math_util.h File Reference

#include <cstdlib>
#include "math_constants.h"
#include "../math_vector_matrix/math_vector.h"
#include "../math_vector_matrix/math_vector_functions.h"
#include "../ugmath_types.h"
#include "../../ug_config.h"
#include "eigenvalues.h"
#include "math_util_impl.hpp"

Go to the source code of this file.

Namespaces
namespace	ug
	the ug namespace

Functions
int	ug::BinomCoeff (int n, int k)
	Returns the BinomialCoefficient.
template<class vector_t >
bool	ug::BoxBoundProbe (const vector_t &v, const vector_t &boxMin, const vector_t &boxMax)
	Returns true if the point lies inside or on the boundary of the box.
template<class vector_t >
bool	ug::BoxBoxIntersection (const vector_t &box1Min, const vector_t &box1Max, const vector_t &box2Min, const vector_t &box2Max)
	checks whether two boxes intersect.
template<class vector_t >
void	ug::CalculateCenter (vector_t &centerOut, const vector_t *pointSet, size_t numPoints)
	calculates the center of a point-set
void	ug::CalculateCovarianceMatrix (matrix33 &matOut, const vector3 *pointSet, const vector3 &center, size_t numPoints)
	Calculates the covariance matrix of a given point-set.
number	ug::CalculateHexahedronVolume (const vector3 &a, const vector3 &b, const vector3 &c, const vector3 &d, const vector3 &e, const vector3 &f, const vector3 &g, const vector3 &h)
number	ug::CalculateOctahedronVolume (const vector3 &a, const vector3 &b, const vector3 &c, const vector3 &d, const vector3 &e, const vector3 &f)
number	ug::CalculatePrismVolume (const vector3 &a, const vector3 &b, const vector3 &c, const vector3 &d, const vector3 &e, const vector3 &f)
number	ug::CalculatePyramidVolume (const vector3 &a, const vector3 &b, const vector3 &c, const vector3 &d, const vector3 &e)
number	ug::CalculateTetrahedronVolume (const vector3 &a, const vector3 &b, const vector3 &c, const vector3 &d)
template<class TNumber >
TNumber	ug::clip (TNumber val, TNumber lowerBound, TNumber upperBound)
	clips a number to the given interval [lowerBound, upperBound].
bool	ug::ConstructOrthonormalSystem (matrix33 &matOut, const vector3 &v, size_t vColInd)
	constructs a orthonormal matrix given a vector in 3d.
template<class TNumber >
TNumber	ug::deg_to_rad (TNumber deg)
number	ug::DistanceLineToLine (const vector3 &a1, const vector3 &a2, const vector3 &b1, const vector3 &b2)
	calculates the distance between two 3d line segments
template<class vector_t >
number	ug::DistancePointToLine (const vector_t &v, const vector_t &v1, const vector_t &v2)
	calculates the distance of a point to a line segment
template<class vector_t >
number	ug::DistancePointToLine (number &tOut, const vector_t &v, const vector_t &v1, const vector_t &v2)
template<class vector_t >
number	ug::DistancePointToPlane (const vector_t &v, const vector_t &p, const vector_t &n)
	Calculates the distance between the specified point and the plane.
template<class vector_t >
number	ug::DistancePointToRay (const vector_t &v, const vector_t &from, const vector_t &dir)
	calculates the distance of a point to a ray
template<class vector_t >
number	ug::DistancePointToRay (number &tOut, const vector_t &v, const vector_t &from, const vector_t &dir)
template<class vector_t >
number	ug::DistancePointToTriangle (vector_t &vOut, number &bc1Out, number &bc2Out, const vector_t &p, const vector_t &v1, const vector_t &v2, const vector_t &v3, const vector_t &n)
	calculates the minimal distance of a point to a triangle.
template<class vector_t >
number	ug::DropAPerpendicular (vector_t &vOut, const vector_t &v, const vector_t &v0, const vector_t &v1)
	finds the projection of v onto the line defined by v0 and v1
bool	ug::FindClosestPlane (vector3 &centerOut, vector3 &normalOut, const vector3 *pointSet, size_t numPoints)
	Finds the plane which minimizes the distance to the given point set.
bool	ug::FindNormal (vector3 &normOut, const vector3 &v)
	finds a normal to the given vector in 3d.
template<class vector_t >
number	ug::GeometricApproximationDegree (vector_t &n1, vector_t &n2, vector_t &n3, vector_t &tn)
	the returned degree lies between 0 and 1. The closer to 1 the better.
template<class vector_t >
bool	ug::LineBoxIntersection (const vector_t &v1, const vector_t &v2, const vector_t &boxMin, const vector_t &boxMax)
	checks whether the given line-segment (v1, v2) intersect the given box.
template<class vector_t >
bool	ug::LineLineIntersection2d (vector_t &vOut, number &t0Out, number &t1Out, const vector_t &from0, const vector_t &to0, const vector_t &from1, const vector_t &to1, const number threshold=0)
	calculates the intersection of a two lines in 2d
bool	ug::LineLineIntersection3d (vector3 &aOut, vector3 &bOut, const vector3 &a1, const vector3 &a2, const vector3 &b1, const vector3 &b2)
	intersects two 3d line segments
template<class vector_t >
bool	ug::LineLineProjection (number &t1Out, number &t2Out, const vector_t &a1, const vector_t &a2, const vector_t &b1, const vector_t &b2)
	calculates the closest point between the rays through the given lines.
template<class vector_t >
int	ug::LineSphereIntersection (number &s1Out, number &s2Out, const vector_t &v1, const vector_t &v2, const vector_t &center, number radius)
template<class vector_t >
bool	ug::PointIsInsideQuadrilateral (const vector_t &v, const vector_t &v0, const vector_t &v1, const vector_t &v2, const vector_t &v3)
	Returns true if the point lies inside or on the boundary of a quadrilateral.
template<class vector_t >
bool	ug::PointIsInsideTetrahedron (const vector_t &v, const vector_t &v0, const vector_t &v1, const vector_t &v2, const vector_t &v3)
	Returns true if the point lies inside or on the boundary of a tetrahedron.
template<class vector_t >
bool	ug::PointIsInsideTriangle (const vector_t &v, const vector_t &v0, const vector_t &v1, const vector_t &v2)
	Returns true if the point lies inside or on the boundary of a triangle.
template<class vector_t >
bool	ug::PointIsInsideTriangle_HighAcc (const vector_t &v, const vector_t &v0, const vector_t &v1, const vector_t &v2)
	Returns true if the point lies inside or on a side of the given triangle.
template<class vector_t >
vector_t	ug::PointOnRay (const vector_t &from, const vector_t &dir, number s)
	returns the point described by a relative ray coordinate
template<class vector_t >
number	ug::ProjectPointToLine (vector_t &vOut, const vector_t &v, const vector_t &from, const vector_t &to)
	finds the projection of v onto the line defined by from and to
template<class vector_t >
void	ug::ProjectPointToPlane (vector_t &vOut, const vector_t &v, const vector_t &p, const vector_t &n)
	projects v onto the plane defined by the point p and the planes normal n.
template<class vector_t >
number	ug::ProjectPointToRay (vector_t &vOut, const vector_t &v, const vector_t &from, const vector_t &dir)
	finds the projection of v onto the ray defined by from and dir
template<class vector_t >
number	ug::QuadrilateralArea (const vector_t &p1, const vector_t &p2, const vector_t &p3, const vector_t &p4)
	calculates the are of the triangle defined by p1, p2 and p3
template<class TNumber >
TNumber	ug::rad_to_deg (TNumber rad)
template<class vector_t >
bool	ug::RayBoxIntersection (const vector_t &rayFrom, const vector_t &rayDir, const vector_t &boxMin, const vector_t &boxMax, number *tNearOut=NULL, number *tFarOut=NULL)
	checks if a ray is intersecting a box
bool	ug::RayCylinderIntersection (number &tMinOut, number &tMaxOut, const vector3 &rayFrom, const vector3 &rayDir, const vector3 &cylCenter, const vector3 &cylAxis, number cylRadius)
	returns the parameter values at which a given ray intersects an infinite cylinder.
template<class vector_t >
bool	ug::RayLineIntersection2d (vector_t &vOut, number &bcOut, number &tOut, const vector_t &p0, const vector_t &p1, const vector_t &vFrom, const vector_t &vDir, number sml=0)
	calculates the intersection of a ray with a Line in 2d
template<class vector_t >
bool	ug::RayPlaneIntersection (vector_t &vOut, number &tOut, const vector_t &rayFrom, const vector_t &rayDir, const vector_t &p, const vector_t &n)
	calculates the intersection of the ray rayFrom+t*rayDir and the plane (x-p)*n=0.
template<class vector_t >
bool	ug::RayRayIntersection2d (vector_t &vOut, number &t0Out, number &t1Out, const vector_t &p0, const vector_t &dir0, const vector_t &p1, const vector_t &dir1)
	calculates the intersection of two Rays in 2d
bool	ug::RayRayIntersection3d (vector3 &aOut, vector3 &bOut, const vector3 &p0, const vector3 &dir0, const vector3 &p1, const vector3 &dir1)
	intersects two 3d rays
template<class vector_t >
bool	ug::RayRayProjection (number &t1Out, number &t2Out, const vector_t &from1, const vector_t &dir1, const vector_t &from2, const vector_t &dir2)
	Calculates the parameter values at wich two rays are closest.
template<class vector_t >
int	ug::RaySphereIntersection (number &s1Out, number &s2Out, const vector_t &v, const vector_t &dir, const vector_t &center, number radius)
	checks whether the line segment (v1, v2) intersect the given sphere.
template<class vector_t >
bool	ug::RayTriangleIntersection (vector_t &vOut, const vector_t &p0, const vector_t &p1, const vector_t &p2, const vector_t &vFrom, const vector_t &vDir)
	calculates the intersection of a ray with a triangle
template<class vector_t >
bool	ug::RayTriangleIntersection (vector_t &vOut, number &bc1Out, number &bc2Out, number &tOut, const vector_t &p0, const vector_t &p1, const vector_t &p2, const vector_t &vFrom, const vector_t &vDir, const number small=SMALL)
	calculates the intersection of a ray with a triangle
template<class vector_t >
void	ug::ReflectVectorAtPlane (vector_t &vReflectedOut, const vector_t &v, const vector_t &n, const vector_t &r0)
	reflects a vector at a plane
template<class TNumber >
TNumber	ug::sq (TNumber val)
	returns the square of a value (val*val)
bool	ug::TransformPointSetTo2D (vector2 *pointSetOut, const vector3 *pointSet, size_t numPoints)
	transforms points from 3d space to 2d space.
template<class vector_t >
number	ug::TriangleArea (const vector_t &p1, const vector_t &p2, const vector_t &p3)
	calculates the are of the triangle defined by p1, p2 and p3
template<class vector_t >
vector_t	ug::TriangleBarycenter (const vector_t &p1, const vector_t &p2, const vector_t &p3)
	Calculates the barycenter of a triangle (1/3) * (p1+p2+p3)
UG_API bool	ug::TriangleBoxIntersection (const MathVector< 3 > &p0, const MathVector< 3 > &p1, const MathVector< 3 > &p2, const MathVector< 3 > &boxMin, const MathVector< 3 > &boxMax)
	checks whether a triangle and an axis-aligned box intersect.
template<class vector_t >
number	ug::TriangleQuality_Area (const vector_t &p1, const vector_t &p2, const vector_t &p3)
	returns a value between 0 and 1. The higher the better.
UG_API bool	ug::TriangleTriangleIntersection (const MathVector< 3 > &p0, const MathVector< 3 > &p1, const MathVector< 3 > &p2, const MathVector< 3 > &q0, const MathVector< 3 > &q1, const MathVector< 3 > &q2, MathVector< 3 > *ip1Out=NULL, MathVector< 3 > *ip2Out=NULL, number snapThreshold=SMALL)
	checks whether two triangles intersect and returns the intervals, if they do.
template<class TNumber >
TNumber	ug::urand (TNumber lowerBound, TNumber upperBound)
	uniform distributed random numbers in [lowerBound, upperBound[. Use srand to set a seed.
bool	ug::TriangleCircumcenter (vector2 &centerOut, const vector2 &p1, const vector2 &p2, const vector2 &p3)
	Calculates the circumcenter of a triangle.
bool	ug::TriangleCircumcenter (vector3 &centerOut, const vector3 &p1, const vector3 &p2, const vector3 &p3)
	Calculates the circumcenter of a triangle.