Detailed Description

Lightweight SE(2)/SE(3) data types, geometry functions, etc.

"lightweight" point & pose classes

The "lightweight" name comes from the fact that these classes are simple structures without special memory alignment requirements and do not have a deep hiearchy of class heritance.

This is in contrast to classes derived from mrpt::poses::CPoseOrPoint, which in turn offer:

Serialization (see: [mrpt-serialization])
Buffered trigronometric calculations (e.g. mrpt::poses::CPose3D), hence they will be preferred to lightweight alternaives (e.g. mrpt::math::TPose3D) if the same pose is to be used over and over again to transform multiple points/poses.

See list of classes below.

Collaboration diagram for Lightweight SE(2)/SE(3) types, geometry functions.:

Classes
class	mrpt::math::CPolygon
	A wrapper of a TPolygon2D class, implementing CSerializable. More...

struct	mrpt::math::TPoint2D_data< T >

struct	mrpt::math::TPoint2D_< T >
	Base template for TPoint2D and TPoint2Df. More...

struct	mrpt::math::TPoint3D_< T >
	Base template for TPoint3D and TPoint3Df. More...

class	mrpt::math::TPolygonWithPlane
	Slightly heavyweight type to speed-up calculations with polygons in 3D. More...

struct	mrpt::math::TPoseOrPoint
	Base type of all TPoseXX and TPointXX classes in mrpt::math. More...

Typedefs
using	mrpt::math::TPoint2D = TPoint2D_< double >
	Lightweight 2D point. More...

Simple intersection operations, relying basically on geometrical
operations.
bool	mrpt::math::intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between two 3D segments. More...

bool	mrpt::math::intersect (const TSegment3D &s1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a plane. More...

bool	mrpt::math::intersect (const TSegment3D &s1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D line. More...

bool	mrpt::math::intersect (const TPlane &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a plane and a 3D segment. More...

bool	mrpt::math::intersect (const TPlane &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between two planes. More...

bool	mrpt::math::intersect (const TPlane &p1, const TLine3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D line. More...

bool	mrpt::math::intersect (const TLine3D &r1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D segment. More...

bool	mrpt::math::intersect (const TLine3D &r1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a plane. More...

bool	mrpt::math::intersect (const TLine3D &r1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between two 3D lines. More...

bool	mrpt::math::intersect (const TLine2D &r1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between two 2D lines. More...

bool	mrpt::math::intersect (const TLine2D &r1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment. More...

bool	mrpt::math::intersect (const TSegment2D &s1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D segment. More...

bool	mrpt::math::intersect (const TSegment2D &s1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between two 2D segments. More...

Angle retrieval methods. Methods which use TSegments will
automatically use TLines' implicit constructors.
double	mrpt::math::getAngle (const TPlane &p1, const TPlane &p2)
	Computes the angle between two planes. More...

double	mrpt::math::getAngle (const TPlane &p1, const TLine3D &r2)
	Computes the angle between a plane and a 3D line or segment (implicit constructor will be used if passing a segment instead of a line). More...

double	mrpt::math::getAngle (const TLine3D &r1, const TPlane &p2)
	Computes the angle between a 3D line or segment and a plane (implicit constructor will be used if passing a segment instead of a line). More...

double	mrpt::math::getAngle (const TLine3D &r1, const TLine3D &r2)
	Computes the accute relative angle (range: [-PI/2,PI/2]) between two lines. More...

double	mrpt::math::getAngle (const TLine2D &r1, const TLine2D &r2)
	Computes the relative angle (range: [-PI,PI]) of line 2 wrt line 1. More...

Creation of lines from poses.
void	mrpt::math::createFromPoseX (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the X axis in a given pose. More...

void	mrpt::math::createFromPoseY (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Y axis in a given pose. More...

void	mrpt::math::createFromPoseZ (const mrpt::math::TPose3D &p, TLine3D &r)
	Gets a 3D line corresponding to the Z axis in a given pose. More...

void	mrpt::math::createFromPoseAndVector (const mrpt::math::TPose3D &p, const double(&vector)[3], TLine3D &r)
	Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose. More...

void	mrpt::math::createFromPoseX (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the X axis in a given pose. More...

void	mrpt::math::createFromPoseY (const TPose2D &p, TLine2D &r)
	Gets a 2D line corresponding to the Y axis in a given pose. More...

void	mrpt::math::createFromPoseAndVector (const TPose2D &p, const double(&vector)[2], TLine2D &r)
	Gets a 2D line corresponding to any arbitrary vector, in the base given the given pose. More...

Other line or plane related methods.
bool	mrpt::math::conformAPlane (const std::vector< TPoint3D > &points)
	Checks whether this polygon or set of points acceptably fits a plane. More...

bool	mrpt::math::conformAPlane (const std::vector< TPoint3D > &points, TPlane &p)
	Checks whether this polygon or set of points acceptably fits a plane, and if it's the case returns it in the second argument. More...

bool	mrpt::math::areAligned (const std::vector< TPoint2D > &points)
	Checks whether this set of points acceptably fits a 2D line. More...

bool	mrpt::math::areAligned (const std::vector< TPoint2D > &points, TLine2D &r)
	Checks whether this set of points acceptably fits a 2D line, and if it's the case returns it in the second argument. More...

bool	mrpt::math::areAligned (const std::vector< TPoint3D > &points)
	Checks whether this set of points acceptably fits a 3D line. More...

bool	mrpt::math::areAligned (const std::vector< TPoint3D > &points, TLine3D &r)
	Checks whether this set of points acceptably fits a 3D line, and if it's the case returns it in the second argument. More...

Projections
void	mrpt::math::project3D (const TPoint3D &point, const mrpt::math::TPose3D &newXYpose, TPoint3D &newPoint)
	Uses the given pose 3D to project a point into a new base. More...

void	mrpt::math::project3D (const TSegment3D &segment, const mrpt::math::TPose3D &newXYpose, TSegment3D &newSegment)
	Uses the given pose 3D to project a segment into a new base. More...

void	mrpt::math::project3D (const TLine3D &line, const mrpt::math::TPose3D &newXYpose, TLine3D &newLine)
	Uses the given pose 3D to project a line into a new base. More...

void	mrpt::math::project3D (const TPlane &plane, const mrpt::math::TPose3D &newXYpose, TPlane &newPlane)
	Uses the given pose 3D to project a plane into a new base. More...

void	mrpt::math::project3D (const TPolygon3D &polygon, const mrpt::math::TPose3D &newXYpose, TPolygon3D &newPolygon)
	Uses the given pose 3D to project a polygon into a new base. More...

void	mrpt::math::project3D (const TObject3D &object, const mrpt::math::TPose3D &newXYPose, TObject3D &newObject)
	Uses the given pose 3D to project any 3D object into a new base. More...

template<class T >
void	mrpt::math::project3D (const T &obj, const TPlane &newXYPlane, T &newObj)
	Projects any 3D object into the plane's base, using its inverse pose. More...

template<class T >
void	mrpt::math::project3D (const T &obj, const TPlane &newXYPlane, const TPoint3D &newOrigin, T &newObj)
	Projects any 3D object into the plane's base, using its inverse pose and forcing the position of the new coordinates origin. More...

template<class T >
void	mrpt::math::project3D (const std::vector< T > &objs, const mrpt::math::TPose3D &newXYpose, std::vector< T > &newObjs)
	Projects a set of 3D objects into the plane's base. More...

void	mrpt::math::project2D (const TPoint2D &point, const TPose2D &newXpose, TPoint2D &newPoint)
	Uses the given pose 2D to project a point into a new base. More...

void	mrpt::math::project2D (const TSegment2D &segment, const TPose2D &newXpose, TSegment2D &newSegment)
	Uses the given pose 2D to project a segment into a new base. More...

void	mrpt::math::project2D (const TLine2D &line, const TPose2D &newXpose, TLine2D &newLine)
	Uses the given pose 2D to project a line into a new base. More...

void	mrpt::math::project2D (const TPolygon2D &polygon, const TPose2D &newXpose, TPolygon2D &newPolygon)
	Uses the given pose 2D to project a polygon into a new base. More...

void	mrpt::math::project2D (const TObject2D &object, const TPose2D &newXpose, TObject2D &newObject)
	Uses the given pose 2D to project any 2D object into a new base. More...

template<class T , class CPOSE2D >
void	mrpt::math::project2D (const T &obj, const TLine2D &newXLine, T &newObj)
	Projects any 2D object into the line's base, using its inverse pose. More...

template<class T , class CPOSE2D >
void	mrpt::math::project2D (const T &obj, const TLine2D &newXLine, const TPoint2D &newOrigin, T &newObj)
	Projects any 2D object into the line's base, using its inverse pose and forcing the position of the new coordinate origin. More...

template<class T >
void	mrpt::math::project2D (const std::vector< T > &objs, const TPose2D &newXpose, std::vector< T > &newObjs)
	Projects a set of 2D objects into the line's base. More...

Polygon intersections. These operations rely more on spatial reasoning
than in raw numerical operations.
bool	mrpt::math::intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D segment. More...

bool	mrpt::math::intersect (const TPolygon2D &p1, const TLine2D &r2, TObject2D &obj)
	Gets the intersection between a 2D polygon and a 2D line. More...

bool	mrpt::math::intersect (const TPolygon2D &p1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between two 2D polygons. More...

bool	mrpt::math::intersect (const TSegment2D &s1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D segment and a 2D polygon. More...

bool	mrpt::math::intersect (const TLine2D &r1, const TPolygon2D &p2, TObject2D &obj)
	Gets the intersection between a 2D line and a 2D polygon. More...

bool	mrpt::math::intersect (const TPolygon3D &p1, const TSegment3D &s2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D segment. More...

bool	mrpt::math::intersect (const TPolygon3D &p1, const TLine3D &r2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a 3D line. More...

bool	mrpt::math::intersect (const TPolygon3D &p1, const TPlane &p2, TObject3D &obj)
	Gets the intersection between a 3D polygon and a plane. More...

bool	mrpt::math::intersect (const TPolygon3D &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between two 3D polygons. More...

bool	mrpt::math::intersect (const TSegment3D &s1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D segment and a 3D polygon. More...

bool	mrpt::math::intersect (const TLine3D &r1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a 3D line and a 3D polygon. More...

bool	mrpt::math::intersect (const TPlane &p1, const TPolygon3D &p2, TObject3D &obj)
	Gets the intersection between a plane and a 3D polygon. More...

size_t	mrpt::math::intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, CSparseMatrixTemplate< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons. More...

size_t	mrpt::math::intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, std::vector< TObject3D > &objs)
	Gets the intersection between two sets of 3D polygons. More...

Other intersections
template<class T , class U , class O >
size_t	mrpt::math::intersect (const std::vector< T > &v1, const std::vector< U > &v2, CSparseMatrixTemplate< O > &objs)
	Gets the intersection between vectors of geometric objects and returns it in a sparse matrix of either TObject2D or TObject3D. More...

template<class T , class U , class O >
size_t	mrpt::math::intersect (const std::vector< T > &v1, const std::vector< U > &v2, std::vector< O > objs)
	Gets the intersection between vectors of geometric objects and returns it in a vector of either TObject2D or TObject3D. More...

bool	mrpt::math::intersect (const TObject2D &o1, const TObject2D &o2, TObject2D &obj)
	Gets the intersection between any pair of 2D objects. More...

bool	mrpt::math::intersect (const TObject3D &o1, const TObject3D &o2, TObject3D &obj)
	Gets the intersection between any pair of 3D objects. More...

Distances
double	mrpt::math::distance (const TPoint2D &p1, const TPoint2D &p2)
	Gets the distance between two points in a 2D space. More...

double	mrpt::math::distance (const TPoint3D &p1, const TPoint3D &p2)
	Gets the distance between two points in a 3D space. More...

double	mrpt::math::distance (const TLine2D &r1, const TLine2D &r2)
	Gets the distance between two lines in a 2D space. More...

double	mrpt::math::distance (const TLine3D &r1, const TLine3D &r2)
	Gets the distance between two lines in a 3D space. More...

double	mrpt::math::distance (const TPlane &p1, const TPlane &p2)
	Gets the distance between two planes. More...

double	mrpt::math::distance (const TPolygon2D &p1, const TPolygon2D &p2)
	Gets the distance between two polygons in a 2D space. More...

double	mrpt::math::distance (const TPolygon2D &p1, const TSegment2D &s2)
	Gets the distance between a polygon and a segment in a 2D space. More...

double	mrpt::math::distance (const TSegment2D &s1, const TPolygon2D &p2)
	Gets the distance between a segment and a polygon in a 2D space. More...

double	mrpt::math::distance (const TPolygon2D &p1, const TLine2D &l2)
	Gets the distance between a polygon and a line in a 2D space. More...

double	mrpt::math::distance (const TLine2D &l1, const TPolygon2D &p2)

double	mrpt::math::distance (const TPolygon3D &p1, const TPolygon3D &p2)
	Gets the distance between two polygons in a 3D space. More...

double	mrpt::math::distance (const TPolygon3D &p1, const TSegment3D &s2)
	Gets the distance between a polygon and a segment in a 3D space. More...

double	mrpt::math::distance (const TSegment3D &s1, const TPolygon3D &p2)
	Gets the distance between a segment and a polygon in a 3D space. More...

double	mrpt::math::distance (const TPolygon3D &p1, const TLine3D &l2)
	Gets the distance between a polygon and a line in a 3D space. More...

double	mrpt::math::distance (const TLine3D &l1, const TPolygon3D &p2)
	Gets the distance between a line and a polygon in a 3D space. More...

double	mrpt::math::distance (const TPolygon3D &po, const TPlane &pl)
	Gets the distance between a polygon and a plane. More...

double	mrpt::math::distance (const TPlane &pl, const TPolygon3D &po)
	Gets the distance between a plane and a polygon. More...

Bound checkers
void	mrpt::math::getRectangleBounds (const std::vector< TPoint2D > &poly, TPoint2D &pMin, TPoint2D &pMax)
	Gets the rectangular bounds of a 2D polygon or set of 2D points. More...

void	mrpt::math::getPrismBounds (const std::vector< TPoint3D > &poly, TPoint3D &pMin, TPoint3D &pMax)
	Gets the prism bounds of a 3D polygon or set of 3D points. More...

Creation of planes from poses
void	mrpt::math::createPlaneFromPoseXY (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Z vector. More...

void	mrpt::math::createPlaneFromPoseXZ (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its Y vector. More...

void	mrpt::math::createPlaneFromPoseYZ (const mrpt::math::TPose3D &pose, TPlane &plane)
	Given a pose, creates a plane orthogonal to its X vector. More...

void	mrpt::math::createPlaneFromPoseAndNormal (const mrpt::math::TPose3D &pose, const double(&normal)[3], TPlane &plane)
	Given a pose and any vector, creates a plane orthogonal to that vector in the pose's coordinates. More...

CMatrixDouble44	mrpt::math::generateAxisBaseFromDirectionAndAxis (const mrpt::math::TVector3D &vec, uint8_t coord)
	Creates a homogeneus matrix (4x4) such that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the provided vector. More...

Linear regression methods
double	mrpt::math::getRegressionLine (const std::vector< TPoint2D > &points, TLine2D &line)
	Using eigenvalues, gets the best fitting line for a set of 2D points. More...

double	mrpt::math::getRegressionLine (const std::vector< TPoint3D > &points, TLine3D &line)
	Using eigenvalues, gets the best fitting line for a set of 3D points. More...

double	mrpt::math::getRegressionPlane (const std::vector< TPoint3D > &points, TPlane &plane)
	Using eigenvalues, gets the best fitting plane for a set of 3D points. More...

Miscellaneous Geometry methods
void	mrpt::math::assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys)
	Tries to assemble a set of segments into a set of closed polygons. More...

void	mrpt::math::assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys, std::vector< TSegment3D > &remainder)
	Tries to assemble a set of segments into a set of closed polygons, returning the unused segments as another out parameter. More...

void	mrpt::math::assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

void	mrpt::math::assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys, std::vector< TObject3D > &remainder)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

void	mrpt::math::assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys, std::vector< TSegment3D > &remainder1, std::vector< TObject3D > &remainder2)
	Extracts all the polygons, including those formed from segments, from the set of objects. More...

bool	mrpt::math::splitInConvexComponents (const TPolygon2D &poly, std::vector< TPolygon2D > &components)
	Splits a 2D polygon into convex components. More...

bool	mrpt::math::splitInConvexComponents (const TPolygon3D &poly, std::vector< TPolygon3D > &components)
	Splits a 3D polygon into convex components. More...

void	mrpt::math::getSegmentBisector (const TSegment2D &sgm, TLine2D &bis)
	Gets the bisector of a 2D segment. More...

void	mrpt::math::getSegmentBisector (const TSegment3D &sgm, TPlane &bis)
	Gets the bisector of a 3D segment. More...

void	mrpt::math::getAngleBisector (const TLine2D &l1, const TLine2D &l2, TLine2D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary) More...

void	mrpt::math::getAngleBisector (const TLine3D &l1, const TLine3D &l2, TLine3D &bis)
	Gets the bisector of two lines or segments (implicit constructor will be used if necessary) More...

bool	mrpt::math::traceRay (const std::vector< TPolygonWithPlane > &vec, const mrpt::math::TPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties. More...

bool	mrpt::math::traceRay (const std::vector< TPolygon3D > &vec, const mrpt::math::TPose3D &pose, double &dist)
	Fast ray tracing method using polygons' properties. More...

template<class T , class U , class V >
void	mrpt::math::crossProduct3D (const T &v0, const U &v1, V &vOut)
	Computes the cross product of two 3D vectors, returning a vector normal to both. More...

template<class T >
void	mrpt::math::crossProduct3D (const std::vector< T > &v0, const std::vector< T > &v1, std::vector< T > &v_out)

template<class VEC1 , class VEC2 >
VEC1	mrpt::math::crossProduct3D (const VEC1 &v0, const VEC2 &v1)
	overload (returning a vector of size 3 by value). More...

template<class VECTOR , class MATRIX >
void	mrpt::math::skew_symmetric3 (const VECTOR &v, MATRIX &M)
	Computes the 3x3 skew symmetric matrix from a 3-vector or 3-array: $M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & -z & y \\ z & 0 & -x \\ -y & x & 0 \end{array} \right)$ . More...

template<class VECTOR >
mrpt::math::CMatrixDouble33	mrpt::math::skew_symmetric3 (const VECTOR &v)

template<class VECTOR , class MATRIX >
void	mrpt::math::skew_symmetric3_neg (const VECTOR &v, MATRIX &M)
	Computes the negative version of a 3x3 skew symmetric matrix from a 3-vector or 3-array: $-M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & z & -y \\ -z & 0 & x \\ y & -x & 0 \end{array} \right)$ . More...

template<class VECTOR >
mrpt::math::CMatrixDouble33	mrpt::math::skew_symmetric3_neg (const VECTOR &v)

template<class T , class U >
bool	mrpt::math::vectorsAreParallel2D (const T &v1, const U &v2)
	Returns true if two 2D vectors are parallel. More...

template<class T , class U >
bool	mrpt::math::vectorsAreParallel3D (const T &v1, const U &v2)
	Returns true if two 3D vectors are parallel. More...

void	mrpt::math::closestFromPointToSegment (double Px, double Py, double x1, double y1, double x2, double y2, double &out_x, double &out_y)
	Computes the closest point from a given point to a segment. More...

void	mrpt::math::closestFromPointToLine (double Px, double Py, double x1, double y1, double x2, double y2, double &out_x, double &out_y)
	Computes the closest point from a given point to a (infinite) line. More...

double	mrpt::math::closestSquareDistanceFromPointToLine (double Px, double Py, double x1, double y1, double x2, double y2)
	Returns the square distance from a point to a line. More...

template<typename T >
T	mrpt::math::distanceBetweenPoints (const T x1, const T y1, const T x2, const T y2)
	Returns the distance between 2 points in 2D. More...

template<typename T >
T	mrpt::math::distanceBetweenPoints (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Returns the distance between 2 points in 3D. More...

template<typename T >
T	mrpt::math::distanceSqrBetweenPoints (const T x1, const T y1, const T x2, const T y2)
	Returns the square distance between 2 points in 2D. More...

template<typename T >
T	mrpt::math::distanceSqrBetweenPoints (const T x1, const T y1, const T z1, const T x2, const T y2, const T z2)
	Returns the square distance between 2 points in 3D. More...

template<typename T >
double	mrpt::math::minimumDistanceFromPointToSegment (const double Px, const double Py, const double x1, const double y1, const double x2, const double y2, T &out_x, T &out_y)
	Computes the closest point from a given point to a segment, and returns that minimum distance. More...

bool	mrpt::math::SegmentsIntersection (const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x4, const double y4, double &ix, double &iy)
	Returns the intersection point, and if it exists, between two segments. More...

bool	mrpt::math::SegmentsIntersection (const double x1, const double y1, const double x2, const double y2, const double x3, const double y3, const double x4, const double y4, float &ix, float &iy)
	Returns the intersection point, and if it exists, between two segments. More...

bool	mrpt::math::pointIntoPolygon2D (double px, double py, unsigned int polyEdges, const double poly_xs, const double poly_ys)
	Returns true if the 2D point (px,py) falls INTO the given polygon. More...

template<typename T >
bool	mrpt::math::pointIntoQuadrangle (T x, T y, T v1x, T v1y, T v2x, T v2y, T v3x, T v3y, T v4x, T v4y)
	Specialized method to check whether a point (x,y) falls into a quadrangle. More...

double	mrpt::math::distancePointToPolygon2D (double px, double py, unsigned int polyEdges, const double poly_xs, const double poly_ys)
	Returns the closest distance of a given 2D point to a polygon, or "0" if the point is INTO the polygon or its perimeter. More...

bool	mrpt::math::minDistBetweenLines (double p1_x, double p1_y, double p1_z, double p2_x, double p2_y, double p2_z, double p3_x, double p3_y, double p3_z, double p4_x, double p4_y, double p4_z, double &x, double &y, double &z, double &dist)
	Calculates the minimum distance between a pair of lines. More...

bool	mrpt::math::RectanglesIntersection (double R1_x_min, double R1_x_max, double R1_y_min, double R1_y_max, double R2_x_min, double R2_x_max, double R2_y_min, double R2_y_max, double R2_pose_x, double R2_pose_y, double R2_pose_phi)
	Returns whether two rotated rectangles intersect. More...

CMatrixDouble33	mrpt::math::generateAxisBaseFromDirection (double dx, double dy, double dz)
	Computes an axis base (a set of three 3D normal vectors) with the given vector being the first of them ("X") NOTE: Make sure of passing all floats or doubles and that the template of the receiving matrix is of the same type! More...

SLERP (Spherical Linear Interpolation) functions
template<typename T >
void	mrpt::math::slerp (const CQuaternion< T > &q0, const CQuaternion< T > &q1, const double t, CQuaternion< T > &q)
	SLERP interpolation between two quaternions. More...

void	mrpt::math::slerp (const TPose3D &q0, const TPose3D &q1, const double t, TPose3D &p)
	SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well. More...

void	mrpt::math::slerp_ypr (const mrpt::math::TPose3D &q0, const mrpt::math::TPose3D &q1, const double t, mrpt::math::TPose3D &p)

Typedef Documentation

◆ TPoint2D

typedef TPoint2D_< double > mrpt::math::TPoint2D

Lightweight 2D point.

Allows coordinate access using [] operator.

See also: mrpt::poses::CPoint2D

Definition at line 213 of file TPoint2D.h.

Function Documentation

◆ areAligned() [1/4]

bool mrpt::math::areAligned ( const std::vector< TPoint2D > & points )

Checks whether this set of points acceptably fits a 2D line.

See also: getEpsilon

Definition at line 990 of file geometry.cpp.

References geometryEpsilon, mrpt::math::MatrixBase< Scalar, Derived >::rank(), mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

Referenced by mrpt::math::areAligned().

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◆ areAligned() [2/4]

bool mrpt::math::areAligned	(	const std::vector< TPoint2D > &	points,
		TLine2D &	r
	)

Checks whether this set of points acceptably fits a 2D line, and if it's the case returns it in the second argument.

See also: getEpsilon

Definition at line 1005 of file geometry.cpp.

References mrpt::math::areAligned().

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◆ areAligned() [3/4]

bool mrpt::math::areAligned ( const std::vector< TPoint3D > & points )

Checks whether this set of points acceptably fits a 3D line.

See also: getEpsilon

Definition at line 1022 of file geometry.cpp.

References geometryEpsilon, mrpt::math::MatrixBase< Scalar, Derived >::rank(), mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

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◆ areAligned() [4/4]

bool mrpt::math::areAligned	(	const std::vector< TPoint3D > &	points,
		TLine3D &	r
	)

Checks whether this set of points acceptably fits a 3D line, and if it's the case returns it in the second argument.

Definition at line 1038 of file geometry.cpp.

References mrpt::math::areAligned().

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◆ assemblePolygons() [1/5]

void mrpt::math::assemblePolygons	(	const std::vector< TSegment3D > &	segms,
		std::vector< TPolygon3D > &	polys
	)

Tries to assemble a set of segments into a set of closed polygons.

Definition at line 2090 of file geometry.cpp.

Referenced by mrpt::math::assemblePolygons().

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◆ assemblePolygons() [2/5]

void mrpt::math::assemblePolygons	(	const std::vector< TSegment3D > &	segms,
		std::vector< TPolygon3D > &	polys,
		std::vector< TSegment3D > &	remainder
	)

Tries to assemble a set of segments into a set of closed polygons, returning the unused segments as another out parameter.

Definition at line 2184 of file geometry.cpp.

References depthFirstSearch(), mrpt::math::distance(), geometryEpsilon, and results.

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◆ assemblePolygons() [3/5]

void mrpt::math::assemblePolygons	(	const std::vector< TObject3D > &	objs,
		std::vector< TPolygon3D > &	polys
	)

Extracts all the polygons, including those formed from segments, from the set of objects.

Definition at line 2231 of file geometry.cpp.

References mrpt::math::assemblePolygons().

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◆ assemblePolygons() [4/5]

void mrpt::math::assemblePolygons	(	const std::vector< TObject3D > &	objs,
		std::vector< TPolygon3D > &	polys,
		std::vector< TObject3D > &	remainder
	)

Extracts all the polygons, including those formed from segments, from the set of objects.

Definition at line 2241 of file geometry.cpp.

References mrpt::math::assemblePolygons().

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◆ assemblePolygons() [5/5]

void mrpt::math::assemblePolygons	(	const std::vector< TObject3D > &	objs,
		std::vector< TPolygon3D > &	polys,
		std::vector< TSegment3D > &	remainder1,
		std::vector< TObject3D > &	remainder2
	)

Extracts all the polygons, including those formed from segments, from the set of objects.

Definition at line 2254 of file geometry.cpp.

References mrpt::math::assemblePolygons().

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◆ closestFromPointToLine()

void mrpt::math::closestFromPointToLine	(	double	Px,
		double	Py,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double &	out_x,
		double &	out_y
	)

Computes the closest point from a given point to a (infinite) line.

See also: closestFromPointToSegment

Definition at line 77 of file geometry.cpp.

Referenced by mrpt::maps::CPointsMap::squareDistanceToClosestCorrespondence().

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◆ closestFromPointToSegment()

void mrpt::math::closestFromPointToSegment	(	double	Px,
		double	Py,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double &	out_x,
		double &	out_y
	)

Computes the closest point from a given point to a segment.

See also: closestFromPointToLine

Definition at line 39 of file geometry.cpp.

◆ closestSquareDistanceFromPointToLine()

double mrpt::math::closestSquareDistanceFromPointToLine	(	double	Px,
		double	Py,
		double	x1,
		double	y1,
		double	x2,
		double	y2
	)

Returns the square distance from a point to a line.

Definition at line 100 of file geometry.cpp.

References mrpt::square().

Referenced by mrpt::slam::CICP::ICP_Method_LM().

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◆ conformAPlane() [1/2]

bool mrpt::math::conformAPlane ( const std::vector< TPoint3D > & points )

Checks whether this polygon or set of points acceptably fits a plane.

See also: TPolygon3D,getEpsilon

Definition at line 969 of file geometry.cpp.

References geometryEpsilon, mrpt::math::MatrixBase< Scalar, Derived >::rank(), mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

Referenced by mrpt::math::TPolygon3D::getPlane(), mrpt::math::TPolygon3D::isSkew(), and TEST().

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◆ conformAPlane() [2/2]

bool mrpt::math::conformAPlane	(	const std::vector< TPoint3D > &	points,
		TPlane &	p
	)

Checks whether this polygon or set of points acceptably fits a plane, and if it's the case returns it in the second argument.

See also: TPolygon3D,getEpsilon

Definition at line 985 of file geometry.cpp.

References geometryEpsilon, and mrpt::math::getRegressionPlane().

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◆ createFromPoseAndVector() [1/2]

void mrpt::math::createFromPoseAndVector	(	const mrpt::math::TPose3D &	p,
		const double(&)	vector[3],
		TLine3D &	r
	)

Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose.

An implicit constructor is used if a TPose3D is given.

See also: createFromPoseX,createFromPoseY,createFromPoseZ

Definition at line 932 of file geometry.cpp.

References mrpt::math::TLine3D::director, mrpt::math::TPose3D::getHomogeneousMatrix(), and mrpt::math::TLine3D::pBase.

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◆ createFromPoseAndVector() [2/2]

void mrpt::math::createFromPoseAndVector	(	const TPose2D &	p,
		const double(&)	vector[2],
		TLine2D &	r
	)

Gets a 2D line corresponding to any arbitrary vector, in the base given the given pose.

An implicit constructor is used if a CPose2D is given.

See also: createFromPoseY,createFromPoseAndVector

Definition at line 959 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TPose2D::phi, mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

◆ createFromPoseX() [1/2]

void mrpt::math::createFromPoseX	(	const mrpt::math::TPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the X axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also: createFromPoseY,createFromPoseZ,createFromPoseAndVector

Definition at line 917 of file geometry.cpp.

References createFromPoseAndAxis().

Referenced by mrpt::opengl::CCylinder::traceRay(), mrpt::opengl::CEllipsoid3D::traceRay(), mrpt::opengl::CEllipsoid2D::traceRay(), and mrpt::math::traceRay().

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◆ createFromPoseX() [2/2]

void mrpt::math::createFromPoseX	(	const TPose2D &	p,
		TLine2D &	r
	)

Gets a 2D line corresponding to the X axis in a given pose.

An implicit constructor is used if a CPose2D is given.

See also: createFromPoseY,createFromPoseAndVector

Definition at line 945 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TPose2D::phi, mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

◆ createFromPoseY() [1/2]

void mrpt::math::createFromPoseY	(	const mrpt::math::TPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the Y axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also: createFromPoseX,createFromPoseZ,createFromPoseAndVector

Definition at line 922 of file geometry.cpp.

References createFromPoseAndAxis().

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◆ createFromPoseY() [2/2]

void mrpt::math::createFromPoseY	(	const TPose2D &	p,
		TLine2D &	r
	)

Gets a 2D line corresponding to the Y axis in a given pose.

An implicit constructor is used if a CPose2D is given.

See also: createFromPoseX,createFromPoseAndVector

Definition at line 952 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TPose2D::phi, mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

◆ createFromPoseZ()

void mrpt::math::createFromPoseZ	(	const mrpt::math::TPose3D &	p,
		TLine3D &	r
	)

Gets a 3D line corresponding to the Z axis in a given pose.

An implicit constructor is used if a TPose3D is given.

See also: createFromPoseX,createFromPoseY,createFromPoseAndVector

Definition at line 927 of file geometry.cpp.

References createFromPoseAndAxis().

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◆ createPlaneFromPoseAndNormal()

void mrpt::math::createPlaneFromPoseAndNormal	(	const mrpt::math::TPose3D &	pose,
		const double(&)	normal[3],
		TPlane &	plane
	)

Given a pose and any vector, creates a plane orthogonal to that vector in the pose's coordinates.

See also: createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseYZ

Definition at line 1979 of file geometry.cpp.

References mrpt::math::TPlane::coefs, and mrpt::math::TPose3D::getHomogeneousMatrix().

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◆ createPlaneFromPoseXY()

void mrpt::math::createPlaneFromPoseXY	(	const mrpt::math::TPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its Z vector.

See also: createPlaneFromPoseXZ,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

Definition at line 1964 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

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◆ createPlaneFromPoseXZ()

void mrpt::math::createPlaneFromPoseXZ	(	const mrpt::math::TPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its Y vector.

See also: createPlaneFromPoseXY,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

Definition at line 1969 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

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◆ createPlaneFromPoseYZ()

void mrpt::math::createPlaneFromPoseYZ	(	const mrpt::math::TPose3D &	pose,
		TPlane &	plane
	)

Given a pose, creates a plane orthogonal to its X vector.

See also: createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseAndNormal

Definition at line 1974 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

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◆ crossProduct3D() [1/3]

template<class T , class U , class V >

void mrpt::math::crossProduct3D	(	const T &	v0,
		const U &	v1,
		V &	vOut
	)

inline

Computes the cross product of two 3D vectors, returning a vector normal to both.

It uses the simple implementation:

$v_out = \left( \begin{array}{c c c} \hat{i} ~ \hat{j} ~ \hat{k} \\ x0 ~ y0 ~ z0 \\ x1 ~ y1 ~ z1 \\ \end{array} \right)$

Definition at line 765 of file geometry.h.

Referenced by mrpt::opengl::TRenderMatrices::applyLookAt(), mrpt::math::distance(), mrpt::topography::ENUToGeocentric(), mrpt::vision::findMultipleChessboardsCorners(), mrpt::math::generateAxisBaseFromDirection(), mrpt::opengl::COpenGLViewport::get3DRayForPixelCoord(), mrpt::math::intersect(), mrpt::opengl::CPolyhedron::onUpdateBuffers_Triangles(), and mrpt::math::TPlane::TPlane().

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◆ crossProduct3D() [2/3]

template<class T >

void mrpt::math::crossProduct3D	(	const std::vector< T > &	v0,
		const std::vector< T > &	v1,
		std::vector< T > &	v_out
	)

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 774 of file geometry.h.

◆ crossProduct3D() [3/3]

template<class VEC1 , class VEC2 >

VEC1 mrpt::math::crossProduct3D	(	const VEC1 &	v0,
		const VEC2 &	v1
	)

inline

overload (returning a vector of size 3 by value).

Definition at line 785 of file geometry.h.

References ASSERT_.

◆ distance() [1/17]

double mrpt::math::distance	(	const TPoint2D &	p1,
		const TPoint2D &	p2
	)

Gets the distance between two points in a 2D space.

Definition at line 1807 of file geometry.cpp.

References mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

Referenced by mrpt::math::assemblePolygons(), mrpt::detectors::CFaceDetection::checkIfDiagonalSurface(), mrpt::detectors::CFaceDetection::checkIfDiagonalSurface2(), mrpt::maps::CPointsMap::compute3DDistanceToMesh(), nanoflann::KDTreeSingleIndexAdaptor< Distance, DatasetAdaptor, DIM, IndexType >::computeInitialDistances(), mrpt::math::confidenceIntervals(), mrpt::math::TSegment3D::contains(), mrpt::math::TSegment2D::contains(), mrpt::hwdrivers::CIbeoLuxETH::convertToCartesian(), mrpt::vision::CFeature::descriptorORBDistanceTo(), mrpt::math::TSegment3D::distance(), mrpt::math::distance(), mrpt::vision::CFeatureLines::extractLines(), mrpt::poses::CPoseInterpolatorBase< 3 >::filter(), find_chessboard_corners_multiple(), mrpt::containers::find_in_vector(), mrpt::obs::CRawlog::findObservationsByClassInRange(), mrpt::obs::CObservationRotatingScan::fromVelodyne(), getHeight(), mrpt::graphslam::deciders::CICPCriteriaERD< GRAPH_T >::getNearbyNodesOf(), mrpt::graphslam::optimizers::CLevMarqGSO< GRAPH_T >::getNearbyNodesOf(), mrpt::poses::CPoseInterpolatorBase< 3 >::getPreviousPoseWithMinDistance(), mrpt::math::CBinaryRelation< T, U, UIsObject >::getRelationFrom(), mrpt::math::CBinaryRelation< T, U, UIsObject >::getRelationTo(), mrpt::math::CBinaryRelation< T, U, UIsObject >::getRelationValue(), mrpt::math::CBinaryRelation< T, U, UIsObject >::insertElement(), mrpt::math::CBinaryRelation< T, U, UIsObject >::insertElements(), mrpt::maps::CLandmarksMap::internal_computeObservationLikelihood(), mrpt::math::intersect(), mrpt::math::TSegment3D::length(), mrpt::math::TSegment2D::length(), mrpt::opengl::CPolyhedron::TPolyhedronEdge::length(), mrpt::slam::PF_implementation< mrpt::math::TPose3D, CMonteCarloLocalization3D, mrpt::bayes::particle_storage_mode::VALUE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), mrpt::math::CBinaryRelation< T, U, UIsObject >::removeElement(), mrpt::math::CBinaryRelation< T, U, UIsObject >::removeElements(), mrpt::math::removeRepVertices(), mrpt::math::removeUnusedVertices(), mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration(), nanoflann::KDTreeSingleIndexAdaptor< Distance, DatasetAdaptor, DIM, IndexType >::searchLevel(), mrpt::math::CBinaryRelation< T, U, UIsObject >::setRelationValue(), mrpt::math::TSegment2D::signedDistance(), mrpt::math::splitInConvexComponents(), mrpt::math::TLine3D::TLine3D(), and velodyne_scan_to_pointcloud().

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◆ distance() [2/17]

double mrpt::math::distance	(	const TPoint3D &	p1,
		const TPoint3D &	p2
	)

Gets the distance between two points in a 3D space.

Definition at line 1814 of file geometry.cpp.

References mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

◆ distance() [3/17]

double mrpt::math::distance	(	const TLine2D &	r1,
		const TLine2D &	r2
	)

Gets the distance between two lines in a 2D space.

Definition at line 1838 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TLine2D::distance(), and geometryEpsilon.

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◆ distance() [4/17]

double mrpt::math::distance	(	const TLine3D &	r1,
		const TLine3D &	r2
	)

Gets the distance between two lines in a 3D space.

Definition at line 1854 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::crossProduct3D(), mrpt::math::TLine3D::director, mrpt::math::TPlane::distance(), mrpt::math::TLine3D::distance(), geometryEpsilon, mrpt::math::getAngle(), and mrpt::math::TLine3D::pBase.

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◆ distance() [5/17]

double mrpt::math::distance	(	const TPlane &	p1,
		const TPlane &	p2
	)

Gets the distance between two planes.

It will be zero if the planes are not parallel.

Definition at line 1870 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TPlane::distance(), geometryEpsilon, and mrpt::math::getAngle().

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◆ distance() [6/17]

double mrpt::math::distance	(	const TPolygon2D &	p1,
		const TPolygon2D &	p2
	)

Gets the distance between two polygons in a 2D space.

◆ distance() [7/17]

double mrpt::math::distance	(	const TPolygon2D &	p1,
		const TSegment2D &	s2
	)

Gets the distance between a polygon and a segment in a 2D space.

◆ distance() [8/17]

double mrpt::math::distance	(	const TSegment2D &	s1,
		const TPolygon2D &	p2
	)

inline

Gets the distance between a segment and a polygon in a 2D space.

Definition at line 560 of file geometry.h.

◆ distance() [9/17]

double mrpt::math::distance	(	const TPolygon2D &	p1,
		const TLine2D &	l2
	)

Gets the distance between a polygon and a line in a 2D space.

◆ distance() [10/17]

double mrpt::math::distance	(	const TLine2D &	l1,
		const TPolygon2D &	p2
	)

inline

Definition at line 566 of file geometry.h.

References mrpt::math::distance().

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◆ distance() [11/17]

double mrpt::math::distance	(	const TPolygon3D &	p1,
		const TPolygon3D &	p2
	)

Gets the distance between two polygons in a 3D space.

◆ distance() [12/17]

double mrpt::math::distance	(	const TPolygon3D &	p1,
		const TSegment3D &	s2
	)

Gets the distance between a polygon and a segment in a 3D space.

◆ distance() [13/17]

double mrpt::math::distance	(	const TSegment3D &	s1,
		const TPolygon3D &	p2
	)

inline

Gets the distance between a segment and a polygon in a 3D space.

Definition at line 575 of file geometry.h.

◆ distance() [14/17]

double mrpt::math::distance	(	const TPolygon3D &	p1,
		const TLine3D &	l2
	)

Gets the distance between a polygon and a line in a 3D space.

◆ distance() [15/17]

double mrpt::math::distance	(	const TLine3D &	l1,
		const TPolygon3D &	p2
	)

inline

Gets the distance between a line and a polygon in a 3D space.

Definition at line 582 of file geometry.h.

References mrpt::math::distance().

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◆ distance() [16/17]

double mrpt::math::distance	(	const TPolygon3D &	po,
		const TPlane &	pl
	)

Gets the distance between a polygon and a plane.

◆ distance() [17/17]

double mrpt::math::distance	(	const TPlane &	pl,
		const TPolygon3D &	po
	)

inline

Gets the distance between a plane and a polygon.

Definition at line 589 of file geometry.h.

References mrpt::math::distance().

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◆ distanceBetweenPoints() [1/2]

template<typename T >

T mrpt::math::distanceBetweenPoints	(	const T	x1,
		const T	y1,
		const T	x2,
		const T	y2
	)

Returns the distance between 2 points in 2D.

Definition at line 902 of file geometry.h.

Referenced by mrpt::slam::CGridMapAligner::AlignPDF_robustMatch(), and mrpt::tfest::se2_l2_robust().

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◆ distanceBetweenPoints() [2/2]

template<typename T >

T mrpt::math::distanceBetweenPoints	(	const T	x1,
		const T	y1,
		const T	z1,
		const T	x2,
		const T	y2,
		const T	z2
	)

Returns the distance between 2 points in 3D.

Definition at line 909 of file geometry.h.

◆ distancePointToPolygon2D()

double mrpt::math::distancePointToPolygon2D	(	double	px,
		double	py,
		unsigned int	polyEdges,
		const double *	poly_xs,
		const double *	poly_ys
	)

Returns the closest distance of a given 2D point to a polygon, or "0" if the point is INTO the polygon or its perimeter.

Definition at line 264 of file geometry.cpp.

References mrpt::math::minimumDistanceFromPointToSegment(), and mrpt::math::pointIntoPolygon2D().

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◆ distanceSqrBetweenPoints() [1/2]

template<typename T >

T mrpt::math::distanceSqrBetweenPoints	(	const T	x1,
		const T	y1,
		const T	x2,
		const T	y2
	)

Returns the square distance between 2 points in 2D.

Definition at line 917 of file geometry.h.

References mrpt::square().

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◆ distanceSqrBetweenPoints() [2/2]

template<typename T >

T mrpt::math::distanceSqrBetweenPoints	(	const T	x1,
		const T	y1,
		const T	z1,
		const T	x2,
		const T	y2,
		const T	z2
	)

Returns the square distance between 2 points in 3D.

Definition at line 924 of file geometry.h.

◆ generateAxisBaseFromDirection()

CMatrixDouble33 mrpt::math::generateAxisBaseFromDirection	(	double	dx,
		double	dy,
		double	dz
	)

Computes an axis base (a set of three 3D normal vectors) with the given vector being the first of them ("X") NOTE: Make sure of passing all floats or doubles and that the template of the receiving matrix is of the same type!

If $ d = [ dx ~ dy ~ dz ] $ is the input vector, then this function returns a matrix $ M $ such as:

$M = \left( \begin{array}{c c c} v^1_x ~ v^2_x ~ v^3_x \\ v^1_y ~ v^2_y ~ v^3_y \\ v^1_z ~ v^2_z ~ v^3_z \end{array} \right)$

And the three normal vectors are computed as:

$v^1 = \frac{d}{|d|}$

If (dx!=0 or dy!=0):

$v^2 = \frac{[-dy ~ dx ~ 0 ]}{\sqrt{dx^2+dy^2}}$

otherwise (the direction vector is vertical):

$v^2 = [1 ~ 0 ~ 0]$

And finally, the third vector is the cross product of the others:

$v^3 = v^1 \times v^2$

Returns: The 3x3 matrix (CMatrixDynamic<T>), containing one vector per column. Throws an std::exception on invalid input (i.e. null direction vector)

See also: generateAxisBaseFromDirectionAndAxis()

(JLB @ 18-SEP-2007)

Definition at line 2502 of file geometry.cpp.

References mrpt::math::MatrixBase< Scalar, Derived >::col(), mrpt::math::crossProduct3D(), MRPT_END, MRPT_START, mrpt::square(), and THROW_EXCEPTION.

Referenced by mrpt::maps::CBeacon::generateRingSOG(), and mrpt::maps::CLandmarksMap::loadSiftFeaturesFromImageObservation().

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◆ generateAxisBaseFromDirectionAndAxis()

CMatrixDouble44 mrpt::math::generateAxisBaseFromDirectionAndAxis	(	const mrpt::math::TVector3D &	vec,
		uint8_t	coord
	)

Creates a homogeneus matrix (4x4) such that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the provided vector.

Parameters

[in] vec must be a unitary vector

See also: generateAxisBaseFromDirectionAndAxis()

Definition at line 1993 of file geometry.cpp.

References geometryEpsilon, and mrpt::math::MatrixVectorBase< Scalar, Derived >::setZero().

Referenced by mrpt::math::TPlane::getAsPose3D(), mrpt::math::TPlane::getAsPose3DForcingOrigin(), and mrpt::opengl::CArrow::onUpdateBuffers_Triangles().

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◆ getAngle() [1/5]

double mrpt::math::getAngle	(	const TPlane &	p1,
		const TPlane &	p2
	)

Computes the angle between two planes.

Definition at line 846 of file geometry.cpp.

References mrpt::math::TPlane::coefs, geometryEpsilon, and M_PI.

Referenced by mrpt::math::TPlane::contains(), mrpt::math::TPlane::distance(), mrpt::math::distance(), mrpt::math::getAngle(), and TEST().

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◆ getAngle() [2/5]

double mrpt::math::getAngle	(	const TPlane &	p1,
		const TLine3D &	r2
	)

Computes the angle between a plane and a 3D line or segment (implicit constructor will be used if passing a segment instead of a line).

Definition at line 863 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TLine3D::director, geometryEpsilon, M_PI, and mrpt::sign().

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◆ getAngle() [3/5]

double mrpt::math::getAngle	(	const TLine3D &	r1,
		const TPlane &	p2
	)

inline

Computes the angle between a 3D line or segment and a plane (implicit constructor will be used if passing a segment instead of a line).

Definition at line 194 of file geometry.h.

References mrpt::math::getAngle().

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◆ getAngle() [4/5]

double mrpt::math::getAngle	(	const TLine3D &	r1,
		const TLine3D &	r2
	)

Computes the accute relative angle (range: [-PI/2,PI/2]) between two lines.

Note: Implicit constructor allows passing a segment as argument too.

Definition at line 880 of file geometry.cpp.

References mrpt::math::TLine3D::director, geometryEpsilon, and M_PI.

◆ getAngle() [5/5]

double mrpt::math::getAngle	(	const TLine2D &	r1,
		const TLine2D &	r2
	)

Computes the relative angle (range: [-PI,PI]) of line 2 wrt line 1.

Note: Implicit constructor allows passing a segment as argument too.

Definition at line 897 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, and mrpt::math::wrapToPi().

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◆ getAngleBisector() [1/2]

void mrpt::math::getAngleBisector	(	const TLine2D &	l1,
		const TLine2D &	l2,
		TLine2D &	bis
	)

Gets the bisector of two lines or segments (implicit constructor will be used if necessary)

Definition at line 2432 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, geometryEpsilon, mrpt::math::TObject2D::getPoint(), intersect(), mrpt::square(), mrpt::math::TLine2D::unitarize(), mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

Referenced by mrpt::math::getAngleBisector().

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◆ getAngleBisector() [2/2]

void mrpt::math::getAngleBisector	(	const TLine3D &	l1,
		const TLine3D &	l2,
		TLine3D &	bis
	)

Gets the bisector of two lines or segments (implicit constructor will be used if necessary)

Exceptions

std::logic_error if the lines do not fit in a single plane.

Definition at line 2470 of file geometry.cpp.

References mrpt::math::getAngleBisector(), mrpt::math::TPlane::getAsPose3D(), and mrpt::math::project3D().

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◆ getPrismBounds()

void mrpt::math::getPrismBounds	(	const std::vector< TPoint3D > &	poly,
		TPoint3D &	pMin,
		TPoint3D &	pMax
	)

Gets the prism bounds of a 3D polygon or set of 3D points.

Definition at line 1934 of file geometry.cpp.

References mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

Referenced by mrpt::math::TPolygon3D::contains(), getMinAndMaxBounds(), and mrpt::math::intersect().

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◆ getRectangleBounds()

void mrpt::math::getRectangleBounds	(	const std::vector< TPoint2D > &	poly,
		TPoint2D &	pMin,
		TPoint2D &	pMax
	)

Gets the rectangular bounds of a 2D polygon or set of 2D points.

Definition at line 1822 of file geometry.cpp.

References mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

◆ getRegressionLine() [1/2]

double mrpt::math::getRegressionLine	(	const std::vector< TPoint2D > &	points,
		TLine2D &	line
	)

Using eigenvalues, gets the best fitting line for a set of 2D points.

Returns an estimation of the error.

See also: spline, leastSquareLinearFit

Definition at line 2022 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::covariancesAndMean(), and mrpt::math::MatrixBase< Scalar, Derived >::eig_symmetric().

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◆ getRegressionLine() [2/2]

double mrpt::math::getRegressionLine	(	const std::vector< TPoint3D > &	points,
		TLine3D &	line
	)

Using eigenvalues, gets the best fitting line for a set of 3D points.

Returns an estimation of the error.

See also: spline, leastSquareLinearFit

Definition at line 2045 of file geometry.cpp.

References mrpt::math::covariancesAndMean(), mrpt::math::TLine3D::director, mrpt::math::MatrixBase< Scalar, Derived >::eig_symmetric(), and mrpt::math::TLine3D::pBase.

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◆ getRegressionPlane()

double mrpt::math::getRegressionPlane	(	const std::vector< TPoint3D > &	points,
		TPlane &	plane
	)

Using eigenvalues, gets the best fitting plane for a set of 3D points.

Returns an estimation of the error.

See also: spline, leastSquareLinearFit

Definition at line 2065 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::covariancesAndMean(), mrpt::math::MatrixBase< Scalar, Derived >::eig_symmetric(), and geometryEpsilon.

Referenced by mrpt::detectors::CFaceDetection::checkIfFacePlane(), mrpt::math::conformAPlane(), mrpt::math::TPolygon3D::getBestFittingPlane(), and getPlanes().

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◆ getSegmentBisector() [1/2]

void mrpt::math::getSegmentBisector	(	const TSegment2D &	sgm,
		TLine2D &	bis
	)

Gets the bisector of a 2D segment.

Definition at line 2410 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TSegment2D::getCenter(), mrpt::math::TSegment2D::point1, mrpt::math::TSegment2D::point2, mrpt::math::TLine2D::unitarize(), mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

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◆ getSegmentBisector() [2/2]

void mrpt::math::getSegmentBisector	(	const TSegment3D &	sgm,
		TPlane &	bis
	)

Gets the bisector of a 3D segment.

Definition at line 2420 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TSegment3D::getCenter(), mrpt::math::TSegment3D::point1, mrpt::math::TSegment3D::point2, mrpt::math::TPlane::unitarize(), mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

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◆ intersect() [1/31]

bool mrpt::math::intersect	(	const TSegment3D &	s1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

Gets the intersection between two 3D segments.

Possible outcomes:

Segments intersect: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
Segments don't intersect & are parallel: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT, obj is the segment "in between" both segments.
Segments don't intersect & aren't parallel: Return=false.
See also
TObject3D

Definition at line 617 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), intersect(), intersectInCommonLine(), and mrpt::math::TObject3D::isPoint().

Referenced by mrpt::opengl::CPolyhedron::getIntersection(), getPlanesIntersection(), mrpt::math::intersect(), mrpt::maps::CHeightGridMap2D_Base::intersectLine3D(), and TEST().

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◆ intersect() [2/31]

bool mrpt::math::intersect	(	const TSegment3D &	s1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between a 3D segment and a plane.

Possible outcomes:

Don't intersect: Return=false
s1 is within the plane: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
s1 intersects the plane at one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 639 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), intersect(), and mrpt::math::TObject3D::isLine().

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◆ intersect() [3/31]

bool mrpt::math::intersect	(	const TSegment3D &	s1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between a 3D segment and a 3D line.

Possible outcomes:

They don't intersect : Return=false
s1 lies within the line: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
s1 intersects the line at a point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 658 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), intersect(), and mrpt::math::TObject3D::isLine().

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◆ intersect() [4/31]

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

inline

Gets the intersection between a plane and a 3D segment.

Possible outcomes:

Don't intersect: Return=false
s2 is within the plane: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
s2 intersects the plane at one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 71 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [5/31]

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between two planes.

Possible outcomes:

Planes are parallel: Return=false
Planes intersect into a line: Return=true, obj.getType()=GEOMETRIC_TYPE_LINE
See also
TObject3D

Definition at line 677 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::crossProduct3D(), mrpt::math::TLine3D::director, geometryEpsilon, mrpt::math::TLine3D::pBase, and mrpt::math::TLine3D::unitarize().

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◆ intersect() [6/31]

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TLine3D &	p2,
		TObject3D &	obj
	)

Gets the intersection between a plane and a 3D line.

Possible outcomes:

Line is parallel to plane but not within it: Return=false
Line is contained in the plane: Return=true, obj.getType()=GEOMETRIC_TYPE_LINE
Line intersects the plane at one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 721 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TLine3D::director, mrpt::math::TPlane::evaluatePoint(), geometryEpsilon, mrpt::math::TLine3D::pBase, mrpt::math::TPoint3D_data< T >::x, mrpt::math::TPoint3D_data< T >::y, and mrpt::math::TPoint3D_data< T >::z.

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◆ intersect() [7/31]

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

inline

Gets the intersection between a 3D line and a 3D segment.

Possible outcomes:

They don't intersect : Return=false
s2 lies within the line: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
s2 intersects the line at a point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 102 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [8/31]

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TPlane &	p2,
		TObject3D &	obj
	)

inline

Gets the intersection between a 3D line and a plane.

Possible outcomes:

Line is parallel to plane but not within it: Return=false
Line is contained in the plane: Return=true, obj.getType()=GEOMETRIC_TYPE_LINE
Line intersects the plane at one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 115 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [9/31]

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between two 3D lines.

Possible outcomes:

Lines do not intersect: Return=false
Lines are parallel and do not coincide: Return=false
Lines coincide (are the same): Return=true, obj.getType()=GEOMETRIC_TYPE_LINE
Lines intesect in a point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject3D

Definition at line 753 of file geometry.cpp.

References mrpt::math::TLine3D::contains(), mrpt::math::TLine3D::director, geometryEpsilon, and mrpt::math::TLine3D::pBase.

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◆ intersect() [10/31]

bool mrpt::math::intersect	(	const TLine2D &	r1,
		const TLine2D &	r2,
		TObject2D &	obj
	)

Gets the intersection between two 2D lines.

Possible outcomes:

Lines do not intersect: Return=false
Lines are parallel and do not coincide: Return=false
Lines coincide (are the same): Return=true, obj.getType()=GEOMETRIC_TYPE_LINE
Lines intesect in a point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject2D

Definition at line 790 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, geometryEpsilon, mrpt::math::TPoint2D_data< T >::x, and mrpt::math::TPoint2D_data< T >::y.

◆ intersect() [11/31]

bool mrpt::math::intersect	(	const TLine2D &	r1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between a 2D line and a 2D segment.

Possible outcomes:

They don't intersect: Return=false
s2 lies within the line: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
Both intersects in one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject2D

Definition at line 817 of file geometry.cpp.

References mrpt::math::TSegment2D::contains(), mrpt::math::TObject2D::getPoint(), intersect(), and mrpt::math::TObject2D::isLine().

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◆ intersect() [12/31]

bool mrpt::math::intersect	(	const TSegment2D &	s1,
		const TLine2D &	r2,
		TObject2D &	obj
	)

inline

Gets the intersection between a 2D line and a 2D segment.

Possible outcomes:

They don't intersect: Return=false
s1 lies within the line: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT
Both intersects in one point: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
See also
TObject2D

Definition at line 160 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [13/31]

bool mrpt::math::intersect	(	const TSegment2D &	s1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between two 2D segments.

Possible outcomes:

Segments intersect: Return=true, obj.getType()=GEOMETRIC_TYPE_POINT
Segments don't intersect & are parallel: Return=true, obj.getType()=GEOMETRIC_TYPE_SEGMENT, obj is the segment "in between" both segments.
Segments don't intersect & aren't parallel: Return=false.
See also
TObject2D

Definition at line 832 of file geometry.cpp.

References mrpt::math::TSegment2D::contains(), mrpt::math::TObject2D::getPoint(), intersect(), intersectInCommonLine(), and mrpt::math::TObject2D::isLine().

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◆ intersect() [14/31]

bool mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TSegment2D &	s2,
		TObject2D &	obj
	)

Gets the intersection between a 2D polygon and a 2D segment.

See also: TObject2D

Definition at line 1221 of file geometry.cpp.

References mrpt::math::TSegment2D::contains(), mrpt::math::TObject2D::getPoint(), mrpt::math::TObject2D::getSegment(), intersect(), and intersectInCommonLine().

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◆ intersect() [15/31]

bool mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TLine2D &	r2,
		TObject2D &	obj
	)

Gets the intersection between a 2D polygon and a 2D line.

See also: TObject2D

Definition at line 1234 of file geometry.cpp.

References geometryEpsilon, mrpt::math::TLine2D::getAsPose2D(), mrpt::math::project2D(), and mrpt::sign().

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◆ intersect() [16/31]

bool mrpt::math::intersect	(	const TPolygon2D &	p1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)

Gets the intersection between two 2D polygons.

See also: TObject2D

Definition at line 1381 of file geometry.cpp.

References mrpt::math::CSparseMatrixTemplate< T >::cols(), fromObject(), getSegmentsWithLine(), intersect(), mrpt::math::CSparseMatrixTemplate< T >::rows(), and THROW_EXCEPTION.

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◆ intersect() [17/31]

bool mrpt::math::intersect	(	const TSegment2D &	s1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)

inline

Gets the intersection between a 2D segment and a 2D polygon.

See also: TObject2D

Definition at line 441 of file geometry.h.

◆ intersect() [18/31]

bool mrpt::math::intersect	(	const TLine2D &	r1,
		const TPolygon2D &	p2,
		TObject2D &	obj
	)

inline

Gets the intersection between a 2D line and a 2D polygon.

See also: TObject2D

Definition at line 447 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [19/31]

bool mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TSegment3D &	s2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a 3D segment.

See also: TObject3D

Definition at line 1429 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TPose3D::fromHomogeneousMatrix(), mrpt::math::TPlane::getAsPose3DForcingOrigin(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::TObject3D::getPoint(), mrpt::math::TObject3D::getSegment(), intersect(), and mrpt::math::project3D().

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◆ intersect() [20/31]

bool mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TLine3D &	r2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a 3D line.

See also: TObject3D

Definition at line 1455 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TPose3D::fromHomogeneousMatrix(), mrpt::math::TPlane::getAsPose3DForcingOrigin(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::TObject3D::getPoint(), intersect(), mrpt::math::TObject3D::isLine(), and mrpt::math::project3D().

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◆ intersect() [21/31]

bool mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TPlane &	p2,
		TObject3D &	obj
	)

Gets the intersection between a 3D polygon and a plane.

See also: TObject3D

Definition at line 1480 of file geometry.cpp.

References mrpt::math::TObject3D::getLine(), mrpt::math::TPolygon3D::getPlane(), intersect(), and mrpt::math::TObject3D::isPlane().

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◆ intersect() [22/31]

bool mrpt::math::intersect	(	const TPolygon3D &	p1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)

Gets the intersection between two 3D polygons.

See also: TObject3D

Definition at line 1539 of file geometry.cpp.

References compatibleBounds(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::getPrismBounds(), and intersectAux().

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◆ intersect() [23/31]

bool mrpt::math::intersect	(	const TSegment3D &	s1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)

inline

Gets the intersection between a 3D segment and a 3D polygon.

See also: TObject3D

Definition at line 462 of file geometry.h.

◆ intersect() [24/31]

bool mrpt::math::intersect	(	const TLine3D &	r1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)

inline

Gets the intersection between a 3D line and a 3D polygon.

See also: TObject3D

Definition at line 468 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [25/31]

bool mrpt::math::intersect	(	const TPlane &	p1,
		const TPolygon3D &	p2,
		TObject3D &	obj
	)

inline

Gets the intersection between a plane and a 3D polygon.

See also: TObject3D

Definition at line 473 of file geometry.h.

References mrpt::math::intersect().

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◆ intersect() [26/31]

size_t mrpt::math::intersect	(	const std::vector< TPolygon3D > &	v1,
		const std::vector< TPolygon3D > &	v2,
		CSparseMatrixTemplate< TObject3D > &	objs
	)

Gets the intersection between two sets of 3D polygons.

The intersection is returned as an sparse matrix with each pair of polygons' intersections, and the return value is the amount of intersections found.

See also: TObject3D,CSparseMatrixTemplate

Definition at line 1579 of file geometry.cpp.

References mrpt::math::CSparseMatrixTemplate< T >::clear(), compatibleBounds(), getMinAndMaxBounds(), mrpt::math::CSparseMatrixTemplate< T >::getNonNullElements(), getPlanes(), intersectAux(), and mrpt::math::CSparseMatrixTemplate< T >::resize().

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◆ intersect() [27/31]

size_t mrpt::math::intersect	(	const std::vector< TPolygon3D > &	v1,
		const std::vector< TPolygon3D > &	v2,
		std::vector< TObject3D > &	objs
	)

Gets the intersection between two sets of 3D polygons.

The intersection is returned as a vector with every intersection found, and the return value is the amount of intersections found.

See also: TObject3D

Definition at line 1603 of file geometry.cpp.

References compatibleBounds(), getMinAndMaxBounds(), getPlanes(), and intersectAux().

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◆ intersect() [28/31]

template<class T , class U , class O >

size_t mrpt::math::intersect	(	const std::vector< T > &	v1,
		const std::vector< U > &	v2,
		CSparseMatrixTemplate< O > &	objs
	)

Gets the intersection between vectors of geometric objects and returns it in a sparse matrix of either TObject2D or TObject3D.

See also: TObject2D,TObject3D,CSparseMatrix

Definition at line 501 of file geometry.h.

References mrpt::math::CSparseMatrixTemplate< T >::clear(), mrpt::math::CSparseMatrixTemplate< T >::getNonNullElements(), mrpt::math::intersect(), and mrpt::math::CSparseMatrixTemplate< T >::resize().

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◆ intersect() [29/31]

template<class T , class U , class O >

size_t mrpt::math::intersect	(	const std::vector< T > &	v1,
		const std::vector< U > &	v2,
		std::vector< O >	objs
	)

Gets the intersection between vectors of geometric objects and returns it in a vector of either TObject2D or TObject3D.

See also: TObject2D,TObject3D

Definition at line 519 of file geometry.h.

◆ intersect() [30/31]

bool mrpt::math::intersect	(	const TObject2D &	o1,
		const TObject2D &	o2,
		TObject2D &	obj
	)

Gets the intersection between any pair of 2D objects.

Definition at line 1637 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TSegment2D::contains(), mrpt::math::TLine2D::contains(), mrpt::math::distance(), geometryEpsilon, mrpt::math::TObject2D::getLine(), mrpt::math::TObject2D::getPoint(), mrpt::math::TObject2D::getPolygon(), mrpt::math::TObject2D::getSegment(), and intersect().

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◆ intersect() [31/31]

bool mrpt::math::intersect	(	const TObject3D &	o1,
		const TObject3D &	o2,
		TObject3D &	obj
	)

Gets the intersection between any pair of 3D objects.

Definition at line 1709 of file geometry.cpp.

References mrpt::math::TPolygon3D::contains(), mrpt::math::TPlane::contains(), mrpt::math::TSegment3D::contains(), mrpt::math::TLine3D::contains(), mrpt::math::distance(), geometryEpsilon, mrpt::math::TObject3D::getLine(), mrpt::math::TObject3D::getPlane(), mrpt::math::TObject3D::getPoint(), mrpt::math::TObject3D::getPolygon(), mrpt::math::TObject3D::getSegment(), and intersect().

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◆ minDistBetweenLines()

bool mrpt::math::minDistBetweenLines	(	double	p1_x,
		double	p1_y,
		double	p1_z,
		double	p2_x,
		double	p2_y,
		double	p2_z,
		double	p3_x,
		double	p3_y,
		double	p3_z,
		double	p4_x,
		double	p4_y,
		double	p4_z,
		double &	x,
		double &	y,
		double &	z,
		double &	dist
	)

Calculates the minimum distance between a pair of lines.

The lines are given by:

Line 1 = P1 + f (P2-P1)
Line 2 = P3 + f (P4-P3) The Euclidean distance is returned in "dist", and the mid point between the lines in (x,y,z)
Returns
It returns false if there is no solution, i.e. lines are (almost, up to EPS) parallel.

Definition at line 298 of file geometry.cpp.

References mrpt::square().

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◆ minimumDistanceFromPointToSegment()

template<typename T >

double mrpt::math::minimumDistanceFromPointToSegment	(	const double	Px,
		const double	Py,
		const double	x1,
		const double	y1,
		const double	x2,
		const double	y2,
		T &	out_x,
		T &	out_y
	)

Computes the closest point from a given point to a segment, and returns that minimum distance.

Definition at line 934 of file geometry.h.

References mrpt::square().

Referenced by mrpt::math::distancePointToPolygon2D(), and mrpt::nav::CHolonomicND::evaluateGaps().

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◆ pointIntoPolygon2D()

bool mrpt::math::pointIntoPolygon2D	(	double	px,
		double	py,
		unsigned int	polyEdges,
		const double *	poly_xs,
		const double *	poly_ys
	)

Returns true if the 2D point (px,py) falls INTO the given polygon.

See also: pointIntoQuadrangle

Definition at line 233 of file geometry.cpp.

Referenced by mrpt::math::distancePointToPolygon2D().

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◆ pointIntoQuadrangle()

template<typename T >

bool mrpt::math::pointIntoQuadrangle	(	T	x,
		T	y,
		T	v1x,
		T	v1y,
		T	v2x,
		T	v2y,
		T	v3x,
		T	v3y,
		T	v4x,
		T	v4y
	)

Specialized method to check whether a point (x,y) falls into a quadrangle.

See also: pointIntoPolygon2D

Definition at line 970 of file geometry.h.

◆ project2D() [1/8]

void mrpt::math::project2D	(	const TPoint2D &	point,
		const TPose2D &	newXpose,
		TPoint2D &	newPoint
	)

Uses the given pose 2D to project a point into a new base.

Definition at line 1152 of file geometry.cpp.

References mrpt::math::TPose2D::composePoint().

Referenced by mrpt::math::intersect(), and mrpt::math::project2D().

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◆ project2D() [2/8]

void mrpt::math::project2D	(	const TSegment2D &	segment,
		const TPose2D &	newXpose,
		TSegment2D &	newSegment
	)

inline

Uses the given pose 2D to project a segment into a new base.

Definition at line 373 of file geometry.h.

◆ project2D() [3/8]

void mrpt::math::project2D	(	const TLine2D &	line,
		const TPose2D &	newXpose,
		TLine2D &	newLine
	)

Uses the given pose 2D to project a line into a new base.

Definition at line 1158 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::TPose2D::phi, mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

◆ project2D() [4/8]

void mrpt::math::project2D	(	const TPolygon2D &	polygon,
		const TPose2D &	newXpose,
		TPolygon2D &	newPolygon
	)

Uses the given pose 2D to project a polygon into a new base.

Definition at line 1170 of file geometry.cpp.

◆ project2D() [5/8]

void mrpt::math::project2D	(	const TObject2D &	object,
		const TPose2D &	newXpose,
		TObject2D &	newObject
	)

Uses the given pose 2D to project any 2D object into a new base.

Definition at line 1179 of file geometry.cpp.

References mrpt::math::GEOMETRIC_TYPE_LINE, mrpt::math::GEOMETRIC_TYPE_POINT, mrpt::math::GEOMETRIC_TYPE_POLYGON, mrpt::math::GEOMETRIC_TYPE_SEGMENT, mrpt::math::TObject2D::getLine(), mrpt::math::TObject2D::getPoint(), mrpt::math::TObject2D::getPolygon(), mrpt::math::TObject2D::getSegment(), mrpt::math::TObject2D::getType(), and mrpt::math::project2D().

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◆ project2D() [6/8]

template<class T , class CPOSE2D >

void mrpt::math::project2D	(	const T &	obj,
		const TLine2D &	newXLine,
		T &	newObj
	)

Projects any 2D object into the line's base, using its inverse pose.

If the object is exactly inside the line, this projection will zero its Y coordinate.

Template Parameters

CPOSE2D set to TPose2D

Definition at line 395 of file geometry.h.

References mrpt::math::TLine2D::getAsPose2D(), and mrpt::math::project2D().

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◆ project2D() [7/8]

template<class T , class CPOSE2D >

void mrpt::math::project2D	(	const T &	obj,
		const TLine2D &	newXLine,
		const TPoint2D &	newOrigin,
		T &	newObj
	)

Projects any 2D object into the line's base, using its inverse pose and forcing the position of the new coordinate origin.

If the object is exactly inside the line, this projection will zero its Y coordinate.

Template Parameters

CPOSE2D set to TPose2D

Definition at line 408 of file geometry.h.

References mrpt::math::TLine2D::getAsPose2DForcingOrigin(), and mrpt::math::project2D().

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◆ project2D() [8/8]

template<class T >

void mrpt::math::project2D	(	const std::vector< T > &	objs,
		const TPose2D &	newXpose,
		std::vector< T > &	newObjs
	)

Projects a set of 2D objects into the line's base.

Definition at line 418 of file geometry.h.

◆ project3D() [1/9]

void mrpt::math::project3D	(	const TPoint3D &	point,
		const mrpt::math::TPose3D &	newXYpose,
		TPoint3D &	newPoint
	)

inline

Uses the given pose 3D to project a point into a new base.

Definition at line 300 of file geometry.h.

Referenced by mrpt::math::TPolygon3D::contains(), mrpt::math::TPolygon3D::distance(), mrpt::math::getAngleBisector(), mrpt::math::intersect(), intersect(), intersectInCommonPlane(), FUnprojectPolygon2D::operator()(), mrpt::math::project3D(), and mrpt::math::splitInConvexComponents().

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◆ project3D() [2/9]

void mrpt::math::project3D	(	const TSegment3D &	segment,
		const mrpt::math::TPose3D &	newXYpose,
		TSegment3D &	newSegment
	)

inline

Uses the given pose 3D to project a segment into a new base.

Definition at line 307 of file geometry.h.

References mrpt::math::TPose3D::composePoint().

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◆ project3D() [3/9]

void mrpt::math::project3D	(	const TLine3D &	line,
		const mrpt::math::TPose3D &	newXYpose,
		TLine3D &	newLine
	)

Uses the given pose 3D to project a line into a new base.

Definition at line 1052 of file geometry.cpp.

References mrpt::math::TPose3D::composePoint(), mrpt::math::TLine3D::director, mrpt::math::TPose3D::getHomogeneousMatrix(), mrpt::math::TLine3D::pBase, and mrpt::math::TLine3D::unitarize().

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◆ project3D() [4/9]

void mrpt::math::project3D	(	const TPlane &	plane,
		const mrpt::math::TPose3D &	newXYpose,
		TPlane &	newPlane
	)

Uses the given pose 3D to project a plane into a new base.

Definition at line 1067 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TPlane::evaluatePoint(), mrpt::math::TPose3D::getHomogeneousMatrix(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), and mrpt::math::TPlane::unitarize().

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◆ project3D() [5/9]

void mrpt::math::project3D	(	const TPolygon3D &	polygon,
		const mrpt::math::TPose3D &	newXYpose,
		TPolygon3D &	newPolygon
	)

Uses the given pose 3D to project a polygon into a new base.

Definition at line 1093 of file geometry.cpp.

References mrpt::math::project3D().

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◆ project3D() [6/9]

void mrpt::math::project3D	(	const TObject3D &	object,
		const mrpt::math::TPose3D &	newXYPose,
		TObject3D &	newObject
	)

Uses the given pose 3D to project any 3D object into a new base.

Definition at line 1102 of file geometry.cpp.

References mrpt::math::GEOMETRIC_TYPE_LINE, mrpt::math::GEOMETRIC_TYPE_PLANE, mrpt::math::GEOMETRIC_TYPE_POINT, mrpt::math::GEOMETRIC_TYPE_POLYGON, mrpt::math::GEOMETRIC_TYPE_SEGMENT, and mrpt::math::project3D().

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◆ project3D() [7/9]

template<class T >

void mrpt::math::project3D	(	const T &	obj,
		const TPlane &	newXYPlane,
		T &	newObj
	)

Projects any 3D object into the plane's base, using its inverse pose.

If the object is exactly inside the plane, this projection will zero its Z coordinates

Definition at line 336 of file geometry.h.

References mrpt::math::TPlane::getAsPose3D(), and mrpt::math::project3D().

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◆ project3D() [8/9]

template<class T >

void mrpt::math::project3D	(	const T &	obj,
		const TPlane &	newXYPlane,
		const TPoint3D &	newOrigin,
		T &	newObj
	)

Projects any 3D object into the plane's base, using its inverse pose and forcing the position of the new coordinates origin.

If the object is exactly inside the plane, this projection will zero its Z coordinates

Definition at line 347 of file geometry.h.

References mrpt::math::TPlane::getAsPose3D(), and mrpt::math::project3D().

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◆ project3D() [9/9]

template<class T >

void mrpt::math::project3D	(	const std::vector< T > &	objs,
		const mrpt::math::TPose3D &	newXYpose,
		std::vector< T > &	newObjs
	)

Projects a set of 3D objects into the plane's base.

Definition at line 359 of file geometry.h.

◆ RectanglesIntersection()

bool mrpt::math::RectanglesIntersection	(	double	R1_x_min,
		double	R1_x_max,
		double	R1_y_min,
		double	R1_y_max,
		double	R2_x_min,
		double	R2_x_max,
		double	R2_y_min,
		double	R2_y_max,
		double	R2_pose_x,
		double	R2_pose_y,
		double	R2_pose_phi
	)

Returns whether two rotated rectangles intersect.

The first rectangle is not rotated and given by (R1_x_min,R1_x_max)-(R1_y_min,R1_y_max). The second rectangle is given is a similar way, but it is internally rotated according to the given coordinates translation (R2_pose_x,R2_pose_y,R2_pose_phi(radians)), relative to the coordinates system of rectangle 1.

Definition at line 367 of file geometry.cpp.

References mrpt::math::CPolygon::AddVertex(), mrpt::math::CPolygon::PointIntoPolygon(), and mrpt::math::SegmentsIntersection().

Referenced by mrpt::hmtslam::CHierarchicalMapMHPartition::computeOverlapProbabilityBetweenNodes(), and TEST().

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◆ SegmentsIntersection() [1/2]

bool mrpt::math::SegmentsIntersection	(	const double	x1,
		const double	y1,
		const double	x2,
		const double	y2,
		const double	x3,
		const double	y3,
		const double	x4,
		const double	y4,
		double &	ix,
		double &	iy
	)

Returns the intersection point, and if it exists, between two segments.

Definition at line 120 of file geometry.cpp.

Referenced by mrpt::math::RectanglesIntersection(), and mrpt::math::SegmentsIntersection().

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◆ SegmentsIntersection() [2/2]

bool mrpt::math::SegmentsIntersection	(	const double	x1,
		const double	y1,
		const double	x2,
		const double	y2,
		const double	x3,
		const double	y3,
		const double	x4,
		const double	y4,
		float &	ix,
		float &	iy
	)

Returns the intersection point, and if it exists, between two segments.

Definition at line 218 of file geometry.cpp.

References mrpt::d2f(), and mrpt::math::SegmentsIntersection().

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◆ skew_symmetric3() [1/2]

template<class VECTOR , class MATRIX >

void mrpt::math::skew_symmetric3	(	const VECTOR &	v,
		MATRIX &	M
	)

inline

Computes the 3x3 skew symmetric matrix from a 3-vector or 3-array:

$M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & -z & y \\ z & 0 & -x \\ -y & x & 0 \end{array} \right)$

.

Definition at line 802 of file geometry.h.

References ASSERT_.

Referenced by TEST().

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◆ skew_symmetric3() [2/2]

template<class VECTOR >

mrpt::math::CMatrixDouble33 mrpt::math::skew_symmetric3 ( const VECTOR & v )

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 818 of file geometry.h.

◆ skew_symmetric3_neg() [1/2]

template<class VECTOR , class MATRIX >

void mrpt::math::skew_symmetric3_neg	(	const VECTOR &	v,
		MATRIX &	M
	)

inline

Computes the negative version of a 3x3 skew symmetric matrix from a 3-vector or 3-array:

$-M([x ~ y ~ z]^\top) = \left( \begin{array}{c c c} 0 & z & -y \\ -z & 0 & x \\ y & -x & 0 \end{array} \right)$

.

Definition at line 836 of file geometry.h.

References ASSERT_.

Referenced by jacob_dA_eps_D_p_deps(), jacob_deps_D_p_deps(), and mrpt::math::vectorsAreParallel2D().

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◆ skew_symmetric3_neg() [2/2]

template<class VECTOR >

mrpt::math::CMatrixDouble33 mrpt::math::skew_symmetric3_neg ( const VECTOR & v )

inline

This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

Definition at line 852 of file geometry.h.

◆ slerp() [1/2]

template<typename T >

void mrpt::math::slerp	(	const CQuaternion< T > &	q0,
		const CQuaternion< T > &	q1,
		const double	t,
		CQuaternion< T > &	q
	)

SLERP interpolation between two quaternions.

Parameters

[in]	q0	The quaternion for t=0
[in]	q1	The quaternion for t=1
[in]	t	A "time" parameter, in the range [0,1].
[out]	q	The output, interpolated quaternion.

Template Parameters

T	The type of the quaternion (e.g. float, double).

Exceptions

std::exception Only in Debug, if t is not in the valid range.

See also: http://en.wikipedia.org/wiki/Slerp

Definition at line 32 of file slerp.h.

References ASSERTDEB_, and mrpt::square().

Referenced by mrpt::math::slerp(), mrpt::math::slerp_ypr(), and TEST().

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◆ slerp() [2/2]

void mrpt::math::slerp	(	const TPose3D &	q0,
		const TPose3D &	q1,
		const double	t,
		TPose3D &	p
	)

SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well.

Parameters

[in]	p0	The pose for t=0
[in]	p1	The pose for t=1
[in]	t	A "time" parameter, in the range [0,1].
[out]	p	The output, interpolated pose.

Exceptions

std::exception Only in Debug, if t is not in the valid range.

Definition at line 17 of file slerp.cpp.

References mrpt::math::TPose3D::getAsQuaternion(), mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, mrpt::math::CQuaternion< T >::rpy(), mrpt::math::slerp(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

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◆ slerp_ypr()

void mrpt::math::slerp_ypr	(	const mrpt::math::TPose3D &	q0,
		const mrpt::math::TPose3D &	q1,
		const double	t,
		mrpt::math::TPose3D &	p
	)

Definition at line 32 of file slerp.cpp.

References mrpt::math::TPose3D::getAsQuaternion(), mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, mrpt::math::CQuaternion< T >::rpy(), mrpt::math::slerp(), mrpt::math::UNINITIALIZED_QUATERNION, mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

Referenced by mrpt::poses::CPoseInterpolatorBase< 3 >::impl_interpolation(), and TEST().

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◆ splitInConvexComponents() [1/2]

bool mrpt::math::splitInConvexComponents	(	const TPolygon2D &	poly,
		std::vector< TPolygon2D > &	components
	)

Splits a 2D polygon into convex components.

Definition at line 2291 of file geometry.cpp.

References mrpt::math::distance(), geometryEpsilon, mrpt::math::TObject2D::getPoint(), intersect(), mrpt::math::TPolygon2D::removeRedundantVertices(), TSegmentWithLine::segment, and mrpt::sign().

Referenced by mrpt::opengl::CPolyhedron::makeConvexPolygons(), and mrpt::math::splitInConvexComponents().

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◆ splitInConvexComponents() [2/2]

bool mrpt::math::splitInConvexComponents	(	const TPolygon3D &	poly,
		std::vector< TPolygon3D > &	components
	)

Splits a 3D polygon into convex components.

Exceptions

std::logic_error if the polygon can't be fit into a plane.

Definition at line 2386 of file geometry.cpp.

References mrpt::math::TPlane::getAsPose3DForcingOrigin(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::project3D(), and mrpt::math::splitInConvexComponents().

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◆ traceRay() [1/2]

bool mrpt::math::traceRay	(	const std::vector< TPolygonWithPlane > &	vec,
		const mrpt::math::TPose3D &	pose,
		double &	dist
	)

Fast ray tracing method using polygons' properties.

See also: CRenderizable::rayTrace

Definition at line 2484 of file geometry.cpp.

References mrpt::math::createFromPoseX(), intersect(), and mrpt::math::TLine3D::unitarize().

Referenced by mrpt::opengl::CTexturedPlane::traceRay(), mrpt::opengl::CSetOfTriangles::traceRay(), mrpt::opengl::CMesh::traceRay(), and mrpt::opengl::CPolyhedron::traceRay().

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◆ traceRay() [2/2]

bool mrpt::math::traceRay	(	const std::vector< TPolygon3D > &	vec,
		const mrpt::math::TPose3D &	pose,
		double &	dist
	)

inline

Fast ray tracing method using polygons' properties.

See also: CRenderizable::rayTrace

Definition at line 743 of file geometry.h.

◆ vectorsAreParallel2D()

template<class T , class U >

bool mrpt::math::vectorsAreParallel2D	(	const T &	v1,
		const U &	v2
	)

inline

Returns true if two 2D vectors are parallel.

The arguments may be points, arrays, etc.

Definition at line 864 of file geometry.h.

References mrpt::math::skew_symmetric3_neg(), and mrpt::math::UNINITIALIZED_MATRIX.

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◆ vectorsAreParallel3D()

template<class T , class U >

bool mrpt::math::vectorsAreParallel3D	(	const T &	v1,
		const U &	v2
	)

inline

Returns true if two 3D vectors are parallel.

The arguments may be points, arrays, etc.

Definition at line 874 of file geometry.h.

References mrpt::math::getEpsilon().

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Detailed Description

Classes

Typedefs

Simple intersection operations, relying basically on geometrical

Angle retrieval methods. Methods which use TSegments will

Creation of lines from poses.

Other line or plane related methods.

Projections

Polygon intersections. These operations rely more on spatial reasoning

Other intersections

Distances

Bound checkers

Creation of planes from poses

Linear regression methods

Miscellaneous Geometry methods

SLERP (Spherical Linear Interpolation) functions

Typedef Documentation

◆ TPoint2D

Function Documentation

◆ areAligned() [1/4]

◆ areAligned() [2/4]

◆ areAligned() [3/4]

◆ areAligned() [4/4]

◆ assemblePolygons() [1/5]

◆ assemblePolygons() [2/5]

◆ assemblePolygons() [3/5]

◆ assemblePolygons() [4/5]

◆ assemblePolygons() [5/5]

◆ closestFromPointToLine()

◆ closestFromPointToSegment()

◆ closestSquareDistanceFromPointToLine()

◆ conformAPlane() [1/2]

◆ conformAPlane() [2/2]

◆ createFromPoseAndVector() [1/2]

◆ createFromPoseAndVector() [2/2]

◆ createFromPoseX() [1/2]

◆ createFromPoseX() [2/2]

◆ createFromPoseY() [1/2]

◆ createFromPoseY() [2/2]

◆ createFromPoseZ()

◆ createPlaneFromPoseAndNormal()

◆ createPlaneFromPoseXY()

◆ createPlaneFromPoseXZ()

◆ createPlaneFromPoseYZ()

◆ crossProduct3D() [1/3]

◆ crossProduct3D() [2/3]

◆ crossProduct3D() [3/3]

◆ distance() [1/17]

◆ distance() [2/17]

◆ distance() [3/17]

◆ distance() [4/17]

◆ distance() [5/17]

◆ distance() [6/17]

◆ distance() [7/17]

◆ distance() [8/17]

◆ distance() [9/17]

◆ distance() [10/17]

◆ distance() [11/17]

◆ distance() [12/17]

◆ distance() [13/17]

◆ distance() [14/17]

◆ distance() [15/17]

◆ distance() [16/17]

◆ distance() [17/17]

◆ distanceBetweenPoints() [1/2]

◆ distanceBetweenPoints() [2/2]

◆ distancePointToPolygon2D()

◆ distanceSqrBetweenPoints() [1/2]

◆ distanceSqrBetweenPoints() [2/2]

◆ generateAxisBaseFromDirection()

◆ generateAxisBaseFromDirectionAndAxis()

◆ getAngle() [1/5]

◆ getAngle() [2/5]

◆ getAngle() [3/5]

◆ getAngle() [4/5]

◆ getAngle() [5/5]

◆ getAngleBisector() [1/2]

◆ getAngleBisector() [2/2]

◆ getPrismBounds()

◆ getRectangleBounds()