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Geometry: lines, planes, intersections, SLERP, "lightweight" point & pose classes

Detailed Description

Collaboration diagram for Geometry: lines, planes, intersections, SLERP, "lightweight" point & pose classes:

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
 Lightweight 2D point. More...
 
struct  mrpt::math::TPose2D
 Lightweight 2D pose. More...
 
struct  mrpt::math::TPoint3Df
 Lightweight 3D point (float version). More...
 
struct  mrpt::math::TPoint3D
 Lightweight 3D point. More...
 
struct  mrpt::math::TPointXYZIu8
 XYZ point (double) + Intensity(u8) More...
 
struct  mrpt::math::TPointXYZRGBu8
 XYZ point (double) + RGB(u8) More...
 
struct  mrpt::math::TPointXYZfIu8
 XYZ point (float) + Intensity(u8) More...
 
struct  mrpt::math::TPointXYZfRGBu8
 XYZ point (float) + RGB(u8) More...
 
struct  mrpt::math::TPose3D
 Lightweight 3D pose (three spatial coordinates, plus three angular coordinates). More...
 
struct  mrpt::math::TPose3DQuat
 Lightweight 3D pose (three spatial coordinates, plus a quaternion ). More...
 
struct  mrpt::math::TSegment2D
 2D segment, consisting of two points. More...
 
struct  mrpt::math::TSegment3D
 3D segment, consisting of two points. More...
 
struct  mrpt::math::TLine2D
 2D line without bounds, represented by its equation $Ax+By+C=0$. More...
 
struct  mrpt::math::TLine3D
 3D line, represented by a base point and a director vector. More...
 
struct  mrpt::math::TPlane
 3D Plane, represented by its equation $Ax+By+Cz+D=0$ More...
 
class  mrpt::math::TPolygon2D
 2D polygon, inheriting from std::vector<TPoint2D>. More...
 
class  mrpt::math::TPolygon3D
 3D polygon, inheriting from std::vector<TPoint3D> More...
 
struct  mrpt::math::TObject2D
 Standard type for storing any lightweight 2D type. More...
 
struct  mrpt::math::TObject3D
 Standard object for storing any 3D lightweight object. More...
 
struct  mrpt::math::TTwist2D
 2D twist: 2D velocity vector (vx,vy) + planar angular velocity (omega) More...
 
struct  mrpt::math::TTwist3D
 3D twist: 3D velocity vector (vx,vy,vz) + angular velocity (wx,wy,wz) More...
 

Typedefs

typedef TPlane mrpt::math::TPlane3D
 

Functions

std::ostream BASE_IMPEXPmrpt::math::operator<< (std::ostream &o, const TPoint2D &p)
 
std::ostream BASE_IMPEXPmrpt::math::operator<< (std::ostream &o, const TPoint3D &p)
 
std::ostream BASE_IMPEXPmrpt::math::operator<< (std::ostream &o, const TPose2D &p)
 
std::ostream BASE_IMPEXPmrpt::math::operator<< (std::ostream &o, const TPose3D &p)
 
std::ostream BASE_IMPEXPmrpt::math::operator<< (std::ostream &o, const TPose3DQuat &p)
 
TPoint3D mrpt::math::operator- (const TPoint3D &p1)
 Unary minus operator for 3D points. More...
 
bool mrpt::math::operator== (const TPoint2D &p1, const TPoint2D &p2)
 Exact comparison between 2D points. More...
 
bool mrpt::math::operator!= (const TPoint2D &p1, const TPoint2D &p2)
 Exact comparison between 2D points. More...
 
bool mrpt::math::operator== (const TPoint3D &p1, const TPoint3D &p2)
 Exact comparison between 3D points. More...
 
bool mrpt::math::operator!= (const TPoint3D &p1, const TPoint3D &p2)
 Exact comparison between 3D points. More...
 
bool mrpt::math::operator== (const TPose2D &p1, const TPose2D &p2)
 Exact comparison between 2D poses, taking possible cycles into account. More...
 
bool mrpt::math::operator!= (const TPose2D &p1, const TPose2D &p2)
 Exact comparison between 2D poses, taking possible cycles into account. More...
 
bool mrpt::math::operator== (const TPose3D &p1, const TPose3D &p2)
 Exact comparison between 3D poses, taking possible cycles into account. More...
 
bool mrpt::math::operator!= (const TPose3D &p1, const TPose3D &p2)
 Exact comparison between 3D poses, taking possible cycles into account. More...
 
bool mrpt::math::operator== (const TSegment2D &s1, const TSegment2D &s2)
 
bool mrpt::math::operator!= (const TSegment2D &s1, const TSegment2D &s2)
 
bool mrpt::math::operator== (const TSegment3D &s1, const TSegment3D &s2)
 
bool mrpt::math::operator!= (const TSegment3D &s1, const TSegment3D &s2)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TPose2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TPose3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment2D &s)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment2D &s)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TLine2D &l)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine2D &l)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TObject2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment3D &s)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment3D &s)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TLine3D &l)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine3D &l)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TPlane &p)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TPlane &p)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TObject3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TTwist2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TTwist2D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator>> (mrpt::utils::CStream &in, mrpt::math::TTwist3D &o)
 
BASE_IMPEXP mrpt::utils::CStreammrpt::math::operator<< (mrpt::utils::CStream &out, const mrpt::math::TTwist3D &o)
 

Variables

double BASE_IMPEXP mrpt::math::geometryEpsilon =1e-5
 Global epsilon to overcome small precision errors (Default=1e-5) More...
 
struct BASE_IMPEXP mrpt::math::TSegment3D
 
struct BASE_IMPEXP mrpt::math::TLine3D
 
class BASE_IMPEXP mrpt::math::TPolygon3D
 
struct BASE_IMPEXP mrpt::math::TObject3D
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_POINT =0
 Object type identifier for TPoint2D or TPoint3D. More...
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_SEGMENT =1
 Object type identifier for TSegment2D or TSegment3D. More...
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_LINE =2
 Object type identifier for TLine2D or TLine3D. More...
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_POLYGON =3
 Object type identifier for TPolygon2D or TPolygon3D. More...
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_PLANE =4
 Object type identifier for TPlane. More...
 
const unsigned char mrpt::math::GEOMETRIC_TYPE_UNDEFINED =255
 Object type identifier for empty TObject2D or TObject3D. More...
 

Simple intersection operations, relying basically on geometrical operations.

bool BASE_IMPEXP mrpt::math::intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between two 3D segments. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TSegment3D &s1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between a 3D segment and a plane. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::intersect (const TPlane &p1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between two planes. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::intersect (const TLine3D &r1, const TLine3D &r2, TObject3D &obj)
 Gets the intersection between two 3D lines. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TLine2D &r1, const TLine2D &r2, TObject2D &obj)
 Gets the intersection between two 2D lines. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::getAngle (const TPlane &p1, const TPlane &p2)
 Computes the angle between two planes. More...
 
double BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::getAngle (const TLine3D &r1, const TLine3D &r2)
 Computes the angle between two 3D lines or segments (implicit constructor will be used if passing a segment instead of a line). More...
 
double BASE_IMPEXP mrpt::math::getAngle (const TLine2D &r1, const TLine2D &r2)
 Computes the angle between two 2D lines or segments (implicit constructor will be used if passing a segment instead of a line). More...
 

Creation of lines from poses.

void BASE_IMPEXP mrpt::math::createFromPoseX (const mrpt::poses::CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the X axis in a given pose. More...
 
void BASE_IMPEXP mrpt::math::createFromPoseY (const mrpt::poses::CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the Y axis in a given pose. More...
 
void BASE_IMPEXP mrpt::math::createFromPoseZ (const mrpt::poses::CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the Z axis in a given pose. More...
 
void BASE_IMPEXP mrpt::math::createFromPoseAndVector (const mrpt::poses::CPose3D &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 BASE_IMPEXP mrpt::math::createFromPoseX (const TPose2D &p, TLine2D &r)
 Gets a 2D line corresponding to the X axis in a given pose. More...
 
void BASE_IMPEXP mrpt::math::createFromPoseY (const TPose2D &p, TLine2D &r)
 Gets a 2D line corresponding to the Y axis in a given pose. More...
 
void BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::conformAPlane (const std::vector< TPoint3D > &points)
 Checks whether this polygon or set of points acceptably fits a plane. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::areAligned (const std::vector< TPoint2D > &points)
 Checks whether this set of points acceptably fits a 2D line. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::areAligned (const std::vector< TPoint3D > &points)
 Checks whether this set of points acceptably fits a 3D line. More...
 
bool BASE_IMPEXP 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::poses::CPose3D &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::poses::CPose3D &newXYpose, TSegment3D &newSegment)
 Uses the given pose 3D to project a segment into a new base. More...
 
void BASE_IMPEXP mrpt::math::project3D (const TLine3D &line, const mrpt::poses::CPose3D &newXYpose, TLine3D &newLine)
 Uses the given pose 3D to project a line into a new base. More...
 
void BASE_IMPEXP mrpt::math::project3D (const TPlane &plane, const mrpt::poses::CPose3D &newXYpose, TPlane &newPlane)
 Uses the given pose 3D to project a plane into a new base. More...
 
void BASE_IMPEXP mrpt::math::project3D (const TPolygon3D &polygon, const mrpt::poses::CPose3D &newXYpose, TPolygon3D &newPolygon)
 Uses the given pose 3D to project a polygon into a new base. More...
 
void BASE_IMPEXP mrpt::math::project3D (const TObject3D &object, const mrpt::poses::CPose3D &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::poses::CPose3D &newXYpose, std::vector< T > &newObjs)
 Projects a set of 3D objects into the plane's base. More...
 
void BASE_IMPEXP mrpt::math::project2D (const TPoint2D &point, const mrpt::poses::CPose2D &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 mrpt::poses::CPose2D &newXpose, TSegment2D &newSegment)
 Uses the given pose 2D to project a segment into a new base. More...
 
void BASE_IMPEXP mrpt::math::project2D (const TLine2D &line, const mrpt::poses::CPose2D &newXpose, TLine2D &newLine)
 Uses the given pose 2D to project a line into a new base. More...
 
void BASE_IMPEXP mrpt::math::project2D (const TPolygon2D &polygon, const mrpt::poses::CPose2D &newXpose, TPolygon2D &newPolygon)
 Uses the given pose 2D to project a polygon into a new base. More...
 
void BASE_IMPEXP mrpt::math::project2D (const TObject2D &object, const mrpt::poses::CPose2D &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 mrpt::poses::CPose2D &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 BASE_IMPEXP mrpt::math::intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
 Gets the intersection between a 2D polygon and a 2D segment. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TPolygon2D &p1, const TLine2D &r2, TObject2D &obj)
 Gets the intersection between a 2D polygon and a 2D line. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::intersect (const TPolygon3D &p1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a 3D segment. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TPolygon3D &p1, const TLine3D &r2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a 3D line. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TPolygon3D &p1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a plane. More...
 
bool BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::intersect (const TObject2D &o1, const TObject2D &o2, TObject2D &obj)
 Gets the intersection between any pair of 2D objects. More...
 
bool BASE_IMPEXP mrpt::math::intersect (const TObject3D &o1, const TObject3D &o2, TObject3D &obj)
 Gets the intersection between any pair of 3D objects. More...
 

Distances

double BASE_IMPEXP mrpt::math::distance (const TPoint2D &p1, const TPoint2D &p2)
 Gets the distance between two points in a 2D space. More...
 
double BASE_IMPEXP mrpt::math::distance (const TPoint3D &p1, const TPoint3D &p2)
 Gets the distance between two points in a 3D space. More...
 
double BASE_IMPEXP mrpt::math::distance (const TLine2D &r1, const TLine2D &r2)
 Gets the distance between two lines in a 2D space. More...
 
double BASE_IMPEXP mrpt::math::distance (const TLine3D &r1, const TLine3D &r2)
 Gets the distance between two lines in a 3D space. More...
 
double BASE_IMPEXP 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. More...
 
double BASE_IMPEXP mrpt::math::distance (const TPolygon2D &p1, const TPolygon2D &p2)
 Gets the distance between two polygons in a 2D space. More...
 
double BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::distance (const TPolygon3D &p1, const TPolygon3D &p2)
 Gets the distance between two polygons in a 3D space. More...
 
double BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::createPlaneFromPoseXY (const mrpt::poses::CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its Z vector. More...
 
void BASE_IMPEXP mrpt::math::createPlaneFromPoseXZ (const mrpt::poses::CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its Y vector. More...
 
void BASE_IMPEXP mrpt::math::createPlaneFromPoseYZ (const mrpt::poses::CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its X vector. More...
 
void BASE_IMPEXP mrpt::math::createPlaneFromPoseAndNormal (const mrpt::poses::CPose3D &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 BASE_IMPEXP mrpt::math::generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], char coord, CMatrixDouble &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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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. More...
 
double mrpt::math::getEpsilon ()
 Gets the value of the geometric epsilon. More...
 
bool BASE_IMPEXP mrpt::math::splitInConvexComponents (const TPolygon2D &poly, std::vector< TPolygon2D > &components)
 Splits a 2D polygon into convex components. More...
 
bool BASE_IMPEXP mrpt::math::splitInConvexComponents (const TPolygon3D &poly, std::vector< TPolygon3D > &components)
 Splits a 3D polygon into convex components. More...
 
void BASE_IMPEXP mrpt::math::getSegmentBisector (const TSegment2D &sgm, TLine2D &bis)
 Gets the bisector of a 2D segment. More...
 
void BASE_IMPEXP mrpt::math::getSegmentBisector (const TSegment3D &sgm, TPlane &bis)
 Gets the bisector of a 3D segment. More...
 
void BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP mrpt::math::traceRay (const std::vector< TPolygonWithPlane > &vec, const mrpt::poses::CPose3D &pose, double &dist)
 Fast ray tracing method using polygons' properties. More...
 
bool mrpt::math::traceRay (const std::vector< TPolygon3D > &vec, const mrpt::poses::CPose3D &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 >
Eigen::Matrix< double, 3, 1 > 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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 BASE_IMPEXP 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...
 
template<class T >
CMatrixTemplateNumeric< T > mrpt::math::generateAxisBaseFromDirection (T dx, T dy, T 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 BASE_IMPEXP mrpt::math::slerp (const mrpt::poses::CPose3D &q0, const mrpt::poses::CPose3D &q1, const double t, mrpt::poses::CPose3D &p)
 SLERP interpolation between two 6D poses - like mrpt::math::slerp for quaternions, but interpolates the [X,Y,Z] coordinates as well. More...
 
void BASE_IMPEXP mrpt::math::slerp (const mrpt::poses::CPose3DQuat &q0, const mrpt::poses::CPose3DQuat &q1, const double t, mrpt::poses::CPose3DQuat &p)
 
void BASE_IMPEXP mrpt::math::slerp_ypr (const mrpt::math::TPose3D &q0, const mrpt::math::TPose3D &q1, const double t, mrpt::math::TPose3D &p)
 

Typedef Documentation

typedef TPlane mrpt::math::TPlane3D

Definition at line 1000 of file lightweight_geom_data.h.

Function Documentation

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

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

See Also
geometryEpsilon

Definition at line 847 of file geometry.cpp.

References mrpt::math::geometryEpsilon, mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

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

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
geometryEpsilon

Definition at line 860 of file geometry.cpp.

References mrpt::math::areAligned().

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

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

See Also
geometryEpsilon

Definition at line 869 of file geometry.cpp.

References mrpt::math::geometryEpsilon, mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

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 883 of file geometry.cpp.

References mrpt::math::areAligned(), and mrpt::math::TLine3D.

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 1727 of file geometry.cpp.

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

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 1786 of file geometry.cpp.

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

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 1819 of file geometry.cpp.

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

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 1827 of file geometry.cpp.

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

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 1836 of file geometry.cpp.

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

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().

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 33 of file geometry.cpp.

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 106 of file geometry.cpp.

References mrpt::math::square().

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

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

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

See Also
TPolygon3D,geometryEpsilon

Definition at line 829 of file geometry.cpp.

References mrpt::math::geometryEpsilon, mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

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

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,geometryEpsilon

Definition at line 843 of file geometry.cpp.

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

void mrpt::math::createFromPoseAndVector ( const mrpt::poses::CPose3D 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 800 of file geometry.cpp.

References mrpt::math::TLine3D::director, mrpt::poses::CPose3D::getHomogeneousMatrixVal(), and mrpt::math::TLine3D::pBase.

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 821 of file geometry.cpp.

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

void mrpt::math::createFromPoseX ( const mrpt::poses::CPose3D 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 788 of file geometry.cpp.

References createFromPoseAndAxis().

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

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 809 of file geometry.cpp.

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

void mrpt::math::createFromPoseY ( const mrpt::poses::CPose3D 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 792 of file geometry.cpp.

References createFromPoseAndAxis().

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 815 of file geometry.cpp.

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

void mrpt::math::createFromPoseZ ( const mrpt::poses::CPose3D 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 796 of file geometry.cpp.

References createFromPoseAndAxis().

void mrpt::math::createPlaneFromPoseAndNormal ( const mrpt::poses::CPose3D 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 1642 of file geometry.cpp.

References mrpt::math::TPlane::coefs, and mrpt::poses::CPose3D::getHomogeneousMatrixVal().

void mrpt::math::createPlaneFromPoseXY ( const mrpt::poses::CPose3D pose,
TPlane plane 
)

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

See Also
createPlaneFromPoseXZ,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

Definition at line 1630 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

void mrpt::math::createPlaneFromPoseXZ ( const mrpt::poses::CPose3D pose,
TPlane plane 
)

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

See Also
createPlaneFromPoseXY,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal

Definition at line 1634 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

void mrpt::math::createPlaneFromPoseYZ ( const mrpt::poses::CPose3D pose,
TPlane plane 
)

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

See Also
createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseAndNormal

Definition at line 1638 of file geometry.cpp.

References createPlaneFromPoseAndAxis().

template<class T , class U , class V >
void mrpt::math::crossProduct3D ( const T &  v0,
const U &  v1,
V &  vOut 
)
inline
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 622 of file geometry.h.

template<class VEC1 , class VEC2 >
Eigen::Matrix<double,3,1> mrpt::math::crossProduct3D ( const VEC1 &  v0,
const VEC2 &  v1 
)
inline

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

Definition at line 637 of file geometry.h.

References ASSERT_.

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

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

Definition at line 1511 of file geometry.cpp.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

Referenced by mrpt::math::assemblePolygons(), mrpt::utils::CArray< size_t, 2 >::assign(), mrpt::detectors::CFaceDetection::checkIfDiagonalSurface(), mrpt::detectors::CFaceDetection::checkIfDiagonalSurface2(), mrpt::slam::TDataAssociationResults::clear(), mrpt::maps::CPointsMap::compute3DDistanceToMesh(), mrpt::math::confidenceIntervals(), mrpt::math::TSegment2D::contains(), mrpt::math::TSegment3D::contains(), mrpt::vision::CFeature::descriptorORBDistanceTo(), mrpt::math::TSegment3D::distance(), mrpt::poses::CPoseInterpolatorBase< DIM >::filter(), find_chessboard_corners_multiple(), mrpt::utils::find_in_vector(), mrpt::obs::CRawlog::findObservationsByClassInRange(), getHeight(), 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::opengl::CPolyhedron::TPolyhedronEdge::length(), mrpt::math::TSegment2D::length(), mrpt::math::TSegment3D::length(), mrpt::slam::PF_implementation< PARTICLE_TYPE, MYSELF >::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< VEH_SIZE, OBS_SIZE, FEAT_SIZE, ACT_SIZE, KFTYPE >::runOneKalmanIteration(), mrpt::math::CBinaryRelation< T, U, UIsObject >::setRelationValue(), mrpt::math::TSegment2D::signedDistance(), mrpt::math::splitInConvexComponents(), mrpt::math::TLine3D::TLine3D(), and velodyne_scan_to_pointcloud().

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

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

Definition at line 1517 of file geometry.cpp.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

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

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

Definition at line 1537 of file geometry.cpp.

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

double mrpt::math::distance ( const TLine3D r1,
const TLine3D r2 
)
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 1559 of file geometry.cpp.

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

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

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

Definition at line 1571 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 1576 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 435 of file geometry.h.

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 1581 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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

Definition at line 439 of file geometry.h.

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

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

Definition at line 1586 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 1591 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 445 of file geometry.h.

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 1596 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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 450 of file geometry.h.

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

Gets the distance between a polygon and a plane.

Definition at line 1601 of file geometry.cpp.

References MRPT_UNUSED_PARAM, and THROW_EXCEPTION.

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

Gets the distance between a plane and a polygon.

Definition at line 455 of file geometry.h.

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 752 of file geometry.h.

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

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 758 of file geometry.h.

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 273 of file geometry.cpp.

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

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 764 of file geometry.h.

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 770 of file geometry.h.

template<class T >
CMatrixTemplateNumeric<T> mrpt::math::generateAxisBaseFromDirection ( dx,
dy,
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 (CMatrixTemplateNumeric<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 916 of file geometry.h.

References mrpt::math::crossProduct3D(), MRPT_END, MRPT_START, mrpt::math::square(), and THROW_EXCEPTION.

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

void mrpt::math::generateAxisBaseFromDirectionAndAxis ( const double(&)  vec[3],
char  coord,
CMatrixDouble 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 1652 of file geometry.cpp.

References mrpt::math::geometryEpsilon.

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

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

Computes the angle between two planes.

Definition at line 726 of file geometry.cpp.

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

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

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 739 of file geometry.cpp.

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

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 179 of file geometry.h.

References mrpt::math::getAngle().

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

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

Definition at line 752 of file geometry.cpp.

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

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

Computes the angle between two 2D lines or segments (implicit constructor will be used if passing a segment instead of a line).

Definition at line 765 of file geometry.cpp.

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

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 1955 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::geometryEpsilon, mrpt::math::TObject2D::getPoint(), mrpt::math::intersect(), mrpt::math::square(), mrpt::math::TLine2D::unitarize(), mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

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

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 1983 of file geometry.cpp.

References mrpt::math::getAngleBisector(), mrpt::math::TPlane::getAsPose3D(), mrpt::math::project3D(), and mrpt::math::TLine3D.

double mrpt::math::getEpsilon ( )
inline

Gets the value of the geometric epsilon.

See Also
geometryEpsilon,setEpsilon

Definition at line 555 of file geometry.h.

References mrpt::math::geometryEpsilon.

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 1606 of file geometry.cpp.

References min, mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

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

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 1524 of file geometry.cpp.

References min, mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

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 1674 of file geometry.cpp.

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

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 1696 of file geometry.cpp.

References mrpt::math::covariancesAndMean(), mrpt::math::TLine3D::director, getIndexOfMax(), and mrpt::math::TLine3D::pBase.

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 1710 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::covariancesAndMean(), mrpt::math::geometryEpsilon, and getIndexOfMin().

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

void mrpt::math::getSegmentBisector ( const TSegment2D sgm,
TLine2D bis 
)
void mrpt::math::getSegmentBisector ( const TSegment3D sgm,
TPlane bis 
)
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 568 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), intersectInCommonLine(), mrpt::math::TObject3D::isPoint(), and mrpt::math::TLine3D.

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().

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 583 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), mrpt::math::intersect(), mrpt::math::TObject3D::isLine(), and mrpt::math::TLine3D.

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 597 of file geometry.cpp.

References mrpt::math::TSegment3D::contains(), mrpt::math::TObject3D::getPoint(), mrpt::math::intersect(), mrpt::math::TObject3D::isLine(), and mrpt::math::TLine3D.

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 80 of file geometry.h.

References mrpt::math::intersect().

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 611 of file geometry.cpp.

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

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 637 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TLine3D::director, mrpt::math::TPlane::evaluatePoint(), mrpt::math::geometryEpsilon, mrpt::math::TLine3D::pBase, mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

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 105 of file geometry.h.

References mrpt::math::intersect().

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().

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 660 of file geometry.cpp.

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

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 687 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::math::geometryEpsilon, mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

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 706 of file geometry.cpp.

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

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 151 of file geometry.h.

References mrpt::math::intersect().

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 717 of file geometry.cpp.

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

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 1027 of file geometry.cpp.

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

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 1037 of file geometry.cpp.

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

bool mrpt::math::intersect ( const TPolygon2D p1,
const TPolygon2D p2,
TObject2D obj 
)
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 356 of file geometry.h.

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 360 of file geometry.h.

References mrpt::math::intersect().

bool mrpt::math::intersect ( const TPolygon3D p1,
const TSegment3D s2,
TObject3D obj 
)
bool mrpt::math::intersect ( const TPolygon3D p1,
const TLine3D r2,
TObject3D obj 
)
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 1300 of file geometry.cpp.

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

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 1339 of file geometry.cpp.

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

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 372 of file geometry.h.

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 376 of file geometry.h.

References mrpt::math::intersect().

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 380 of file geometry.h.

References mrpt::math::intersect().

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 1372 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().

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 1388 of file geometry.cpp.

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

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 397 of file geometry.h.

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

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 408 of file geometry.h.

bool mrpt::math::intersect ( const TObject2D o1,
const TObject2D o2,
TObject2D obj 
)
bool mrpt::math::intersect ( const TObject3D o1,
const TObject3D o2,
TObject3D obj 
)
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 304 of file geometry.cpp.

References mrpt::math::square().

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 777 of file geometry.h.

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

bool mrpt::math::operator!= ( const TPoint2D &  p1,
const TPoint2D &  p2 
)
inline

Exact comparison between 2D points.

Definition at line 545 of file lightweight_geom_data.h.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

bool mrpt::math::operator!= ( const TPoint3D &  p1,
const TPoint3D &  p2 
)
inline

Exact comparison between 3D points.

Definition at line 557 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

bool mrpt::math::operator!= ( const TPose2D &  p1,
const TPose2D &  p2 
)
inline

Exact comparison between 2D poses, taking possible cycles into account.

Definition at line 569 of file lightweight_geom_data.h.

References mrpt::math::TPose2D::phi, mrpt::math::wrapTo2Pi(), mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

bool mrpt::math::operator!= ( const TPose3D &  p1,
const TPose3D &  p2 
)
inline

Exact comparison between 3D poses, taking possible cycles into account.

Definition at line 581 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, mrpt::math::wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

bool mrpt::math::operator!= ( const TSegment2D &  s1,
const TSegment2D &  s2 
)
inline
bool mrpt::math::operator!= ( const TSegment3D &  s1,
const TSegment3D &  s2 
)
inline
TPoint3D mrpt::math::operator- ( const TPoint3D &  p1)
inline

Unary minus operator for 3D points.

Definition at line 533 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

std::ostream & mrpt::math::operator<< ( std::ostream &  o,
const TPoint2D &  p 
)

Definition at line 256 of file lightweight_geom_data.cpp.

std::ostream & mrpt::math::operator<< ( std::ostream &  o,
const TPoint3D &  p 
)

Definition at line 257 of file lightweight_geom_data.cpp.

std::ostream & mrpt::math::operator<< ( std::ostream &  o,
const TPose2D &  p 
)

Definition at line 258 of file lightweight_geom_data.cpp.

std::ostream & mrpt::math::operator<< ( std::ostream &  o,
const TPose3D &  p 
)

Definition at line 259 of file lightweight_geom_data.cpp.

std::ostream & mrpt::math::operator<< ( std::ostream &  o,
const TPose3DQuat &  p 
)

Definition at line 260 of file lightweight_geom_data.cpp.

mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TPoint2D o 
)

Definition at line 957 of file lightweight_geom_data.cpp.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TPoint3D o 
)
mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TPose2D o 
)
mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TPose3D o 
)
CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TSegment2D s 
)
CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TLine2D l 
)

Definition at line 265 of file lightweight_geom_data.cpp.

References mrpt::math::TLine2D::coefs.

mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TObject2D o 
)
mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TSegment3D s 
)
mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TLine3D l 
)
mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TPlane p 
)

Definition at line 272 of file lightweight_geom_data.cpp.

References mrpt::math::TPlane::coefs.

mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TObject3D o 
)
BASE_IMPEXP mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TTwist2D o 
)

Definition at line 990 of file lightweight_geom_data.cpp.

References mrpt::math::TTwist2D::size().

BASE_IMPEXP mrpt::utils::CStream & mrpt::math::operator<< ( mrpt::utils::CStream out,
const mrpt::math::TTwist3D o 
)

Definition at line 1001 of file lightweight_geom_data.cpp.

References mrpt::math::TTwist3D::size().

bool mrpt::math::operator== ( const TPoint2D &  p1,
const TPoint2D &  p2 
)
inline

Exact comparison between 2D points.

Definition at line 539 of file lightweight_geom_data.h.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

bool mrpt::math::operator== ( const TPoint3D &  p1,
const TPoint3D &  p2 
)
inline

Exact comparison between 3D points.

Definition at line 551 of file lightweight_geom_data.h.

References mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

bool mrpt::math::operator== ( const TPose2D &  p1,
const TPose2D &  p2 
)
inline

Exact comparison between 2D poses, taking possible cycles into account.

Definition at line 563 of file lightweight_geom_data.h.

References mrpt::math::TPose2D::phi, mrpt::math::wrapTo2Pi(), mrpt::math::TPose2D::x, and mrpt::math::TPose2D::y.

bool mrpt::math::operator== ( const TPose3D &  p1,
const TPose3D &  p2 
)
inline

Exact comparison between 3D poses, taking possible cycles into account.

Definition at line 575 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, mrpt::math::wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::z.

bool mrpt::math::operator== ( const TSegment2D &  s1,
const TSegment2D &  s2 
)
inline
bool mrpt::math::operator== ( const TSegment3D &  s1,
const TSegment3D &  s2 
)
inline
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TPoint2D o 
)

Definition at line 952 of file lightweight_geom_data.cpp.

References mrpt::math::TPoint2D::x, and mrpt::math::TPoint2D::y.

mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TPoint3D o 
)
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TPose2D o 
)
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TPose3D o 
)
CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TSegment2D s 
)
CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TLine2D l 
)

Definition at line 264 of file lightweight_geom_data.cpp.

References mrpt::math::TLine2D::coefs.

mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TObject2D o 
)
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TSegment3D s 
)
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TLine3D l 
)
mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TPlane p 
)

Definition at line 271 of file lightweight_geom_data.cpp.

References mrpt::math::TPlane::coefs.

mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TObject3D o 
)
BASE_IMPEXP mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TTwist2D o 
)

Definition at line 985 of file lightweight_geom_data.cpp.

References mrpt::math::TTwist2D::size().

BASE_IMPEXP mrpt::utils::CStream & mrpt::math::operator>> ( mrpt::utils::CStream in,
mrpt::math::TTwist3D o 
)

Definition at line 996 of file lightweight_geom_data.cpp.

References mrpt::math::TTwist3D::size().

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 246 of file geometry.cpp.

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

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 822 of file geometry.h.

void mrpt::math::project2D ( const TPoint2D point,
const mrpt::poses::CPose2D newXpose,
TPoint2D newPoint 
)

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

Definition at line 968 of file geometry.cpp.

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

void mrpt::math::project2D ( const TSegment2D &  segment,
const mrpt::poses::CPose2D newXpose,
TSegment2D &  newSegment 
)
inline

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

Definition at line 310 of file geometry.h.

void mrpt::math::project2D ( const TLine2D line,
const mrpt::poses::CPose2D newXpose,
TLine2D newLine 
)

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

Definition at line 972 of file geometry.cpp.

References mrpt::math::TLine2D::coefs, mrpt::poses::CPose2D::phi(), mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::x(), and mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::y().

void mrpt::math::project2D ( const TPolygon2D polygon,
const mrpt::poses::CPose2D newXpose,
TPolygon2D newPolygon 
)

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

Definition at line 981 of file geometry.cpp.

void mrpt::math::project2D ( const TObject2D object,
const mrpt::poses::CPose2D newXpose,
TObject2D newObject 
)
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 mrpt::poses::CPose2D

Definition at line 323 of file geometry.h.

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

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 mrpt::poses::CPose2D

Definition at line 332 of file geometry.h.

References mrpt::math::TLine2D::getAsPose2DForcingOrigin().

template<class T >
void mrpt::math::project2D ( const std::vector< T > &  objs,
const mrpt::poses::CPose2D newXpose,
std::vector< T > &  newObjs 
)

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

Definition at line 339 of file geometry.h.

void mrpt::math::project3D ( const TPoint3D &  point,
const mrpt::poses::CPose3D newXYpose,
TPoint3D &  newPoint 
)
inline
void mrpt::math::project3D ( const TSegment3D &  segment,
const mrpt::poses::CPose3D newXYpose,
TSegment3D &  newSegment 
)
inline

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

Definition at line 274 of file geometry.h.

References mrpt::poses::CPose3D::composePoint(), mrpt::math::TPoint3D::x, mrpt::math::TPoint3D::y, and mrpt::math::TPoint3D::z.

void mrpt::math::project3D ( const TLine3D line,
const mrpt::poses::CPose3D newXYpose,
TLine3D newLine 
)
void mrpt::math::project3D ( const TPlane plane,
const mrpt::poses::CPose3D newXYpose,
TPlane newPlane 
)

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

Definition at line 902 of file geometry.cpp.

References mrpt::math::TPlane::coefs, mrpt::math::TPlane::evaluatePoint(), mrpt::poses::CPose3D::getHomogeneousMatrixVal(), and mrpt::math::TPlane::unitarize().

void mrpt::math::project3D ( const TPolygon3D polygon,
const mrpt::poses::CPose3D newXYpose,
TPolygon3D newPolygon 
)

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

Definition at line 915 of file geometry.cpp.

References mrpt::math::project3D().

void mrpt::math::project3D ( const TObject3D object,
const mrpt::poses::CPose3D newXYPose,
TObject3D newObject 
)
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 285 of file geometry.h.

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 292 of file geometry.h.

template<class T >
void mrpt::math::project3D ( const std::vector< T > &  objs,
const mrpt::poses::CPose3D newXYpose,
std::vector< T > &  newObjs 
)

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

Definition at line 300 of file geometry.h.

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 374 of file geometry.cpp.

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

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

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 133 of file geometry.cpp.

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

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 228 of file geometry.cpp.

References mrpt::math::SegmentsIntersection().

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

Changes the value of the geometric epsilon.

See Also
geometryEpsilon,getEpsilon

Definition at line 548 of file geometry.h.

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 655 of file geometry.h.

Referenced by mrpt::poses::CPose3DRotVec::composeFrom(), mrpt::poses::dVinvt_dR(), mrpt::poses::CPose3D::ln_jacob(), and TEST().

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 664 of file geometry.h.

References ASSERT_.

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 680 of file geometry.h.

Referenced by mrpt::poses::CPose3DRotVec::composeFrom(), jacob_dA_eps_D_p_deps(), mrpt::poses::CPose3D::jacob_dAexpeD_de(), jacob_deps_D_p_deps(), mrpt::poses::CPose3D::jacob_dexpeD_de(), and mrpt::math::vectorsAreParallel2D().

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 689 of file geometry.h.

References ASSERT_.

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 35 of file slerp.h.

References ASSERTDEB_, and mrpt::math::square().

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

void mrpt::mrpt::math::slerp ( const mrpt::poses::CPose3D q0,
const mrpt::poses::CPose3D q1,
const double  t,
mrpt::poses::CPose3D 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 21 of file slerp.cpp.

References mrpt::poses::CPose3D::getAsQuaternion(), mrpt::math::slerp(), mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::x(), and mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::y().

void mrpt::mrpt::math::slerp ( const mrpt::poses::CPose3DQuat q0,
const mrpt::poses::CPose3DQuat q1,
const double  t,
mrpt::poses::CPose3DQuat p 
)

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 40 of file slerp.cpp.

References mrpt::poses::CPose3DQuat::quat(), mrpt::math::slerp(), mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::x(), and mrpt::poses::CPoseOrPoint< DERIVEDCLASS >::y().

void mrpt::mrpt::math::slerp_ypr ( const mrpt::math::TPose3D q0,
const mrpt::math::TPose3D q1,
const double  t,
mrpt::math::TPose3D p 
)
bool mrpt::math::splitInConvexComponents ( const TPolygon2D poly,
std::vector< TPolygon2D > &  components 
)
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 1919 of file geometry.cpp.

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

bool mrpt::math::traceRay ( const std::vector< TPolygonWithPlane > &  vec,
const mrpt::poses::CPose3D pose,
double &  dist 
)
bool mrpt::math::traceRay ( const std::vector< TPolygon3D > &  vec,
const mrpt::poses::CPose3D pose,
double &  dist 
)
inline

Fast ray tracing method using polygons' properties.

See Also
CRenderizable::rayTrace

Definition at line 596 of file geometry.h.

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 699 of file geometry.h.

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

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 707 of file geometry.h.

References mrpt::math::geometryEpsilon.

Variable Documentation

const unsigned char mrpt::math::GEOMETRIC_TYPE_LINE =2
const unsigned char mrpt::math::GEOMETRIC_TYPE_PLANE =4
const unsigned char mrpt::math::GEOMETRIC_TYPE_POINT =0
const unsigned char mrpt::math::GEOMETRIC_TYPE_POLYGON =3
const unsigned char mrpt::math::GEOMETRIC_TYPE_SEGMENT =1
const unsigned char mrpt::math::GEOMETRIC_TYPE_UNDEFINED =255
double mrpt::mrpt::math::geometryEpsilon =1e-5



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