

Definition at line 857 of file CG_elem.cpp.

◆ restrictPointTriangle() [1/2]

array3D bitpit::CGElem::restrictPointTriangle	(	array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		array3D &	lambda )

Restricts a point given in barycentric coordinates on the triangle

Parameters

[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[in,out]	lambda	barycentric coordinates before and after restriction

Returns: coordinates of restricted point

Definition at line 1096 of file CG_elem.cpp.

◆ restrictPointTriangle() [2/2]

array3D bitpit::CGElem::restrictPointTriangle	(	array3D const &	Q0,
		array3D const &	Q1,
		array3D const &	Q2,
		double *	lambda )

Restricts a point given in barycentric coordinates on the triangle

Parameters

[in]	Q0	first triangle vertex
[in]	Q1	second triangle vertex
[in]	Q2	third triangle vertex
[in,out]	lambda	barycentric coordinates before and after restriction

Returns: coordinates of restricted point

Definition at line 1109 of file CG_elem.cpp.

◆ rotatePoint()

array3D bitpit::CGElem::rotatePoint	(	const array3D &	P,
		const array3D &	n0,
		const array3D &	n1,
		double	angle )

Rotates the point.

If the axis points are coincident, the function will return the given point with no rotation applied.

Parameters

[in]	P	is the point that will be rotated
[in]	n0	is a first point on the rotation axis
[in]	n1	is a second point on the rotation axis
[in]	angle	is the rotation angle, expressed in radiants and positive for counterclockwise rotations

Returns: The rotated point.

Definition at line 892 of file CG_elem.cpp.

◆ rotateVector()

array3D bitpit::CGElem::rotateVector	(	array3D const &	vector,
		array3D const &	axis,
		double	theta )

rotates a vector in 3D using Rodrigues' formula.

Parameters

[in]	vector	vector to be rotated
[in]	axis	rotation axis
[in]	theta	rotation angle

Returns: rotated vector

Definition at line 2968 of file CG_elem.cpp.

◆ subtractionAABB()

void bitpit::CGElem::subtractionAABB	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	B0,
		array3D const &	B1,
		array3D &	C0,
		array3D &	C1 )

computes the bounding box of the relative complement two axis aligned bounding boxes

Parameters

[in]	A0	min point of first bounding box
[in]	A1	max point of first bounding box
[in]	B0	min point of second bounding box
[in]	B1	max point of second bounding box
[out]	C0	min point of relative complement
[out]	C1	max point of relative complement

Definition at line 2725 of file CG_elem.cpp.

◆ subtriangleOfPolygon() [1/2]

void bitpit::CGElem::subtriangleOfPolygon	(	int	triangle,
		std::size_t	nV,
		array3D const *	V,
		array3D &	V0,
		array3D &	V1,
		array3D &	V2 )

Gets the subtriangle vertices' coordinates of a convex polygon

The vertices of the n-th subtriangle will be defined as follows: V0: is the centroid of the polygon; V1: is the n-th vertex of the polygon; V2: is the vertex following the n-th vertex of the polygon.

Parameters

[in]	triangle	index of triangle
[in]	nV	number of polygon vertices
[in]	V	polgon vertices
[in]	V0	coordinates of first triangle's vertex
[in]	V1	coordinates of second triangle's vertex
[in]	V2	coordinates of third triangle's vertex

Definition at line 3107 of file CG_elem.cpp.

◆ subtriangleOfPolygon() [2/2]

void bitpit::CGElem::subtriangleOfPolygon	(	int	triangle,
		std::vector< array3D > const &	V,
		array3D &	V0,
		array3D &	V1,
		array3D &	V2 )

Gets the subtriangle vertices' coordinates of a convex polygon

The vertices of the n-th subtriangle are be defined as follows: V0: is the centroid of the polygon; V1: is the n-th vertex of the polygon; V2: is the vertex following the n-th vertex of the polygon.

Parameters

[in]	triangle	index of triangle
[in]	V	polgon vertices
[in]	V0	coordinates of first triangle's vertex
[in]	V1	coordinates of second triangle's vertex
[in]	V2	coordinates of third triangle's vertex

Definition at line 3087 of file CG_elem.cpp.

◆ unionAABB() [1/2]

void bitpit::CGElem::unionAABB	(	array3D const &	A0,
		array3D const &	A1,
		array3D const &	B0,
		array3D const &	B1,
		array3D &	C0,
		array3D &	C1 )

computes the bounding box of the union of two axis aligned bounding boxes

Parameters

[in]	A0	min point of first bounding box
[in]	A1	max point of first bounding box
[in]	B0	min point of second bounding box
[in]	B1	max point of second bounding box
[out]	C0	min point of union bounding box
[out]	C1	max point of union bounding box

Definition at line 2667 of file CG_elem.cpp.

◆ unionAABB() [2/2]

void bitpit::CGElem::unionAABB	(	std::vector< array3D > const &	A0,
		std::vector< array3D > const &	A1,
		array3D &	C0,
		array3D &	C1 )

computes the bounding box of the union of several axis aligned bounding boxes

Parameters

[in]	A0	min points of bounding boxes
[in]	A1	max points of bounding boxes
[out]	C0	min point of union bounding box
[out]	C1	max point of union bounding box

Definition at line 2684 of file CG_elem.cpp.

◆ validBarycentric()

bool bitpit::CGElem::validBarycentric	(	double const *	lambdaPtr,
		int	n )

Checks if barycentric coordinates is valid

Parameters

[in]	lambdaPtr	pointer to barycentric coordinates
[in]	n	number of points

Returns: true if valid

Definition at line 585 of file CG_elem.cpp.

◆ validLine()

bool bitpit::CGElem::validLine	(	const array3D &	P,
		const array3D &	n )

Checks if a line is valid

Parameters

[in]	P	point on line;
[in]	n	line direction

Returns: true if valid

Definition at line 528 of file CG_elem.cpp.

◆ validPlane()

bool bitpit::CGElem::validPlane	(	const array3D &	P,
		const array3D &	n )

Checks if a plane is valid

Parameters

[in]	P	point on plane
[in]	n	plane normal

Returns: true if valid

Definition at line 540 of file CG_elem.cpp.

◆ validSegment()

bool bitpit::CGElem::validSegment	(	const array3D &	P0,
		const array3D &	P1 )

Checks if a segment is valid

Parameters

[in]	P0	start point of segment
[in]	P1	end point of segment

Returns: true if valid

Definition at line 517 of file CG_elem.cpp.

◆ validTriangle()

bool bitpit::CGElem::validTriangle	(	const array3D &	P0,
		const array3D &	P1,
		const array3D &	P2 )

Checks if a triangle is valid

Parameters

[in]	P0	first triangle vertex
[in]	P1	second triangle vertex
[in]	P2	third triangle vertex

Returns: true if valid

Definition at line 553 of file CG_elem.cpp.

◆ vertexOfBox()

void bitpit::CGElem::vertexOfBox	(	int	i,
		array3D const &	A0,
		array3D const &	A1,
		array3D &	P )

computes the vertex coordiantes of a box

Parameters

[in]	i	vertex index
[in]	A0	min point of bounding box
[in]	A1	max point of bounding box
[out]	P	vertex coordinates

Definition at line 2899 of file CG_elem.cpp.

◆ vertexOfSegment()

void bitpit::CGElem::vertexOfSegment	(	int	i,
		array3D const &	V0,
		array3D const &	V1,
		array3D &	P )

returns the vertex coordiantes of a segment given its index

Parameters

[in]	i	edge index
[in]	V0	first vertex of segment
[in]	V1	second vertex of segment
[out]	P	vertex

Definition at line 2755 of file CG_elem.cpp.

◆ vertexOfTriangle()

void bitpit::CGElem::vertexOfTriangle	(	int	i,
		array3D const &	V0,
		array3D const &	V1,
		array3D const &	V2,
		array3D &	P )

returns the vertex coordiantes of a triangle given its index

Parameters

[in]	i	edge index
[in]	V0	first vertex of triangle
[in]	V1	second vertex of triangle
[in]	V2	third vertex of triangle
[out]	P	vertex

Definition at line 2783 of file CG_elem.cpp.

Variable Documentation

◆ boxEdgeVertexConnectivity

const std::array< std::array<int,2>,12> bitpit::CGElem::boxEdgeVertexConnectivity

Initial value:

=
{{
    std::array<int,2>{ {0,2} },
    std::array<int,2>{ {1,3} },
    std::array<int,2>{ {0,1} },
    std::array<int,2>{ {2,3} },
    std::array<int,2>{ {4,6} },
    std::array<int,2>{ {5,7} },
    std::array<int,2>{ {4,5} },
    std::array<int,2>{ {6,7} },
    std::array<int,2>{ {0,4} },
    std::array<int,2>{ {1,5} },
    std::array<int,2>{ {2,6} },
    std::array<int,2>{ {3,7} }
 
}}

The edge vertex connectivty of a box

Definition at line 53 of file CG.hpp.

◆ boxFaceVertexConnectivity

const std::array< std::array<int,4>, 6> bitpit::CGElem::boxFaceVertexConnectivity

Initial value:

=
{{
    std::array<int,4>{ {0,2,6,4} },
    std::array<int,4>{ {1,3,7,5} },
    std::array<int,4>{ {0,4,5,1} },
    std::array<int,4>{ {2,6,7,3} },
    std::array<int,4>{ {0,1,3,2} },
    std::array<int,4>{ {4,5,7,6} }
}}

The face vertex connectivty of a box

Definition at line 73 of file CG.hpp.

◆ DEFAULT_COPLANARITY_TOLERANCE

const double bitpit::CGElem::DEFAULT_COPLANARITY_TOLERANCE = 1.e-12

Definition at line 48 of file CG.hpp.

◆ DEFAULT_DISTANCE_TOLERANCE

const double bitpit::CGElem::DEFAULT_DISTANCE_TOLERANCE = 1.e-12

Definition at line 47 of file CG.hpp.