Groups utilitary routines for working with geometry. More...

Functions
static double	angleScore2D (const GmVector &a, const GmVector &b, const GmVector &c)
	Returns the angle score of the ca and cb vectors in 2D. If score is: More...

static double	orientScore2D (const GmVector &a, const GmVector &b, const GmVector &c)
	Returns the orientation score of the a, b and c points in 2D. Returns a positive value if the points a, b and c are arranged in CCW order, a negative value if the points are in CW order, and zero if the points are collinear. A more common (but less symmetric) interpretation is that it returns a positive value if a lies to the left of the directed line bc (see https://people.eecs.berkeley.edu/~jrs/meshpapers/robnotes.pdf). Can be used in 3D but only x and y coordinates will be considered.

static double	orientScore3D (const GmVector &a, const GmVector &b, const GmVector &c, const GmVector &d)
	Given four points a, b, c, and d, returns the signed volume of the parallelepiped determined by the vectors ad, bd and cd. It is positive if the points occur in the orientation illustrated in Figure 3 (see https://people.eecs.berkeley.edu/~jrs/meshpapers/robnotes.pdf), negative if they occur in the mirror-image orientation, and zero if the four points are coplanar. You can apply a right-hand rule : orient your right hand with fingers curled to follow the circular sequence bcd. If your thumb points toward a, a positive value is returned.

static bool	sameSide3D (const GmVector &p, const GmVector &n, const GmVector &a, const GmVector &b)
	Returns true if points a and b are on the same side of plane defined by point p and normal n.

static bool	sameSide3D (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &a, const GmVector &b)
	Returns true if points a and b are on the same side of plane defined by points p1, p2 and p3.

static GmMatrix	rotationMatrix (const GmVector &u, double angle)

double	edgeLength (const GmVector &p1, const GmVector &p2)
	Calculates the length of the edge determined by points p1 and p2.

double	triangleArea (const GmVector &p1, const GmVector &p2, const GmVector &p3)
	Calculates the area of the triangle determined by points p1, p2 and p3 (2D or 3D), organized in CCW order.

double	quadArea (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4)
	Calculates the area of a quad defined by points p1 to p4 (2D or 3D), defined in CCW order.

double	hexahedronVolume (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5, const GmVector &p6, const GmVector &p7, const GmVector &p8)
	Calculates the volume of the given hexahedron. Points follow the standard Hex cell definition.

double	tetrahedronVolume (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4)
	Calculates the volume of the given tetrahedron. Points follow the standard Tet cell definition.

double	wedgeVolume (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5, const GmVector &p6)
	Calculates the volume of the given wedge. Points follow the standard Wedge cell definition.

double	pyramidVolume (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5)
	Calculates the volume of the given pyramid. Points follow the standard pyramid cell definition.

void	edgeCentroid (const GmVector &p1, const GmVector &p2, GmVector &coord)
	Returns the cartesian coordinate of the edge centroid.

void	triangleCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, GmVector &coord)
	Returns the cartesian coordinate of the triangle centroid.

void	quadCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, GmVector &coord)
	Returns the cartesian coordinate of the quad centroid.

void	hexahedronCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5, const GmVector &p6, const GmVector &p7, const GmVector &p8, GmVector &coord)

void	tetrahedronCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, GmVector &coord)
	Returns the cartesian coordinate of the tetrahedron centroid.

void	wedgeCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5, const GmVector &p6, GmVector &coord)
	Returns the cartesian coordinate of the wedge centroid.

void	pyramidCentroid (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4, const GmVector &p5, GmVector &coord)
	Returns the cartesian coordinate of the pyramid centroid.

double	intersectionLength (double a0, double a1, double b0, double b1)
	Intersection length between two intervals Positive for intervals intersecting, negative otherwise.

bool	lineIntersection (GmVector &A, GmVector &B, GmVector &C, GmVector &D, double eps=1e-7)
	Returns true if the lines AB and CD intersect Assumes A, B, C and D are 2D, doesnt cosider the segments extreme points for intersection.

bool	polygon2DIsSelfIntersecting (const GmMatrix &X)
	Returns true if the polygon delimited by the cell vertices is self-intersecting, or false otherwise. More...

bool	polygon2DIsCCW (const GmMatrix &X)
	Returns true if the polygon delimited by the cell vertices is oriented CCW. More...

bool	polygonIsConvex (const GmMatrix &X)
	Returns true if the polygon delimited by the cell vertices is convex, or false otherwise. More...

bool	polygon3DIsPlanar (const GmMatrix &X, double tol)
	Returns true if the polygon delimited by the cell vertices is planar. More...

GmMatrix	shuffle (const GmMatrix &X, const int order[], int size)
	Returns quad8 vertices in circular order. More...

bool	tri3DIsColinear (const GmMatrix &X, double eps)

bool	pointInConvexPolygon (const GmMatrix &X, const GmVector &p)
	Returns true if the point p is inside the polygon delimited by the cell vertices (convex hull), or false otherwise. More...

bool	pointInTesselatedPolygon_T6 (const GmMatrix &X, const GmVector &p)
	Returns true if the point p is inside the tesselated T6 polygon or false otherwise. More...

bool	pointInTesselatedPolygon_Q8 (const GmMatrix &X, const GmVector &p)
	Returns true if the point p is inside the tesselated Q8 polygon or false otherwise. More...

bool	pointInPolygon (const GmMatrix &X, const GmCellGeometry &g, const GmVector &p)
	Returns true if the point p is inside the polygon delimited by the cell vertices, or false otherwise. More...

static bool	pointInTetrahedron (const GmMatrix &X, const GmVector &p, QVector< bool > &ss)
	Helper function for pointInTetrahedron(X, p) also returning the "same side" vector.

bool	pointInTetrahedron (const GmMatrix &X, const GmVector &p)
	Returns true if the point p is inside the tetrahedron, or false otherwise. The X matrix should be the node matrix for a GeMA TET4 element with nodes in columns.

bool	pointInHexahedron (const GmMatrix &X, const GmVector &p)

bool	isTriNormalOutward (const GmVector &p0, const GmVector &p1, const GmVector &p2, const GmVector &ref)

bool	isQuadNormalOutward (const GmVector &p0, const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &ref)

bool	hex8PlanarFaces (const GmMatrix &X, double tol)

bool	hex8IsWellDefined (const GmMatrix &X)

void	lineProjection (const GmVector &a, const GmVector &b, const GmVector &p, double t, double u)

template<int N>
bool	checkQuadraticEdges (const GmMatrix &X, double proportion_max, int edges[N][3])

bool	tet10ValidEdges (const GmMatrix &X, double proportion_max)

bool	hex20ValidEdges (const GmMatrix &X, double proportion_max)
	Returns true if the points defined between the edges of hex20 follows: 1) Their projection to the 3d line containing the edge is within the edge, i.e., their parametrization is in (0,1) 2) The distance to the projection is not greater than a proportion of the edge length.

bool	hex27ValidFacesCenter (const GmMatrix &X, double tol)
	Returns true if face center point is collinear with the face. Assumes that the quad faces are planar.

bool	pyra5IsWellDefined (const GmMatrix &X, double tol)

bool	pyra13ValidEdges (const GmMatrix &X, double proportion_max)

bool	wedge6IsWellDefined (const GmMatrix &X, double tol)

bool	wedge15ValidEdges (const GmMatrix &X, double proportion_max)

double	pointToConvexPolygon (const GmMatrix &X, const GmVector &p, GmVector &proj)
	Returns the dquared distance of point p to the polygon delimited by the cell vertices (convex hull) and fills the coordinates of the corresponding projected point on cell. More...

double	pointToTetrahedron (const GmMatrix &X, const GmVector &p, GmVector &proj)
	Returns the squared distance of point p to the tetrahedron delimited by its vertices and fills the coordinates of the corresponding projected point on tetrahedron. More...

bool	tet4IsWellDefined (const GmVector &p1, const GmVector &p2, const GmVector &p3, const GmVector &p4)

bool	isCoplanar3D (const GmVector &a, const GmVector &b, const GmVector &c, const GmVector &d, double tol)

void	get2DPlaneRotationVectors (const GmVector &origin, const GmVector &v1, const GmVector &v2, GmVector &ix, GmVector &iy)

GmMatrix	get2DProjectionMatCol (const GmMatrix &X)
	Returns a 2x3 rigid transform matrix taking v1-origin and v2-origin 3D vectors to the 2D xy plane.

GmMatrix	get2DProjectionMatRow (const GmMatrix &X)
	Returns a 3x2 (transposed) rigid transform matrix taking v1-origin and v2-origin 3D vectors to the 2D xy plane.

QVector< QVector< int > >	edgeFaceList (const QVector< QVector< int >> &faceEdgeList, int edgeCount)
	Returns a edgeFace Vector of faces indexed by edge Its input is the inverse map faceEdge Vector.

Variables
static int	hex2tet [6][4]
	Returns true if the point p is inside the hexahedron, or false otherwise. The X matrix should be the node matrix for a GeMA HEX8 element with nodes in columns. More...

Detailed Description

Groups utilitary routines for working with geometry.

Function Documentation

◆ angleScore2D()

static double GmGeometryUtils::angleScore2D	(	const GmVector &	a,
		const GmVector &	b,
		const GmVector &	c
	)

static

Returns the angle score of the ca and cb vectors in 2D. If score is:

positive it means that angle is acute (< 90Âº);
equals to zero, angle is right (= 90Âº);
negative, angle is obtuse (> 90Âº). Can be used in 3D but only x and y coordinates will be considered.

◆ hexahedronCentroid()

GMC_API_EXPORT void GmGeometryUtils::hexahedronCentroid	(	const GmVector &	p1,
		const GmVector &	p2,
		const GmVector &	p3,
		const GmVector &	p4,
		const GmVector &	p5,
		const GmVector &	p6,
		const GmVector &	p7,
		const GmVector &	p8,
		GmVector &	coord
	)

Returns the cartesian coordinate of the hexahedron centroid fails for non-convex

◆ pointInConvexPolygon()

GMC_API_EXPORT bool GmGeometryUtils::pointInConvexPolygon	(	const GmMatrix &	X,
		const GmVector &	p
	)

Returns true if the point p is inside the polygon delimited by the cell vertices (convex hull), or false otherwise.

The X matrix should be 2 x n where n is the number of polygon vertices and it should provide the nodes in a "circular" order. Keep in mind that this is NOT true for the standard GeMA node matrix for QUADRATIC elements.

◆ pointInPolygon()

GMC_API_EXPORT bool GmGeometryUtils::pointInPolygon	(	const GmMatrix &	X,
		const GmCellGeometry &	g,
		const GmVector &	p
	)

Returns true if the point p is inside the polygon delimited by the cell vertices, or false otherwise.

Based on point-in-polygon algorithm, see http://alienryderflex.com/polygon/ for more details. If the node is exactly on the edge of the polygon, then the function may return true or false. Note that division by zero is avoided because the division is protected by the "if" clause which surrounds it.

The X matrix should be the node matrix for a GeMA surfcae element with nodes in columns. The cell geometry object is used to traverse the polygon nodes in a "circular" order, even for quadratic elements.

◆ pointInTesselatedPolygon_Q8()

GMC_API_EXPORT bool GmGeometryUtils::pointInTesselatedPolygon_Q8	(	const GmMatrix &	X,
		const GmVector &	p
	)

Returns true if the point p is inside the tesselated Q8 polygon or false otherwise.

The Quad8 surface is approximated by converting the Quad8 into 4 quad4. The X matrix should be the node matrix for a GeMA QUAD8 element with nodes in columns.

◆ pointInTesselatedPolygon_T6()

GMC_API_EXPORT bool GmGeometryUtils::pointInTesselatedPolygon_T6	(	const GmMatrix &	X,
		const GmVector &	p
	)

Returns true if the point p is inside the tesselated T6 polygon or false otherwise.

The Tri6 surface is approximated by converting the TRI6 into 4 triangles. The X matrix should be the node matrix for a GeMA TRI6 element with nodes in columns.

◆ pointToConvexPolygon()

GMC_API_EXPORT double GmGeometryUtils::pointToConvexPolygon	(	const GmMatrix &	X,
		const GmVector &	p,
		GmVector &	proj
	)

Returns the dquared distance of point p to the polygon delimited by the cell vertices (convex hull) and fills the coordinates of the corresponding projected point on cell.

Assume p is outside of the polygon. The X matrix should be 2 x n where n is the number of polygon vertices and it should provide the nodes in a "circular" order. Keep in mind that this is NOT true for the standard GeMA node matrix for QUADRATIC elements.

◆ pointToTetrahedron()

GMC_API_EXPORT double GmGeometryUtils::pointToTetrahedron	(	const GmMatrix &	X,
		const GmVector &	p,
		GmVector &	proj
	)

Returns the squared distance of point p to the tetrahedron delimited by its vertices and fills the coordinates of the corresponding projected point on tetrahedron.

Assume p is outside of the tetrahedron. The X matrix should be the node matrix for a GeMA TET4 element with nodes in columns.

IMPORTANT (by cmendes): Does this function work? Was it even tested? I don't think so.... :(

◆ polygon2DIsCCW()

GMC_API_EXPORT bool GmGeometryUtils::polygon2DIsCCW ( const GmMatrix & X )

Returns true if the polygon delimited by the cell vertices is oriented CCW.

The X matrix should be 2 x n where n is the number of polygon vertices.

◆ polygon2DIsSelfIntersecting()

GMC_API_EXPORT bool GmGeometryUtils::polygon2DIsSelfIntersecting ( const GmMatrix & X )

Returns true if the polygon delimited by the cell vertices is self-intersecting, or false otherwise.

The X matrix should be 2 x n where n is the number of polygon vertices and it should provide the nodes in a "circular" order. Keep in mind that this is NOT true for the standard GeMA node matrix for QUADRATIC elements.

◆ polygon3DIsPlanar()

GMC_API_EXPORT bool GmGeometryUtils::polygon3DIsPlanar	(	const GmMatrix &	X,
		double	tol
	)

Returns true if the polygon delimited by the cell vertices is planar.

The X matrix should be 3 x n where n is the number of polygon vertices. The eps is the floating point comparison tolerance, default is 1e-7.

We could probably speed up it by re-using the cross product of each vertice but the function 'isCoplanar3D' is already implemented, tested and uses a formula with smaller fp error.

◆ polygonIsConvex()

GMC_API_EXPORT bool GmGeometryUtils::polygonIsConvex ( const GmMatrix & X )

Returns true if the polygon delimited by the cell vertices is convex, or false otherwise.

The X matrix should be 2 x n where n is the number of polygon vertices and it should provide the nodes in a "circular" order. Keep in mind that this is NOT true for the standard GeMA node matrix for QUADRATIC elements.

◆ shuffle()

GMC_API_EXPORT GmMatrix GmGeometryUtils::shuffle	(	const GmMatrix &	X,
		const int	order[],
		int	size
	)

Returns quad8 vertices in circular order.

The X matrix should be n x 8 where n is the number of dimensions. The original ordering of quad8 vertices can be found in gmQuadCellGeometryInfo.cpp

Variable Documentation

◆ hex2tet

int GmGeometryUtils::hex2tet[6][4]

static

Initial value:

= {
    {0, 5, 7, 4},
    {0, 1, 7, 5},
    {1, 6, 7, 5},
    {0, 7, 2, 3},
    {0, 7, 1, 2},
    {1, 7, 6, 2},
}

Returns true if the point p is inside the hexahedron, or false otherwise. The X matrix should be the node matrix for a GeMA HEX8 element with nodes in columns.

Functions

Variables

Detailed Description

Function Documentation

◆ angleScore2D()

◆ hexahedronCentroid()

◆ pointInConvexPolygon()

◆ pointInPolygon()

◆ pointInTesselatedPolygon_Q8()

◆ pointInTesselatedPolygon_T6()

◆ pointToConvexPolygon()

◆ pointToTetrahedron()

◆ polygon2DIsCCW()

◆ polygon2DIsSelfIntersecting()

◆ polygon3DIsPlanar()

◆ polygonIsConvex()

◆ shuffle()

Variable Documentation

◆ hex2tet