MRPT  1.9.9
Lightweight SE(2)/SE(3) types, geometry functions.

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:

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...
 
class  mrpt::math::TPolygonWithPlane
 Slightly heavyweight type to speed-up calculations with polygons in 3D. More...
 
struct  mrpt::math::TPoint2D_data
 
struct  mrpt::math::TPoint2D
 Lightweight 2D point. More...
 
struct  mrpt::math::TPoseOrPoint
 Base type of all TPoseXX and TPointXX classes in mrpt::math. 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...
 
void mrpt::math::generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], uint8_t coord, CMatrixDouble44 &matrix)
 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...
 
void mrpt::math::setEpsilon (double nE)
 Changes the value of the geometric epsilon (default = 1e-5) More...
 
double mrpt::math::getEpsilon ()
 Gets the value of the geometric epsilon (default = 1e-5) 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 (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2, double &out_x, double &out_y)
 Computes the closest point from a given point to a segment. More...
 
void mrpt::math::closestFromPointToLine (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const 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 (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2)
 Returns the square distance from a point to a line. More...
 
template<typename 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 >
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 >
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 >
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 (const double &px, const 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 (const double &px, const 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 (const double &p1_x, const double &p1_y, const double &p1_z, const double &p2_x, const double &p2_y, const double &p2_z, const double &p3_x, const double &p3_y, const double &p3_z, const double &p4_x, const double &p4_y, const 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 (const double &R1_x_min, const double &R1_x_max, const double &R1_y_min, const double &R1_y_max, const double &R2_x_min, const double &R2_x_max, const double &R2_y_min, const double &R2_y_max, const double &R2_pose_x, const double &R2_pose_y, const 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)
 

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 1010 of file geometry.cpp.

References mrpt::math::MatrixBase< Scalar, Derived >::rank(), mrpt::math::TPoint2D_data::x, and mrpt::math::TPoint2D_data::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 1025 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 1042 of file geometry.cpp.

References mrpt::math::MatrixBase< Scalar, Derived >::rank(), mrpt::math::TPoint3D_data::x, mrpt::math::TPoint3D_data::y, and mrpt::math::TPoint3D_data::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 1058 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 2173 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 2267 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 2314 of file geometry.cpp.

References mrpt::math::assemblePolygons(), mrpt::math::TObject3D::getPolygons(), and mrpt::math::TObject3D::getSegments().

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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 2324 of file geometry.cpp.

References mrpt::math::assemblePolygons(), mrpt::math::TObject3D::getPolygons(), and mrpt::math::TObject3D::getSegments().

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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 2337 of file geometry.cpp.

References mrpt::math::assemblePolygons(), mrpt::math::TObject3D::getPolygons(), and mrpt::math::TObject3D::getSegments().

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◆ closestFromPointToLine()

void mrpt::math::closestFromPointToLine ( const double &  Px,
const double &  Py,
const double &  x1,
const double &  y1,
const double &  x2,
const 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 ( const double &  Px,
const double &  Py,
const double &  x1,
const double &  y1,
const double &  x2,
const 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 ( const double &  Px,
const double &  Py,
const double &  x1,
const double &  y1,
const double &  x2,
const 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 989 of file geometry.cpp.

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

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

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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 1005 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 952 of file geometry.cpp.

◆ 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 979 of file geometry.cpp.

◆ 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 937 of file geometry.cpp.

References createFromPoseAndAxis().

Referenced by mrpt::opengl::CCylinder::traceRay(), mrpt::opengl::CEllipsoid::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 965 of file geometry.cpp.

◆ 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 942 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 972 of file geometry.cpp.

◆ 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 947 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 2064 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 2049 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 2054 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 2059 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 804 of file geometry.h.

Referenced by mrpt::math::distance(), mrpt::topography::ENUToGeocentric(), mrpt::vision::findMultipleChessboardsCorners(), mrpt::math::generateAxisBaseFromDirection(), mrpt::opengl::COpenGLViewport::get3DRayForPixelCoord(), mrpt::math::intersect(), mrpt::opengl::CArrow::render_dl(), 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 813 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 824 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 1889 of file geometry.cpp.

References mrpt::math::TPoint2D_data::x, and mrpt::math::TPoint2D_data::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::TSegment2D::contains(), mrpt::math::TSegment3D::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(), 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::TSegment2D::length(), mrpt::math::TSegment3D::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 1896 of file geometry.cpp.

References mrpt::math::TPoint3D_data::x, mrpt::math::TPoint3D_data::y, and mrpt::math::TPoint3D_data::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 1920 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 1936 of file geometry.cpp.

References mrpt::math::crossProduct3D(), mrpt::math::TLine3D::director, 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 1952 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.

Definition at line 1970 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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.

Definition at line 1977 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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 589 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.

Definition at line 1984 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ distance() [10/17]

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

Definition at line 595 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.

Definition at line 1991 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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.

Definition at line 1998 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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 604 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.

Definition at line 2005 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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 611 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.

Definition at line 2012 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

◆ 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 618 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 942 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 949 of file geometry.h.

◆ distancePointToPolygon2D()

double mrpt::math::distancePointToPolygon2D ( const double &  px,
const 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 265 of file geometry.cpp.

References min, 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 957 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 964 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 2585 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()

void mrpt::math::generateAxisBaseFromDirectionAndAxis ( const double(&)  vec[3],
uint8_t  coord,
CMatrixDouble44 matrix 
)

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]vecmust be a unitary vector
See also
generateAxisBaseFromDirectionAndAxis()

Definition at line 2078 of file geometry.cpp.

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

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

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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 866 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 883 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 223 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 900 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 917 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 2515 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, geometryEpsilon, mrpt::math::intersect(), mrpt::square(), and mrpt::math::TLine2D::unitarize().

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_errorif the lines do not fit in a single plane.

Definition at line 2553 of file geometry.cpp.

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

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◆ getEpsilon()

◆ 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 2019 of file geometry.cpp.

References min, mrpt::math::TPoint3D_data::x, mrpt::math::TPoint3D_data::y, and mrpt::math::TPoint3D_data::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 1904 of file geometry.cpp.

References min, mrpt::math::TPoint2D_data::x, and mrpt::math::TPoint2D_data::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 2105 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 2128 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 2148 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 2493 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::x, and mrpt::math::TPoint2D_data::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 2503 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::x, mrpt::math::TPoint3D_data::y, and mrpt::math::TPoint3D_data::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 638 of file geometry.cpp.

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

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

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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 660 of file geometry.cpp.

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

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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 679 of file geometry.cpp.

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

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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 100 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 698 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 741 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::x, mrpt::math::TPoint3D_data::y, and mrpt::math::TPoint3D_data::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 131 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 144 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 773 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 810 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, and geometryEpsilon.

◆ 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 837 of file geometry.cpp.

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

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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 189 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 852 of file geometry.cpp.

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

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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 1241 of file geometry.cpp.

References mrpt::math::TSegment2D::contains(), mrpt::math::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 1254 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 1463 of file geometry.cpp.

References mrpt::math::CSparseMatrixTemplate< T >::cols(), fromObject(), getSegmentsWithLine(), mrpt::math::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 470 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 476 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 1511 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TPose3D::fromHomogeneousMatrix(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::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 1537 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TPose3D::fromHomogeneousMatrix(), mrpt::math::TPose3D::getInverseHomogeneousMatrix(), mrpt::math::TPolygon3D::getPlane(), mrpt::math::intersect(), 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 1562 of file geometry.cpp.

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

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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 1621 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 491 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 497 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 502 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 1661 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 1685 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 530 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 548 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 1719 of file geometry.cpp.

References mrpt::math::TPolygon2D::contains(), mrpt::math::TLine2D::contains(), mrpt::math::TSegment2D::contains(), mrpt::math::distance(), geometryEpsilon, mrpt::math::TObject2D::getLine(), mrpt::math::TObject2D::getPoint(), mrpt::math::TObject2D::getPolygon(), mrpt::math::TObject2D::getSegment(), and mrpt::math::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 1791 of file geometry.cpp.

References mrpt::math::TPolygon3D::contains(), mrpt::math::TLine3D::contains(), mrpt::math::TPlane::contains(), mrpt::math::TSegment3D::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 mrpt::math::intersect().

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◆ minDistBetweenLines()

bool mrpt::math::minDistBetweenLines ( const double &  p1_x,
const double &  p1_y,
const double &  p1_z,
const double &  p2_x,
const double &  p2_y,
const double &  p2_z,
const double &  p3_x,
const double &  p3_y,
const double &  p3_z,
const double &  p4_x,
const double &  p4_y,
const 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 299 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 974 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 ( const double &  px,
const 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 234 of file geometry.cpp.

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

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◆ pointIntoQuadrangle()

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

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

See also
pointIntoPolygon2D

Definition at line 1010 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 1172 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 402 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 1178 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 1190 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 1199 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, 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
CPOSE2Dset to TPose2D

Definition at line 424 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
CPOSE2Dset to TPose2D

Definition at line 437 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 447 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 329 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 336 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 1072 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 1087 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 1113 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 1122 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 365 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 376 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 388 of file geometry.h.

◆ RectanglesIntersection()

bool mrpt::math::RectanglesIntersection ( const double &  R1_x_min,
const double &  R1_x_max,
const double &  R1_y_min,
const double &  R1_y_max,
const double &  R2_x_min,
const double &  R2_x_max,
const double &  R2_y_min,
const double &  R2_y_max,
const double &  R2_pose_x,
const double &  R2_pose_y,
const 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 370 of file geometry.cpp.

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

Referenced by mrpt::hmtslam::CHierarchicalMapMHPartition::computeOverlapProbabilityBetweenNodes().

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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 121 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 219 of file geometry.cpp.

References mrpt::math::SegmentsIntersection().

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◆ setEpsilon()

void mrpt::math::setEpsilon ( double  nE)

Changes the value of the geometric epsilon (default = 1e-5)

See also
geometryEpsilon,getEpsilon

Definition at line 35 of file geometry.cpp.

References eps, and geometryEpsilon.

◆ 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 841 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 857 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 875 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 891 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]q0The quaternion for t=0
[in]q1The quaternion for t=1
[in]tA "time" parameter, in the range [0,1].
[out]qThe output, interpolated quaternion.
Template Parameters
TThe type of the quaternion (e.g. float, double).
Exceptions
std::exceptionOnly 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]p0The pose for t=0
[in]p1The pose for t=1
[in]tA "time" parameter, in the range [0,1].
[out]pThe output, interpolated pose.
Exceptions
std::exceptionOnly 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::slerp(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, 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::slerp(), and mrpt::math::UNINITIALIZED_QUATERNION.

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 2374 of file geometry.cpp.

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

Referenced by generatePolygon(), 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_errorif the polygon can't be fit into a plane.

Definition at line 2469 of file geometry.cpp.

References 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 2567 of file geometry.cpp.

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

Referenced by mrpt::opengl::CTexturedPlane::traceRay(), mrpt::opengl::CGeneralizedCylinder::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 782 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 903 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 913 of file geometry.h.

References mrpt::math::getEpsilon().

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