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mrpt::math Namespace Reference

This base provides a set of functions for maths stuff. More...

Namespaces

namespace  detail
namespace  jacobians
 

A collection of functions to compute jacobians of diverse transformations, etc (some functions are redirections to existing methods elsewhere, so this namespace is actually used with grouping purposes).


Classes

class  CArray
 A STL container (as wrapper) for arrays of constant size defined at compile time - Users will most likely prefer to use CArrayPOD and its derived classes instead. More...
class  CArray< T, 0 >
class  CArrayPOD
 A CArray for Plain Old Datatypes (POD), that is, int's, double's, etc or struct's with only PODs. More...
class  CArrayNumeric
 A CArrayPOD for numeric types, supporting several mathematical operations. More...
class  CArrayFloat
 A partial specialization of CArrayNumeric for float numbers. More...
class  CArrayDouble
 A partial specialization of CArrayNumeric for double numbers. More...
class  CArrayInt
 A partial specialization of CArrayNumeric for int numbers. More...
class  CArrayUInt
 A partial specialization of CArrayNumeric for unsigned int numbers. More...
struct  CMatrixTemplateSize
 Auxiliary class used in CMatrixTemplate:size(), CMatrixTemplate::resize(), CMatrixFixedNumeric::size(), CMatrixFixedNumeric::resize(), to mimic the behavior of STL-containers. More...
class  CAStarAlgorithm
 This class is intended to efficiently solve graph-search problems using heuristics to determine the best path. More...
class  CBinaryRelation
 This class models a binary relation through the elements of any given set. More...
class  CGraphPartitioner
 Algorithms for finding the min-normalized-cut of a weighted undirected graph. More...
class  CHistogram
 This class provides an easy way of computing histograms for unidimensional real valued variables. More...
class  CLevenbergMarquardtTempl
 An implementation of the Levenberg-Marquardt algorithm for least-square minimization. More...
class  CMatrix
 This class is a "CSerializable" wrapper for "CMatrixFloat". More...
class  CMatrixB
 This class is a "CSerializable" wrapper for "CMatrixBool". More...
class  CMatrixD
 This class is a "CSerializable" wrapper for "CMatrixTemplateNumeric<double>". More...
class  CMatrixFixedNumeric
 A numeric matrix of compile-time fixed size. More...
class  CMatrixTemplate
 This template class provides the basic functionality for a general 2D any-size, resizable container of numerical or non-numerical elements. More...
class  CMatrixTemplateNumeric
 This template class extends the class "CMatrixTemplate" with many common operations with numerical matrixes. More...
class  CMatrixTemplateObjects
 This template class extends the class "CMatrixTemplate" for storing "objects" at each matrix entry. More...
class  CMatrixView
 The base for all matrix views. More...
class  CMatrixViewTranspose
 A wrapper around an existing matrix (of any kind) that allows operating on the transposed matrix. More...
class  CConstMatrixViewTranspose
 A wrapper around an existing const matrix (of any kind) that allows operating on the transposed matrix. More...
class  CSubmatrixView
 A wrapper around an existing matrix (of any kind) that allows operating on a subrange of the elements. More...
class  CConstSubmatrixView
 A const wrapper around an existing matrix (of any kind) that allows operating on a subrange of the elements. More...
class  CArbitrarySubmatrixView
 A wrapper around an existing matrix (of any kind) that allows operating on a subrange of the elements. More...
class  CConstArbitrarySubmatrixView
class  CDiagonalMatrixView
 View the diagonal of an existing NxN matrix as a 1xN matrix (or equivalently for many MRPT methods, an N-vector). More...
class  CMatrixColumnAccessor
 A vector-like wrapper for a Matrix for accessing the elements of a given column with a [] operator. More...
class  CMatrixColumnAccessorExtended
 A vector-like wrapper for a Matrix for accessing the elements of a given column with a [] operator, with offset and custom spacing. More...
class  CConstMatrixColumnAccessor
 A vector-like wrapper for a const Matrix for accessing the elements of a given column with a [] operator. More...
class  CConstMatrixColumnAccessorExtended
 A vector-like wrapper for a const Matrix for accessing the elements of a given column with a [] operator, with offset and custom spacing. More...
class  CMatrixRowAccessor
 A vector-like wrapper for a Matrix for accessing the elements of a given row with a [] operator. More...
class  CMatrixRowAccessorExtended
 A vector-like wrapper for a Matrix for accessing the elements of a given row with a [] operator, with offset and custom spacing. More...
class  CConstMatrixRowAccessor
 A vector-like wrapper for a const Matrix for accessing the elements of a given row with a [] operator. More...
class  CConstMatrixRowAccessorExtended
 A vector-like wrapper for a const Matrix for accessing the elements of a given row with a [] operator, with offset and custom spacing. More...
class  CVectorRowWrapper
class  CConstVectorRowWrapper
class  CVectorColumnWrapper
class  CConstVectorColumnWrapper
class  JointHorizontalAccessor
 Access to two matrices joint horizontally [A|B]. More...
class  JointVerticalAccessor
 Access to two matrices joint vertically [A;B]. More...
class  JointAccessor
 For usage with JointVerticalAccessor and JointHorizontalAccessor. More...
class  IndirectAccessWrapper
class  CMonteCarlo
 Montecarlo simulation for experiments in 1D. More...
class  CPolygon
 A wrapper of a TPolygon2D class, implementing CSerializable. More...
class  CQuaternion
 A quaternion, which can represent a 3D rotation as pair $ (r,\mathbf{u}) $, with a real part "r" and a 3D vector $ \mathbf{u} = (x,y,z) $, or alternatively, q = r + ix + jy + kz. More...
class  CSparseMatrixTemplate
 A sparse matrix container (with cells of any type), with iterators. More...
class  CSparseSymmetricalMatrix
 A sparse matrix container for square symmetrical content around the main diagonal. More...
class  CSplineInterpolator1D
 A (persistent) sequence of (x,y) coordinates, allowing queries of intermediate points through spline interpolation, where possible. More...
class  CVectorTemplate
 This template class provides the basic functionality for a general 1D any-size, resizable container of numerical or non-numerical elements. More...
class  CDijkstra
 The Dijkstra algorithm for finding the shortest path between a given source node in a (weighted) directed graph and all other nodes. More...
class  TPolygonWithPlane
 Slightly heavyweight type to speed-up calculations with polygons in 3D. More...
class  CDirectedGraph
 A directed graph with the argument of the template specifying the type of the annotations in the edges. More...
struct  TPoint2D
 Lightweight 2D point. More...
struct  TPose2D
 Lightweight 2D pose. More...
struct  TPoint3D
 Lightweight 3D point. More...
struct  TPoint3Df
 Lightweight 3D point (float version). More...
struct  TPose3D
 Lightweight 3D pose (three spatial coordinates, plus three angular coordinates). More...
struct  TPose3DQuat
 Lightweight 3D pose (three spatial coordinates, plus a quaternion ). More...
struct  TSegment2D
 2D segment, consisting of two points. More...
struct  TSegment3D
 3D segment, consisting of two points. More...
struct  TLine2D
 2D line without bounds, represented by its equation $Ax+By+C=0$. More...
struct  TLine3D
 3D line, represented by a base point and a director vector. More...
struct  TPlane
 3D Plane, represented by its equation $Ax+By+Cz+D=0$ More...
class  TPolygon2D
 2D polygon, inheriting from std::vector<TPoint2D>. More...
class  TPolygon3D
 3D polygon, inheriting from std::vector<TPoint3D> More...
struct  TObject2D
 Standard type for storing any lightweight 2D type. More...
struct  TObject3D
 Standard object for storing any 3D lightweight object. More...
class  RANSAC_Template

Typedefs

typedef
CLevenbergMarquardtTempl
< vector_double > 		CLevenbergMarquardt
 The default name for the LM class is an instantiation for "double".
typedef CMatrixTemplateNumeric
< float > 		CMatrixFloat
 Declares a matrix of float numbers (non serializable).
typedef CMatrixTemplateNumeric
< double > 		CMatrixDouble
 Declares a matrix of double numbers (non serializable).
typedef CMatrixTemplateNumeric
< unsigned int > 		CMatrixUInt
 Declares a matrix of unsigned ints (non serializable).
typedef CMatrixTemplate< bool > CMatrixBool
 Declares a matrix of booleans (non serializable).
typedef CMatrixTemplateNumeric
< double > 		CMatrixLongDouble
 Declares a matrix of "long doubles" (non serializable), or of "doubles" if the compiler does not support "long double".
typedef CQuaternion< double > CQuaternionDouble
 A quaternion of data type "double".
typedef CQuaternion< float > CQuaternionFloat
 A quaternion of data type "float".
typedef CVectorTemplate< float > CVectorFloat
 Declares a vector of float elements.
typedef CVectorTemplate< double > CVectorDouble
 Declares a vector of double elements.
typedef TPlane TPlane3D
typedef RANSAC_Template< double > RANSAC
 The default instance of RANSAC, for double type.
Typedefs for common sizes



typedef CMatrixFixedNumeric
< double, 2, 2 > 		CMatrixDouble22
typedef CMatrixFixedNumeric
< double, 3, 3 > 		CMatrixDouble33
typedef CMatrixFixedNumeric
< double, 4, 4 > 		CMatrixDouble44
typedef CMatrixFixedNumeric
< double, 6, 6 > 		CMatrixDouble66
typedef CMatrixFixedNumeric
< double, 7, 7 > 		CMatrixDouble77
typedef CMatrixFixedNumeric
< double, 1, 3 > 		CMatrixDouble13
typedef CMatrixFixedNumeric
< double, 3, 1 > 		CMatrixDouble31
typedef CMatrixFixedNumeric
< double, 1, 2 > 		CMatrixDouble12
typedef CMatrixFixedNumeric
< double, 2, 1 > 		CMatrixDouble21
typedef CMatrixFixedNumeric
< double, 6, 1 > 		CMatrixDouble61
typedef CMatrixFixedNumeric
< double, 1, 6 > 		CMatrixDouble16
typedef CMatrixFixedNumeric
< double, 7, 1 > 		CMatrixDouble71
typedef CMatrixFixedNumeric
< double, 1, 7 > 		CMatrixDouble17
typedef CMatrixFixedNumeric
< double, 5, 1 > 		CMatrixDouble51
typedef CMatrixFixedNumeric
< double, 1, 5 > 		CMatrixDouble15
typedef CMatrixFixedNumeric
< float, 2, 2 > 		CMatrixFloat22
typedef CMatrixFixedNumeric
< float, 3, 3 > 		CMatrixFloat33
typedef CMatrixFixedNumeric
< float, 4, 4 > 		CMatrixFloat44
typedef CMatrixFixedNumeric
< float, 6, 6 > 		CMatrixFloat66
typedef CMatrixFixedNumeric
< float, 7, 7 > 		CMatrixFloat77
typedef CMatrixFixedNumeric
< float, 1, 3 > 		CMatrixFloat13
typedef CMatrixFixedNumeric
< float, 3, 1 > 		CMatrixFloat31
typedef CMatrixFixedNumeric
< float, 1, 2 > 		CMatrixFloat12
typedef CMatrixFixedNumeric
< float, 2, 1 > 		CMatrixFloat21
typedef CMatrixFixedNumeric
< float, 6, 1 > 		CMatrixFloat61
typedef CMatrixFixedNumeric
< float, 1, 6 > 		CMatrixFloat16
typedef CMatrixFixedNumeric
< float, 7, 1 > 		CMatrixFloat71
typedef CMatrixFixedNumeric
< float, 1, 7 > 		CMatrixFloat17
typedef CMatrixFixedNumeric
< float, 5, 1 > 		CMatrixFloat51
typedef CMatrixFixedNumeric
< float, 1, 5 > 		CMatrixFloat15

Enumerations

enum  TMatrixTextFileFormat { MATRIX_FORMAT_ENG = 0, MATRIX_FORMAT_FIXED = 1, MATRIX_FORMAT_INT = 2 }

Functions

template<class T , std::size_t N>
bool operator== (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool operator< (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool operator!= (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool operator> (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool operator<= (const CArray< T, N > &x, const CArray< T, N > &y)
template<class T , std::size_t N>
bool operator>= (const CArray< T, N > &x, const CArray< T, N > &y)
template<typename U >
U myStaticCast (double val)
template<>
bool myStaticCast (double val)
template<typename MAT >
CMatrixViewTranspose< MAT > getTransposed (MAT &m)
template<typename MAT >
CConstMatrixViewTranspose< MAT > getTransposed (const MAT &m)
template<typename MAT >
CMatrixColumnAccessor< MAT > getColumnAccessor (MAT &m, size_t colIdx)
template<typename MAT >
CMatrixColumnAccessorExtended
< MAT > 		getColumnAccessor (MAT &m, size_t colIdx, size_t offset, size_t space=1)
template<typename MAT >
CConstMatrixColumnAccessor< MAT > getColumnAccessor (const MAT &m, size_t colIdx)
template<typename MAT >
CConstMatrixColumnAccessorExtended
< MAT > 		getColumnAccessor (const MAT &m, size_t colIdx, size_t offset, size_t space=1)
template<typename MAT >
CMatrixRowAccessor< MAT > getRowAccessor (MAT &m, size_t rowIdx)
template<typename MAT >
CMatrixRowAccessorExtended< MAT > getRowAccessor (MAT &m, size_t rowIdx, size_t offset, size_t space=1)
template<typename MAT >
CConstMatrixRowAccessor< MAT > getRowAccessor (const MAT &m, size_t rowIdx)
template<typename MAT >
CConstMatrixRowAccessorExtended
< MAT > 		getRowAccessor (const MAT &m, size_t rowIdx, size_t offset, size_t space=1)
template<typename VEC >
CVectorRowWrapper< VEC > getAsRow (VEC &v)
template<typename VEC >
CConstVectorRowWrapper< VEC > getAsRow (const VEC &v)
bool BASE_IMPEXP traceRay (const vector< TPolygonWithPlane > &vec, const mrpt::poses::CPose3D &pose, double &dist)
 Fast ray tracing method using polygons' properties.
bool traceRay (const vector< TPolygon3D > &vec, const mrpt::poses::CPose3D &pose, double &dist)
 Fast ray tracing method using polygons' properties.
template<class T , class U , class V >
void crossProduct3D (const T &v0, const U &v1, V &vOut)
 Computes the cross product of two 3D vectors, returning a vector normal to both.
template<class T >
void crossProduct3D (const std::vector< T > &v0, const std::vector< T > &v1, std::vector< T > &v_out)
 Computes the cross product of two 3D vectors, returning a vector normal to both.
template<class T , class U >
bool vectorsAreParallel2D (const T &v1, const U &v2)
 Returns true if two 2D vectors are parallel.
template<class T , class U >
bool vectorsAreParallel3D (const T &v1, const U &v2)
 Returns true if two 3D vectors are parallel.
double BASE_IMPEXP minimumDistanceFromPointToSegment (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, and returns that minimum distance.
double BASE_IMPEXP minimumDistanceFromPointToSegment (const double &Px, const double &Py, const double &x1, const double &y1, const double &x2, const double &y2, float &out_x, float &out_y)
 Computes the closest point from a given point to a segment, and returns that minimum distance.
void BASE_IMPEXP 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.
void BASE_IMPEXP 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.
double BASE_IMPEXP 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.
template<typename T >
T distanceBetweenPoints (const T x1, const T y1, const T x2, const T y2)
 Returns the distance between 2 points in 2D.
template<typename T >
T 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.
template<typename T >
T distanceSqrBetweenPoints (const T x1, const T y1, const T x2, const T y2)
 Returns the square distance between 2 points in 2D.
template<typename T >
T 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.
bool BASE_IMPEXP 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.
bool BASE_IMPEXP 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.
bool BASE_IMPEXP 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.
template<typename T >
bool 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.
double BASE_IMPEXP 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.
bool BASE_IMPEXP 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.
bool BASE_IMPEXP 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 wether two rotated rectangles intersect.
template<class T >
CMatrixTemplateNumeric< T > 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.
TPoint3D operator- (const TPoint3D &p1)
 Unary minus operator for 3D points.
bool operator== (const TPoint2D &p1, const TPoint2D &p2)
 Exact comparison between 2D points.
bool operator!= (const TPoint2D &p1, const TPoint2D &p2)
 Exact comparison between 2D points.
bool operator== (const TPoint3D &p1, const TPoint3D &p2)
 Exact comparison between 3D points.
bool operator!= (const TPoint3D &p1, const TPoint3D &p2)
 Exact comparison between 3D points.
bool operator== (const TPose2D &p1, const TPose2D &p2)
 Exact comparison between 2D poses, taking possible cycles into account.
bool operator!= (const TPose2D &p1, const TPose2D &p2)
 Exact comparison between 2D poses, taking possible cycles into account.
bool operator== (const TPose3D &p1, const TPose3D &p2)
 Exact comparison between 3D poses, taking possible cycles into account.
bool operator!= (const TPose3D &p1, const TPose3D &p2)
 Exact comparison between 3D poses, taking possible cycles into account.
bool operator== (const TSegment2D &s1, const TSegment2D &s2)
bool operator!= (const TSegment2D &s1, const TSegment2D &s2)
bool operator== (const TSegment3D &s1, const TSegment3D &s2)
bool operator!= (const TSegment3D &s1, const TSegment3D &s2)
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint2D &o)
 TPoint2D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint2D &o)
 TPoint2D binary output.
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TPoint3D &o)
 TPoint3D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TPoint3D &o)
 TPoint3D binary output.
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TPose2D &o)
 TPose2D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose2D &o)
 TPose2D binary output.
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TPose3D &o)
 TPose3D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TPose3D &o)
 TPose3D binary output.
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment2D &s)
 TSegment2D binary input.
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment2D &s)
 TSegment2D binary output.
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TLine2D &l)
 TLine2D binary input.
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine2D &l)
 TLine2D binary output.
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TObject2D &o)
 TObject2D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject2D &o)
 TObject2D binary input.
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TSegment3D &s)
 TSegment3D binary input.
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TSegment3D &s)
 TSegment3D binary output.
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TLine3D &l)
 TLine3D binary input.
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TLine3D &l)
 TLine3D binary output.
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TPlane &p)
 TPlane binary input.
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TPlane &p)
 TPlane binary output.
BASE_IMPEXP mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, mrpt::math::TObject3D &o)
 TObject3D binary input.
BASE_IMPEXP mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const mrpt::math::TObject3D &o)
 TObject3D binary output.
template<class CONTAINER >
size_t countNonZero (const CONTAINER &a)
template<class CONTAINER >
CONTAINER::value_type maximum (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type minimum (const CONTAINER &v, size_t *minIndex=NULL)
template<class CONTAINER >
void minimum_maximum (const CONTAINER &v, typename CONTAINER::mrpt_autotype::value_type &out_min, typename CONTAINER::mrpt_autotype::value_type &out_max, size_t *minIndex=static_cast< size_t * >(NULL), size_t *maxIndex=static_cast< size_t * >(NULL))
template<class CONTAINER >
CONTAINER::value_type norm_inf (const CONTAINER &v, size_t *maxIndex=NULL)
template<class CONTAINER >
CONTAINER::value_type squareNorm (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type norm (const CONTAINER &v)
template<class CONTAINER >
double mean (const CONTAINER &v)
template<class CONTAINER >
CONTAINER::value_type sum (const CONTAINER &v)
template<class CONTAINER , typename RET >
RET sumRetType (const CONTAINER &v)
template<class CONTAINER >
void adjustRange (CONTAINER &m, const typename CONTAINER::value_type minVal, const typename CONTAINER::value_type maxVal)
template<class CONTAINER1 , class CONTAINER2 >
void cumsum (const CONTAINER1 &in_data, CONTAINER2 &out_cumsum)
template<class CONTAINER1 , class CONTAINER2 >
size_t countCommonElements (const CONTAINER1 &a, const CONTAINER2 &b)
template<class CONTAINER >
std::vector< double > histogram (const CONTAINER &v, double limit_min, double limit_max, size_t number_bins, bool do_normalization=false, std::vector< double > *out_bin_centers=NULL)
template<class VECTORLIKE >
double stddev (const VECTORLIKE &v, bool unbiased=true)
template<class VECTORLIKE >
void meanAndStd (const VECTORLIKE &v, double &out_mean, double &out_std, bool unbiased=true)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const TPoint2D &p)
 Conversion of poses to MRPT containers (vector/matrix).
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const TPoint3D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const TPose2D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const TPose3D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const TPose3DQuat &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPoint2D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPoint3D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose2D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose3D &p)
template<class CONTAINER >
CONTAINER & containerFromPoseOrPoint (CONTAINER &C, const mrpt::poses::CPose3DQuat &p)
template<class T >
T wrapTo2Pi (T a)
 Modifies the given angle to translate it into the [0,2pi[ range.
template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, CMatrixFixedNumeric< float, NROWS, NCOLS > &M)
 Read operator from a CStream.
template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream & operator>> (mrpt::utils::CStream &in, CMatrixFixedNumeric< double, NROWS, NCOLS > &M)
 Read operator from a CStream.
template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const CMatrixFixedNumeric< float, NROWS, NCOLS > &M)
 Write operator for writing into a CStream.
template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream & operator<< (mrpt::utils::CStream &out, const CMatrixFixedNumeric< double, NROWS, NCOLS > &M)
 Write operator for writing into a CStream.
template<class T , size_t NROWS, size_t NCOLS>
bool operator== (const CMatrixFixedNumeric< T, NROWS, NCOLS > &M1, const CMatrixFixedNumeric< T, NROWS, NCOLS > &M2)
 Equal comparison (==).
template<class MATRIX >
 RET_TYPE_ASSERT_MRPTMATRIX (MATRIX, std::ostream)&operator<< (std
 Textual output stream function.
template<class MAT1 , class MAT2 >
MAT1::value_type multiply_HCHt_scalar (const MAT1 &H, const MAT2 &C)
 Just like s=H.multiply_HCHt_scalar(C), but defined in mrpt::math for backward compatibility.
template<class T >
CMatrixTemplateNumeric< T > operator/ (const CMatrixTemplateNumeric< T > &m1, const CMatrixTemplateNumeric< T > &m2)
 Binary matrix division operator A/B = A*inv(B).
template<class T >
CMatrixTemplateNumeric< T > operator^ (const CMatrixTemplateNumeric< T > &m, const unsigned int pow)
 binary power operator
template<class MAT >
 MAT_TYPE_TRANSPOSE_OF (MAT) operator~(const MAT &m)
 unary transpose operator ~
template<class MATRIX >
 RET_MAT_ASSERT_MRPTMATRIX (MATRIX) operator!(const MATRIX &m)
 Unary inversion operator.
template<class MAT1 , class MAT2 >
 MAT_TYPE_PRODUCT_OF (MAT1, MAT2) operator*(const MAT1 &A
 Matrix multiplication operator: A * B -> RES The meaning of the lengthy macros in the declaration is:

  • MAT_TYPE_PRODUCT_OF: Return type is the correct one for A*B, e.g.

class MAT_OUT void meanAndCov (const MAT_IN &v, vector_double &out_mean, MAT_OUT &out_cov)
template<class MATRIX >
 MAT_TYPE_COVARIANCE_OF (MATRIX) cov(const MATRIX &v)
 Computes the covariance matrix from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM.
bool BASE_IMPEXP loadVector (utils::CFileStream &f, std::vector< int > &d)
 Loads one row of a text file as a numerical std::vector.
bool BASE_IMPEXP loadVector (utils::CFileStream &f, std::vector< double > &d)
 Loads one row of a text file as a numerical std::vector.
bool BASE_IMPEXP isNaN (float f) MRPT_NO_THROWS
 Returns true if the number is NaN.
bool BASE_IMPEXP isNaN (double f) MRPT_NO_THROWS
 Returns true if the number is NaN.
bool BASE_IMPEXP isFinite (float f) MRPT_NO_THROWS
 Returns true if the number is non infinity.
bool BASE_IMPEXP isFinite (double f) MRPT_NO_THROWS
 Returns true if the number is non infinity.
template<typename T , typename K >
void linspace (T first, T last, size_t count, std::vector< K > &out_vector)
 Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.
template<class T >
std::vector< T > linspace (T first, T last, size_t count)
 Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.
template<class T , T STEP>
std::vector< T > sequence (T first, size_t length)
 Generates a sequence of values [first,first+STEP,first+2*STEP,.
template<class T >
std::vector< T > ones (size_t count)
 Generates a vector of all ones of the given length.
template<class T >
std::vector< T > zeros (size_t count)
 Generates a vector of all zeros of the given length.
template<class T >
void wrapTo2PiInPlace (T &a)
 Modifies the given angle to translate it into the [0,2pi[ range.
template<class T >
T wrapToPi (T a)
 Modifies the given angle to translate it into the ]-pi,pi] range.
template<class T >
void wrapToPiInPlace (T &a)
 Modifies the given angle to translate it into the ]-pi,pi] range.
template<class T >
void normalize (const std::vector< T > &v, std::vector< T > &out_v)
 Normalize a vector, such as its norm is the unity.
template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >
void meanAndCovVector (const VECTOR_OF_VECTOR &v, VECTORLIKE &out_mean, MATRIXLIKE &out_cov)
 Computes the mean vector and covariance from a list of values given as a vector of vectors, where each row is a sample.
template<class VECTOR_OF_VECTOR >
CMatrixDouble covVector (const VECTOR_OF_VECTOR &v)
 Computes the covariance matrix from a list of values given as a vector of vectors, where each row is a sample.
template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 >
void covariancesAndMeanWeighted (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const VECTORLIKE2 *weights_mean, const VECTORLIKE3 *weights_cov, const bool *elem_do_wrap2pi=NULL)
 Computes covariances and mean of any vector of containers, given optional weights for the different samples.
template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE >
void covariancesAndMean (const VECTOR_OF_VECTORS &elements, MATRIXLIKE &covariances, VECTORLIKE &means, const bool *elem_do_wrap2pi=NULL)
 Computes covariances and mean of any vector of containers.
template<class VECTORLIKE1 , class VECTORLIKE2 >
void weightedHistogram (const VECTORLIKE1 &values, const VECTORLIKE1 &weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)
 Computes the weighted histogram for a vector of values and their corresponding weights.
template<class VECTORLIKE1 , class VECTORLIKE2 >
void weightedHistogramLog (const VECTORLIKE1 &values, const VECTORLIKE1 &log_weights, float binWidth, VECTORLIKE2 &out_binCenters, VECTORLIKE2 &out_binValues)
 Computes the weighted histogram for a vector of values and their corresponding log-weights.
template<class VECTOR_OF_VECTORS , class VECTORLIKE >
void extractColumnFromVectorOfVectors (const size_t colIndex, const VECTOR_OF_VECTORS &data, VECTORLIKE &out_column)
 Extract a column from a vector of vectors, and store it in another vector.
uint64_t BASE_IMPEXP factorial64 (unsigned int n)
 Computes the factorial of an integer number and returns it as a 64-bit integer number.
double BASE_IMPEXP factorial (unsigned int n)
 Computes the factorial of an integer number and returns it as a double value (internally it uses logarithms for avoiding overflow).
template<class T >
T round2up (T val)
 Round up to the nearest power of two of a given number.
template<class T >
T round_10power (T val, int power10)
 Round a decimal number up to the given 10'th power (eg, to 1000,100,10, and also fractions) power10 means round up to: 1 -> 10, 2 -> 100, 3 -> 1000, .
template<class T >
double correlate_matrix (const CMatrixTemplateNumeric< T > &a1, const CMatrixTemplateNumeric< T > &a2)
 Calculate the correlation between two matrices (by AJOGD @ JAN-2007).
template<class T >
void BASE_IMPEXP qr_decomposition (CMatrixTemplateNumeric< T > &A, CMatrixTemplateNumeric< T > &R, CMatrixTemplateNumeric< T > &Q, CVectorTemplate< T > &c, int &sing)
 Matrix QR decomposition.
template<class T >
void BASE_IMPEXP UpdateCholesky (CMatrixTemplateNumeric< T > &chol, CVectorTemplate< T > &r1Modification)
 If R = CHOL(A) is the original Cholesky factorization of A, then R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X', where X is a column vector of appropriate length.
void BASE_IMPEXP computeEigenValues2x2 (const CMatrixFloat &in_matrix, float &min_eigenvalue, float &max_eigenvalue)
 Compute the two eigenvalues of a 2x2 matrix.
double BASE_IMPEXP averageLogLikelihood (const vector_double &logLikelihoods)
 A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean).
double BASE_IMPEXP averageWrap2Pi (const vector_double &angles)
 Computes the average of a sequence of angles in radians taking into account the correct wrapping in the range $ ]-\pi,\pi [ $, for example, the mean of (2,-2) is $ \pi $, not 0.
double BASE_IMPEXP averageLogLikelihood (const vector_double &logWeights, const vector_double &logLikelihoods)
 A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods).
std::string BASE_IMPEXP MATLAB_plotCovariance2D (const CMatrixFloat &cov22, const CVectorFloat &mean, const float &stdCount, const std::string &style=std::string("b"), const size_t &nEllipsePoints=30)
 Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('float' version).
template<class MATRIXLIKE1 , class MATRIXLIKE2 >
 RET_VOID_ASSERT_MRPTMATRICES (MATRIXLIKE1, MATRIXLIKE2) homogeneousMatrixInverse(const MATRIXLIKE1 &M
 Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products.
class VECTORLIKE3 class
MATRIXLIKE class USERPARAM
void 		estimateJacobian (const VECTORLIKE &x, void(*functor)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out), const VECTORLIKE2 &increments, const USERPARAM &userParam, MATRIXLIKE &out_Jacobian)
template<typename T , typename At , size_t N>
std::vector< T > & loadVector (std::vector< T > &v, At(&theArray)[N])
 Assignment operator for initializing a std::vector from a C array (The vector will be automatically set to the correct size).
void unwrap2PiSequence (vector_double &x)
 Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value.
template<size_t N, typename T >
std::vector< T > make_vector (const T val1,...)
 A versatile template to build vectors on-the-fly in a style close to MATLAB's v=[a b c d .
template<class MATRIXLIKE >
size_t size (const MATRIXLIKE &m, int dim)
Array operators



template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N > operator+ (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
 Operator ARRAY <- ARRAY + VECTORorARRAY.
template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N > operator- (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
 Operator ARRAY <- ARRAY - VECTORorARRAY.
template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric< T, N > operator* (const CArrayNumeric< T, N > &A, const VECTORLIKE &B)
 Dot product: ARRAY <- ARRAY .
template<typename T , size_t N>
std::ostream & operator<< (std::ostream &ostrm, const CArray< T, N > &a)
 Textual output stream function.
Statistics functions



double BASE_IMPEXP normalPDF (double x, double mu, double std)
 Evaluates the univariate normal (Gaussian) distribution at a given point "x".
template<class VECTORLIKE1 , class VECTORLIKE2 , class MATRIXLIKE >
MATRIXLIKE::value_type normalPDF (const VECTORLIKE1 &x, const VECTORLIKE2 &mu, const MATRIXLIKE &cov, const bool scaled_pdf=false)
 Evaluates the multivariate normal (Gaussian) distribution at a given point "x".
template<typename VECTORLIKE , typename MATRIXLIKE >
MATRIXLIKE::value_type normalPDF (const VECTORLIKE &d, const MATRIXLIKE &cov)
 Evaluates the multivariate normal (Gaussian) distribution at a given point given its distance vector "d" from the Gaussian mean.
template<typename VECTORLIKE1 , typename MATRIXLIKE1 , typename VECTORLIKE2 , typename MATRIXLIKE2 >
double KLD_Gaussians (const VECTORLIKE1 &mu0, const MATRIXLIKE1 &cov0, const VECTORLIKE2 &mu1, const MATRIXLIKE2 &cov1)
 Kullback-Leibler divergence (KLD) between two independent multivariate Gaussians.
double BASE_IMPEXP erfc (double x)
 The complementary error function of a Normal distribution.
double BASE_IMPEXP erf (double x)
 The error function of a Normal distribution.
double BASE_IMPEXP normalQuantile (double p)
 Evaluates the Gaussian distribution quantile for the probability value p=[0,1].
double BASE_IMPEXP normalCDF (double p)
 Evaluates the Gaussian cumulative density function.
double BASE_IMPEXP chi2inv (double P, unsigned int dim=1)
 The "quantile" of the Chi-Square distribution, for dimension "dim" and probability 0<P<1 (the inverse of chi2CDF) An aproximation from the Wilson-Hilferty transformation is used.
template<class T >
double noncentralChi2CDF (unsigned int degreesOfFreedom, T noncentrality, T arg)
double chi2CDF (unsigned int degreesOfFreedom, double arg)
double chi2PDF (unsigned int degreesOfFreedom, double arg, double accuracy=1e-7)
template<typename CONTAINER >
void condidenceIntervals (const CONTAINER &data, typename CONTAINER::value_type &out_mean, typename CONTAINER::value_type &out_lower_conf_interval, typename CONTAINER::value_type &out_upper_conf_interval, const double confidenceInterval=0.1, const size_t histogramNumBins=1000)
 Return the mean and the 10-90% confidence points (or with any other confidence value) of a set of samples by building the cummulative CDF of all the elements of the container.
Fourier functions



void BASE_IMPEXP fft_real (vector_float &in_realData, vector_float &out_FFT_Re, vector_float &out_FFT_Im, vector_float &out_FFT_Mag)
 Computes the FFT of a 2^N-size vector of real numbers, and returns the Re+Im+Magnitude parts.
void BASE_IMPEXP dft2_real (const CMatrixFloat &in_data, CMatrixFloat &out_real, CMatrixFloat &out_imag)
 Compute the 2D Discrete Fourier Transform (DFT) of a real matrix, returning the real and imaginary parts separately.
void BASE_IMPEXP idft2_real (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_data)
 Compute the 2D inverse Discrete Fourier Transform (DFT).
void BASE_IMPEXP dft2_complex (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_real, CMatrixFloat &out_imag)
 Compute the 2D Discrete Fourier Transform (DFT) of a complex matrix, returning the real and imaginary parts separately.
void BASE_IMPEXP idft2_complex (const CMatrixFloat &in_real, const CMatrixFloat &in_imag, CMatrixFloat &out_real, CMatrixFloat &out_imag)
 Compute the 2D inverse Discrete Fourier Transform (DFT).
void BASE_IMPEXP cross_correlation_FFT (const CMatrixFloat &A, const CMatrixFloat &B, CMatrixFloat &out_corr)
 Correlation of two matrixes using 2D FFT.
Simple intersection operations, relying basically on geometrical operations.



bool BASE_IMPEXP intersect (const TSegment3D &s1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between two 3D segments.
bool BASE_IMPEXP intersect (const TSegment3D &s1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between a 3D segment and a plane.
bool BASE_IMPEXP intersect (const TSegment3D &s1, const TLine3D &r2, TObject3D &obj)
 Gets the intersection between a 3D segment and a 3D line.
bool intersect (const TPlane &p1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between a plane and a 3D segment.
bool BASE_IMPEXP intersect (const TPlane &p1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between two planes.
bool BASE_IMPEXP intersect (const TPlane &p1, const TLine3D &p2, TObject3D &obj)
 Gets the intersection between a plane and a 3D line.
bool intersect (const TLine3D &r1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between a 3D line and a 3D segment.
bool intersect (const TLine3D &r1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between a 3D line and a plane.
bool BASE_IMPEXP intersect (const TLine3D &r1, const TLine3D &r2, TObject3D &obj)
 Gets the intersection between two 3D lines.
bool BASE_IMPEXP intersect (const TLine2D &r1, const TLine2D &r2, TObject2D &obj)
 Gets the intersection between two 2D lines.
bool BASE_IMPEXP intersect (const TLine2D &r1, const TSegment2D &s2, TObject2D &obj)
 Gets the intersection between a 2D line and a 2D segment.
bool intersect (const TSegment2D &s1, const TLine2D &r2, TObject2D &obj)
 Gets the intersection between a 2D line and a 2D segment.
bool BASE_IMPEXP intersect (const TSegment2D &s1, const TSegment2D &s2, TObject2D &obj)
 Gets the intersection between two 2D segments.
Angle retrieval methods. Methods which use TSegments will automatically use TLines' implicit constructors.



double BASE_IMPEXP getAngle (const TPlane &p1, const TPlane &p2)
 Computes the angle between two planes.
double BASE_IMPEXP 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).
double 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).
double BASE_IMPEXP 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).
double BASE_IMPEXP 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).
Creation of lines from poses.



void BASE_IMPEXP createFromPoseX (const CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the X axis in a given pose.
void BASE_IMPEXP createFromPoseY (const CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the Y axis in a given pose.
void BASE_IMPEXP createFromPoseZ (const CPose3D &p, TLine3D &r)
 Gets a 3D line corresponding to the Z axis in a given pose.
void BASE_IMPEXP createFromPoseAndVector (const CPose3D &p, const double(&vector)[3], TLine3D &r)
 Gets a 3D line corresponding to any arbitrary vector, in the base given by the pose.
void BASE_IMPEXP createFromPoseX (const TPose2D &p, TLine2D &r)
 Gets a 2D line corresponding to the X axis in a given pose.
void BASE_IMPEXP createFromPoseY (const TPose2D &p, TLine2D &r)
 Gets a 2D line corresponding to the Y axis in a given pose.
void BASE_IMPEXP 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.
Other line or plane related methods.



bool BASE_IMPEXP conformAPlane (const std::vector< TPoint3D > &points)
 Checks whether this polygon or set of points acceptably fits a plane.
bool BASE_IMPEXP 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.
bool BASE_IMPEXP areAligned (const std::vector< TPoint2D > &points)
 Checks whether this set of points acceptably fits a 2D line.
bool BASE_IMPEXP 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.
bool BASE_IMPEXP areAligned (const std::vector< TPoint3D > &points)
 Checks whether this set of points acceptably fits a 3D line.
bool BASE_IMPEXP 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.
Projections



void project3D (const TPoint3D &point, const CPose3D &newXYpose, TPoint3D &newPoint)
 Uses the given pose 3D to project a point into a new base.
void project3D (const TSegment3D &segment, const CPose3D &newXYpose, TSegment3D &newSegment)
 Uses the given pose 3D to project a segment into a new base.
void BASE_IMPEXP project3D (const TLine3D &line, const CPose3D &newXYpose, TLine3D &newLine)
 Uses the given pose 3D to project a line into a new base.
void BASE_IMPEXP project3D (const TPlane &plane, const CPose3D &newXYpose, TPlane &newPlane)
 Uses the given pose 3D to project a plane into a new base.
void BASE_IMPEXP project3D (const TPolygon3D &polygon, const CPose3D &newXYpose, TPolygon3D &newPolygon)
 Uses the given pose 3D to project a polygon into a new base.
void BASE_IMPEXP project3D (const TObject3D &object, const CPose3D &newXYPose, TObject3D &newObject)
 Uses the given pose 3D to project any 3D object into a new base.
template<class T >
void project3D (const T &obj, const TPlane &newXYPlane, T &newObj)
 Projects any 3D object into the plane's base, using its inverse pose.
template<class T >
void 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.
template<class T >
void project3D (const std::vector< T > &objs, const CPose3D &newXYpose, std::vector< T > &newObjs)
 Projects a set of 3D objects into the plane's base.
void project2D (const TPoint2D &point, const CPose2D &newXpose, TPoint2D &newPoint)
 Uses the given pose 2D to project a point into a new base.
void project2D (const TSegment2D &segment, const CPose2D &newXpose, TSegment2D &newSegment)
 Uses the given pose 2D to project a segment into a new base.
void BASE_IMPEXP project2D (const TLine2D &line, const CPose2D &newXpose, TLine2D &newLine)
 Uses the given pose 2D to project a line into a new base.
void BASE_IMPEXP project2D (const TPolygon2D &polygon, const CPose2D &newXpose, TPolygon2D &newPolygon)
 Uses the given pose 2D to project a polygon into a new base.
void BASE_IMPEXP project2D (const TObject2D &object, const CPose2D &newXpose, TObject2D &newObject)
 Uses the given pose 2D to project any 2D object into a new base.
template<class T >
void project2D (const T &obj, const TLine2D &newXLine, T &newObj)
 Projects any 2D object into the line's base, using its inverse pose.
template<class T >
void 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.
template<class T >
void project2D (const std::vector< T > &objs, const CPose2D &newXpose, std::vector< T > &newObjs)
 Projects a set of 2D objects into the line's base.
Polygon intersections. These operations rely more on spatial reasoning than in raw numerical operations.



bool BASE_IMPEXP intersect (const TPolygon2D &p1, const TSegment2D &s2, TObject2D &obj)
 Gets the intersection between a 2D polygon and a 2D segment.
bool BASE_IMPEXP intersect (const TPolygon2D &p1, const TLine2D &r2, TObject2D &obj)
 Gets the intersection between a 2D polygon and a 2D line.
bool BASE_IMPEXP intersect (const TPolygon2D &p1, const TPolygon2D &p2, TObject2D &obj)
 Gets the intersection between two 2D polygons.
bool intersect (const TSegment2D &s1, const TPolygon2D &p2, TObject2D &obj)
 Gets the intersection between a 2D segment and a 2D polygon.
bool intersect (const TLine2D &r1, const TPolygon2D &p2, TObject2D &obj)
 Gets the intersection between a 2D line and a 2D polygon.
bool BASE_IMPEXP intersect (const TPolygon3D &p1, const TSegment3D &s2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a 3D segment.
bool BASE_IMPEXP intersect (const TPolygon3D &p1, const TLine3D &r2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a 3D line.
bool BASE_IMPEXP intersect (const TPolygon3D &p1, const TPlane &p2, TObject3D &obj)
 Gets the intersection between a 3D polygon and a plane.
bool BASE_IMPEXP intersect (const TPolygon3D &p1, const TPolygon3D &p2, TObject3D &obj)
 Gets the intersection between two 3D polygons.
bool intersect (const TSegment3D &s1, const TPolygon3D &p2, TObject3D &obj)
 Gets the intersection between a 3D segment and a 3D polygon.
bool intersect (const TLine3D &r1, const TPolygon3D &p2, TObject3D &obj)
 Gets the intersection between a 3D line and a 3D polygon.
bool intersect (const TPlane &p1, const TPolygon3D &p2, TObject3D &obj)
 Gets the intersection between a plane and a 3D polygon.
size_t BASE_IMPEXP intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, CSparseMatrixTemplate< TObject3D > &objs)
 Gets the intersection between two sets of 3D polygons.
size_t BASE_IMPEXP intersect (const std::vector< TPolygon3D > &v1, const std::vector< TPolygon3D > &v2, std::vector< TObject3D > &objs)
 Gets the intersection between two sets of 3D polygons.
Other intersections



template<class T , class U , class O >
size_t 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.
template<class T , class U , class O >
size_t 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.
bool BASE_IMPEXP intersect (const TObject2D &o1, const TObject2D &o2, TObject2D &obj)
 Gets the intersection between any pair of 2D objects.
bool BASE_IMPEXP intersect (const TObject3D &o1, const TObject3D &o2, TObject3D &obj)
 Gets the intersection between any pair of 3D objects.
Distances



double BASE_IMPEXP distance (const TPoint2D &p1, const TPoint2D &p2)
 Gets the distance between two points in a 2D space.
double BASE_IMPEXP distance (const TPoint3D &p1, const TPoint3D &p2)
 Gets the distance between two points in a 3D space.
double BASE_IMPEXP distance (const TLine2D &r1, const TLine2D &r2)
 Gets the distance between two lines in a 2D space.
double BASE_IMPEXP distance (const TLine3D &r1, const TLine3D &r2)
 Gets the distance between two lines in a 3D space.
double BASE_IMPEXP distance (const TPlane &p1, const TPlane &p2)
 Gets the distance between two planes.
double BASE_IMPEXP distance (const TPolygon2D &p1, const TPolygon2D &p2)
 Gets the distance between two polygons in a 2D space.
double BASE_IMPEXP distance (const TPolygon2D &p1, const TSegment2D &s2)
 Gets the distance between a polygon and a segment in a 2D space.
double distance (const TSegment2D &s1, const TPolygon2D &p2)
 Gets the distance between a segment and a polygon in a 2D space.
double BASE_IMPEXP distance (const TPolygon2D &p1, const TLine2D &l2)
 Gets the distance between a polygon and a line in a 2D space.
double distance (const TLine2D &l1, const TPolygon2D &p2)
double BASE_IMPEXP distance (const TPolygon3D &p1, const TPolygon3D &p2)
 Gets the distance between two polygons in a 3D space.
double BASE_IMPEXP distance (const TPolygon3D &p1, const TSegment3D &s2)
 Gets the distance between a polygon and a segment in a 3D space.
double distance (const TSegment3D &s1, const TPolygon3D &p2)
 Gets the distance between a segment and a polygon in a 3D space.
double BASE_IMPEXP distance (const TPolygon3D &p1, const TLine3D &l2)
 Gets the distance between a polygon and a line in a 3D space.
double distance (const TLine3D &l1, const TPolygon3D &p2)
 Gets the distance between a line and a polygon in a 3D space.
double BASE_IMPEXP distance (const TPolygon3D &po, const TPlane &pl)
 Gets the distance between a polygon and a plane.
double distance (const TPlane &pl, const TPolygon3D &po)
 Gets the distance between a plane and a polygon.
Bound checkers



void BASE_IMPEXP getRectangleBounds (const std::vector< TPoint2D > &poly, TPoint2D &pMin, TPoint2D &pMax)
 Gets the rectangular bounds of a 2D polygon or set of 2D points.
void BASE_IMPEXP getPrismBounds (const std::vector< TPoint3D > &poly, TPoint3D &pMin, TPoint3D &pMax)
 Gets the prism bounds of a 3D polygon or set of 3D points.
Creation of planes from poses



void BASE_IMPEXP createPlaneFromPoseXY (const CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its Z vector.
void BASE_IMPEXP createPlaneFromPoseXZ (const CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its Y vector.
void BASE_IMPEXP createPlaneFromPoseYZ (const CPose3D &pose, TPlane &plane)
 Given a pose, creates a plane orthogonal to its X vector.
void BASE_IMPEXP createPlaneFromPoseAndNormal (const 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.
void BASE_IMPEXP generateAxisBaseFromDirectionAndAxis (const double(&vec)[3], char coord, CMatrixDouble &matrix)
 Creates a rotation matrix so that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the vector.
Linear regression methods



double BASE_IMPEXP getRegressionLine (const std::vector< TPoint2D > &points, TLine2D &line)
 Using eigenvalues, gets the best fitting line for a set of 2D points.
double BASE_IMPEXP getRegressionLine (const std::vector< TPoint3D > &points, TLine3D &line)
 Using eigenvalues, gets the best fitting line for a set of 3D points.
double BASE_IMPEXP getRegressionPlane (const std::vector< TPoint3D > &points, TPlane &plane)
 Using eigenvalues, gets the best fitting plane for a set of 3D points.
Miscellaneous methods



void BASE_IMPEXP assemblePolygons (const std::vector< TSegment3D > &segms, std::vector< TPolygon3D > &polys)
 Tries to assemble a set of segments into a set of closed polygons.
void BASE_IMPEXP 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.
void BASE_IMPEXP assemblePolygons (const std::vector< TObject3D > &objs, std::vector< TPolygon3D > &polys)
 Extracts all the polygons, including those formed from segments, from the set of objects.
void BASE_IMPEXP 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.
void BASE_IMPEXP 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.
void setEpsilon (double nE)
 Changes the value of the geometric epsilon.
double getEpsilon ()
 Gets the value of the geometric epsilon.
bool BASE_IMPEXP splitInConvexComponents (const TPolygon2D &poly, vector< TPolygon2D > &components)
 Splits a 2D polygon into convex components.
bool BASE_IMPEXP splitInConvexComponents (const TPolygon3D &poly, vector< TPolygon3D > &components)
 Splits a 3D polygon into convex components.
void BASE_IMPEXP getSegmentBisector (const TSegment2D &sgm, TLine2D &bis)
 Gets the bisector of a 2D segment.
void BASE_IMPEXP getSegmentBisector (const TSegment3D &sgm, TPlane &bis)
 Gets the bisector of a 3D segment.
void BASE_IMPEXP getAngleBisector (const TLine2D &l1, const TLine2D &l2, TLine2D &bis)
 Gets the bisector of two lines or segments (implicit constructor will be used if necessary).
void BASE_IMPEXP getAngleBisector (const TLine3D &l1, const TLine3D &l2, TLine3D &bis)
 Gets the bisector of two lines or segments (implicit constructor will be used if necessary).
RANSAC detectors



template<typename NUMTYPE >
void BASE_IMPEXP ransac_detect_3D_planes (const std::vector< NUMTYPE > &x, const std::vector< NUMTYPE > &y, const std::vector< NUMTYPE > &z, std::vector< std::pair< size_t, TPlane > > &out_detected_planes, const double threshold, const size_t min_inliers_for_valid_plane=10)
 Fit a number of 3-D planes to a given point cloud, automatically determining the number of existing planes by means of the provided threshold and minimum number of supporting inliers.
template<typename NUMTYPE >
void BASE_IMPEXP ransac_detect_2D_lines (const std::vector< NUMTYPE > &x, const std::vector< NUMTYPE > &y, std::vector< std::pair< size_t, TLine2D > > &out_detected_lines, const double threshold, const size_t min_inliers_for_valid_line=5)
 Fit a number of 2-D lines to a given point cloud, automatically determining the number of existing lines by means of the provided threshold and minimum number of supporting inliers.
template<class POINTSMAP >
void ransac_detect_3D_planes (const POINTSMAP *points_map, vector< pair< size_t, TPlane > > &out_detected_planes, const double threshold, const size_t min_inliers_for_valid_plane)
 A stub for ransac_detect_3D_planes() with the points given as a mrpt::slam::CPointsMap.
Gaussian PDF transformation functions



template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void transform_gaussian_unscented (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const bool *elem_do_wrap2pi=NULL, const double alpha=1e-3, const double K=0, const double beta=2.0)
 Scaled unscented transformation (SUT) for estimating the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.
template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void transform_gaussian_montecarlo (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const size_t num_samples=1000, std::vector< VECTORLIKE3 > *out_samples_y=NULL)
 Simple Montecarlo-base estimation of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.
template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void transform_gaussian_linear (const VECTORLIKE1 &x_mean, const MATLIKE1 &x_cov, void(*functor)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y), const USERPARAM &fixed_param, VECTORLIKE2 &y_mean, MATLIKE2 &y_cov, const VECTORLIKE1 &x_increments)
 First order uncertainty propagation estimator of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.
Interpolation functions



template<class T >
T interpolate (const T &x, const std::vector< T > &ys, const T &x0, const T &x1)
 Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x".
double BASE_IMPEXP interpolate2points (const double x, const double x0, const double y0, const double x1, const double y1, bool wrap2pi=false)
 Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1).
double BASE_IMPEXP spline (const double t, const std::vector< double > &x, const std::vector< double > &y, bool wrap2pi=false)
 Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).
template<typename NUMTYPE , class VECTORLIKE >
NUMTYPE leastSquareLinearFit (const NUMTYPE t, const VECTORLIKE &x, const VECTORLIKE &y, bool wrap2pi=false)
 Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t".
template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 >
void leastSquareLinearFit (const VECTORLIKE1 &ts, VECTORLIKE2 &outs, const VECTORLIKE3 &x, const VECTORLIKE3 &y, bool wrap2pi=false)
 Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs".
Probability density distributions (pdf) distance metrics



template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type mahalanobisDistance2 (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)
 Computes the squared mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv

\[ d^2 = (X-MU)^\top \Sigma^{-1} (X-MU) \]

.

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type mahalanobisDistance (const VECTORLIKE1 &X, const VECTORLIKE2 &MU, const MAT &COV)
 Computes the mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv

\[ d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) } \]

.

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type mahalanobisDistance2 (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)
 Computes the squared mahalanobis distance between two *non-independent* Gaussians, given the two covariance matrices and the vector with the difference of their means.
template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type mahalanobisDistance (const VECTORLIKE &mean_diffs, const MAT1 &COV1, const MAT2 &COV2, const MAT3 &CROSS_COV12)
 Computes the mahalanobis distance between two *non-independent* Gaussians (or independent if CROSS_COV12=NULL), given the two covariance matrices and the vector with the difference of their means.
template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type mahalanobisDistance2 (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)
 Computes the squared mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point.
template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type mahalanobisDistance (const VECTORLIKE &delta_mu, const MATRIXLIKE &cov)
 Computes the mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point.
template<typename T >
T productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixTemplateNumeric< T > &COV1, const CMatrixTemplateNumeric< T > &COV2)
 Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2".
template<typename T , size_t DIM>
T productIntegralTwoGaussians (const std::vector< T > &mean_diffs, const CMatrixFixedNumeric< T, DIM, DIM > &COV1, const CMatrixFixedNumeric< T, DIM, DIM > &COV2)
 Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2".
template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 >
void productIntegralAndMahalanobisTwoGaussians (const VECLIKE &mean_diffs, const MATLIKE1 &COV1, const MATLIKE2 &COV2, T &maha2_out, T &intprod_out, const MATLIKE1 *CROSS_COV12=NULL)
 Computes both, the integral of the product of two Gaussians and their square Mahalanobis distance.
template<typename T , class VECLIKE , class MATRIXLIKE >
void mahalanobisDistance2AndLogPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &log_pdf_out)
 Computes both, the logarithm of the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian.
template<typename T , class VECLIKE , class MATRIXLIKE >
void mahalanobisDistance2AndPDF (const VECLIKE &diff_mean, const MATRIXLIKE &cov, T &maha2_out, T &pdf_out)
 Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian.

Variables

double BASE_IMPEXP geometryEpsilon
 Global epsilon to overcome small precision errors.
struct BASE_IMPEXP TSegment3D
struct BASE_IMPEXP TLine3D
class BASE_IMPEXP TPolygon3D
struct BASE_IMPEXP TObject3D
const unsigned char GEOMETRIC_TYPE_POINT = 0
 Object type identifier for TPoint2D or TPoint3D.
const unsigned char GEOMETRIC_TYPE_SEGMENT = 1
 Object type identifier for TSegment2D or TSegment3D.
const unsigned char GEOMETRIC_TYPE_LINE = 2
 Object type identifier for TLine2D or TLine3D.
const unsigned char GEOMETRIC_TYPE_POLYGON = 3
 Object type identifier for TPolygon2D or TPolygon3D.
const unsigned char GEOMETRIC_TYPE_PLANE = 4
 Object type identifier for TPlane.
const unsigned char GEOMETRIC_TYPE_UNDEFINED = 255
 Object type identifier for empty TObject2D or TObject3D.
class BASE_IMPEXP CMatrixTemplateNumeric
class BASE_IMPEXP CMatrix
class BASE_IMPEXP CMatrixD

Detailed Description

This base provides a set of functions for maths stuff.

Typedef Documentation

typedef CLevenbergMarquardtTempl<vector_double> mrpt::math::CLevenbergMarquardt

The default name for the LM class is an instantiation for "double".

Definition at line 234 of file CLevenbergMarquardt.h.

typedef CMatrixTemplate<bool> mrpt::math::CMatrixBool

Declares a matrix of booleans (non serializable).

See also:
CMatrixDouble, CMatrixFloat, CMatrixB

Definition at line 465 of file CMatrixTemplateNumeric.h.

typedef CMatrixTemplateNumeric<double> mrpt::math::CMatrixDouble

Declares a matrix of double numbers (non serializable).

For a serializable version, use math::CMatrixD

See also:
CMatrixFloat, CMatrix, CMatrixD

Definition at line 455 of file CMatrixTemplateNumeric.h.

typedef CMatrixFixedNumeric<double,1,2> mrpt::math::CMatrixDouble12

Definition at line 462 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,1,3> mrpt::math::CMatrixDouble13

Definition at line 460 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,1,5> mrpt::math::CMatrixDouble15

Definition at line 469 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,1,6> mrpt::math::CMatrixDouble16

Definition at line 465 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,1,7> mrpt::math::CMatrixDouble17

Definition at line 467 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,2,1> mrpt::math::CMatrixDouble21

Definition at line 463 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,2,2> mrpt::math::CMatrixDouble22

Definition at line 455 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,3,1> mrpt::math::CMatrixDouble31

Definition at line 461 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,3,3> mrpt::math::CMatrixDouble33

Definition at line 456 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,4,4> mrpt::math::CMatrixDouble44

Definition at line 457 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,5,1> mrpt::math::CMatrixDouble51

Definition at line 468 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,6,1> mrpt::math::CMatrixDouble61

Definition at line 464 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,6,6> mrpt::math::CMatrixDouble66

Definition at line 458 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,7,1> mrpt::math::CMatrixDouble71

Definition at line 466 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<double,7,7> mrpt::math::CMatrixDouble77

Definition at line 459 of file CMatrixFixedNumeric.h.

typedef CMatrixTemplateNumeric<float> mrpt::math::CMatrixFloat

Declares a matrix of float numbers (non serializable).

For a serializable version, use math::CMatrix

See also:
CMatrixDouble, CMatrix, CMatrixD

Definition at line 449 of file CMatrixTemplateNumeric.h.

typedef CMatrixFixedNumeric<float,1,2> mrpt::math::CMatrixFloat12

Definition at line 478 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,1,3> mrpt::math::CMatrixFloat13

Definition at line 476 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,1,5> mrpt::math::CMatrixFloat15

Definition at line 485 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,1,6> mrpt::math::CMatrixFloat16

Definition at line 481 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,1,7> mrpt::math::CMatrixFloat17

Definition at line 483 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,2,1> mrpt::math::CMatrixFloat21

Definition at line 479 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,2,2> mrpt::math::CMatrixFloat22

Definition at line 471 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,3,1> mrpt::math::CMatrixFloat31

Definition at line 477 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,3,3> mrpt::math::CMatrixFloat33

Definition at line 472 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,4,4> mrpt::math::CMatrixFloat44

Definition at line 473 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,5,1> mrpt::math::CMatrixFloat51

Definition at line 484 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,6,1> mrpt::math::CMatrixFloat61

Definition at line 480 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,6,6> mrpt::math::CMatrixFloat66

Definition at line 474 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,7,1> mrpt::math::CMatrixFloat71

Definition at line 482 of file CMatrixFixedNumeric.h.

typedef CMatrixFixedNumeric<float,7,7> mrpt::math::CMatrixFloat77

Definition at line 475 of file CMatrixFixedNumeric.h.

typedef CMatrixTemplateNumeric<double> mrpt::math::CMatrixLongDouble

Declares a matrix of "long doubles" (non serializable), or of "doubles" if the compiler does not support "long double".

See also:
CMatrixDouble, CMatrixFloat

Definition at line 476 of file CMatrixTemplateNumeric.h.

typedef CMatrixTemplateNumeric<unsigned int> mrpt::math::CMatrixUInt

Declares a matrix of unsigned ints (non serializable).

See also:
CMatrixDouble, CMatrixFloat

Definition at line 460 of file CMatrixTemplateNumeric.h.

typedef CQuaternion<double> mrpt::math::CQuaternionDouble

A quaternion of data type "double".

Definition at line 345 of file CQuaternion.h.

typedef CQuaternion<float> mrpt::math::CQuaternionFloat

A quaternion of data type "float".

Definition at line 346 of file CQuaternion.h.

typedef CVectorTemplate<double> mrpt::math::CVectorDouble

Declares a vector of double elements.

See also:
CVectorFloat

Definition at line 473 of file CVectorTemplate.h.

typedef CVectorTemplate<float> mrpt::math::CVectorFloat

Declares a vector of float elements.

See also:
CVectorDouble

Definition at line 468 of file CVectorTemplate.h.

typedef RANSAC_Template<double> mrpt::math::RANSAC

The default instance of RANSAC, for double type.

Definition at line 90 of file ransac.h.

typedef TPlane mrpt::math::TPlane3D

Definition at line 1060 of file lightweight_geom_data.h.

Enumeration Type Documentation

enum mrpt::math::TMatrixTextFileFormat

Selection of the number format in CMatrixTemplate::saveToTextFile

Enumerator:
MATRIX_FORMAT_ENG 

engineering format 'e'

MATRIX_FORMAT_FIXED 

fixed floating point 'f'

MATRIX_FORMAT_INT 

intergers 'i'

Definition at line 70 of file math_frwds.h.

Function Documentation

template<class CONTAINER >
void mrpt::math::adjustRange ( CONTAINER &  m,
const typename CONTAINER::value_type  minVal,
const typename CONTAINER::value_type  maxVal 
) [inline]
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.

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

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

See also:
geometryEpsilon
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.

See also:
geometryEpsilon
bool BASE_IMPEXP mrpt::math::areAligned ( const std::vector< TPoint2D > &  points  ) 

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

See also:
geometryEpsilon
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.

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.

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.

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.

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.

double BASE_IMPEXP mrpt::math::averageLogLikelihood ( const vector_double &  logWeights,
const vector_double &  logLikelihoods 
)

A numerically-stable method to average likelihood values with strongly different ranges (weighted likelihoods).

This method implements this equation:

\[ return = \log \left( \frac{1}{\sum_i e^{lw_i}} \sum_i e^{lw_i} e^{ll_i} \right) \]

See also the tutorial page.

double BASE_IMPEXP mrpt::math::averageLogLikelihood ( const vector_double &  logLikelihoods  ) 

A numerically-stable method to compute average likelihood values with strongly different ranges (unweighted likelihoods: compute the arithmetic mean).

This method implements this equation:

\[ return = - \log N + \log \sum_{i=1}^N e^{ll_i-ll_{max}} + ll_{max} \]

See also the tutorial page.

Referenced by mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_particlesEvaluator_AuxPFOptimal(), and mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_particlesEvaluator_AuxPFStandard().

double BASE_IMPEXP mrpt::math::averageWrap2Pi ( const vector_double &  angles  ) 

Computes the average of a sequence of angles in radians taking into account the correct wrapping in the range $ ]-\pi,\pi [ $, for example, the mean of (2,-2) is $ \pi $, not 0.

double mrpt::math::chi2CDF ( unsigned int  degreesOfFreedom,
double  arg 
) [inline]

Cumulative chi square distribution.

Computes the cumulative density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg by calling noncentralChi2CDF(degreesOfFreedom, 0.0, arg, accuracy).

Note:
Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 181 of file distributions.h.

References noncentralChi2CDF().

double BASE_IMPEXP mrpt::math::chi2inv ( double  P,
unsigned int  dim = 1 
)

The "quantile" of the Chi-Square distribution, for dimension "dim" and probability 0<P<1 (the inverse of chi2CDF) An aproximation from the Wilson-Hilferty transformation is used.

Referenced by mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), and mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfStandardProposal().

double mrpt::math::chi2PDF ( unsigned int  degreesOfFreedom,
double  arg,
double  accuracy = 1e-7 
) [inline]

Chi square distribution.

Computes the density of a chi square distribution with degreesOfFreedom and tolerance accuracy at the given argument arg by calling noncentralChi2(degreesOfFreedom, 0.0, arg, accuracy).

Note:
Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 283 of file distributions.h.

References mrpt::math::detail::noncentralChi2CDF_exact().

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.

See also:
closestFromPointToSegment
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.

See also:
closestFromPointToLine
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.

void BASE_IMPEXP mrpt::math::computeEigenValues2x2 ( const CMatrixFloat &  in_matrix,
float &  min_eigenvalue,
float &  max_eigenvalue 
)

Compute the two eigenvalues of a 2x2 matrix.

Parameters:
in_matrx The 2x2 input matrix.
min_eigenvalue (out) The minimum eigenvalue of the matrix.
max_eigenvalue (out) The maximum eigenvalue of the matrix. by FAMD, MAR-2007
template<typename CONTAINER >
void mrpt::math::condidenceIntervals ( const CONTAINER &  data,
typename CONTAINER::value_type &  out_mean,
typename CONTAINER::value_type &  out_lower_conf_interval,
typename CONTAINER::value_type &  out_upper_conf_interval,
const double  confidenceInterval = 0.1,
const size_t  histogramNumBins = 1000 
) [inline]

Return the mean and the 10-90% confidence points (or with any other confidence value) of a set of samples by building the cummulative CDF of all the elements of the container.

The container can be any MRPT container (CArray, matrices, vectors).

Parameters:
confidenceInterval A number in the range (0,1) such as the confidence interval will be [100*confidenceInterval, 100*(1-confidenceInterval)].

Definition at line 293 of file distributions.h.

References ASSERT_, cumsum(), distance(), histogram(), maximum(), mean(), minimum_maximum(), MRPT_END, and MRPT_START.

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.

See also:
TPolygon3D,geometryEpsilon
bool BASE_IMPEXP mrpt::math::conformAPlane ( const std::vector< TPoint3D > &  points  ) 

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

See also:
TPolygon3D,geometryEpsilon
template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const mrpt::poses::CPose3DQuat &  p 
) [inline]

Definition at line 545 of file math_frwds.h.

References containerFromPoseOrPoint(), and mrpt::math::detail::lightFromPose().

template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const mrpt::poses::CPose3D &  p 
) [inline]

Definition at line 544 of file math_frwds.h.

References containerFromPoseOrPoint(), and mrpt::math::detail::lightFromPose().

template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const mrpt::poses::CPose2D &  p 
) [inline]

Definition at line 543 of file math_frwds.h.

References containerFromPoseOrPoint(), and mrpt::math::detail::lightFromPose().

template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const mrpt::poses::CPoint3D &  p 
) [inline]

Definition at line 542 of file math_frwds.h.

References containerFromPoseOrPoint(), and mrpt::math::detail::lightFromPose().

template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const mrpt::poses::CPoint2D &  p 
) [inline]

Definition at line 541 of file math_frwds.h.

References containerFromPoseOrPoint(), and mrpt::math::detail::lightFromPose().

template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const TPose3DQuat &  p 
) [inline]
template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const TPose3D &  p 
) [inline]
template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const TPose2D &  p 
) [inline]
template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const TPoint3D &  p 
) [inline]
template<class CONTAINER >
CONTAINER& mrpt::math::containerFromPoseOrPoint ( CONTAINER &  C,
const TPoint2D &  p 
) [inline]

Conversion of poses to MRPT containers (vector/matrix).

Referenced by mrpt::math::CMatrixTemplateNumeric< KFTYPE >::CMatrixTemplateNumeric(), and containerFromPoseOrPoint().

template<class T >
double mrpt::math::correlate_matrix ( const CMatrixTemplateNumeric< T > &  a1,
const CMatrixTemplateNumeric< T > &  a2 
) [inline]

Calculate the correlation between two matrices (by AJOGD @ JAN-2007).

Definition at line 549 of file base/include/mrpt/math/utils.h.

References mrpt::math::CMatrixTemplate< T >::getColCount(), mrpt::math::CMatrixTemplate< T >::getRowCount(), and THROW_EXCEPTION.

template<class CONTAINER1 , class CONTAINER2 >
size_t mrpt::math::countCommonElements ( const CONTAINER1 &  a,
const CONTAINER2 &  b 
) [inline]
template<class CONTAINER >
size_t mrpt::math::countNonZero ( const CONTAINER &  a  )  [inline]
template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE >
void mrpt::math::covariancesAndMean ( const VECTOR_OF_VECTORS &  elements,
MATRIXLIKE &  covariances,
VECTORLIKE &  means,
const bool *  elem_do_wrap2pi = NULL 
) [inline]

Computes covariances and mean of any vector of containers.

Parameters:
elements Any kind of vector of vectors/arrays, eg. std::vector<vector_double>, with all the input samples, each sample in a "row".
covariances Output estimated covariance; it can be a fixed/dynamic matrix or a matrixview.
means Output estimated mean; it can be vector_double/CArrayDouble, etc...
elem_do_wrap2pi If !=NULL; it must point to an array of "bool" of size()==dimension of each element, stating if it's needed to do a wrap to [-pi,pi] to each dimension.

Definition at line 380 of file base/include/mrpt/math/utils.h.

Referenced by transform_gaussian_montecarlo().

template<class VECTOR_OF_VECTORS , class MATRIXLIKE , class VECTORLIKE , class VECTORLIKE2 , class VECTORLIKE3 >
void mrpt::math::covariancesAndMeanWeighted ( const VECTOR_OF_VECTORS &  elements,
MATRIXLIKE &  covariances,
VECTORLIKE &  means,
const VECTORLIKE2 *  weights_mean,
const VECTORLIKE3 *  weights_cov,
const bool *  elem_do_wrap2pi = NULL 
) [inline]

Computes covariances and mean of any vector of containers, given optional weights for the different samples.

Parameters:
elements Any kind of vector of vectors/arrays, eg. std::vector<vector_double>, with all the input samples, each sample in a "row".
covariances Output estimated covariance; it can be a fixed/dynamic matrix or a matrixview.
means Output estimated mean; it can be vector_double/CArrayDouble, etc...
weights_mean If !=NULL, it must point to a vector of size()==number of elements, with normalized weights to take into account for the mean.
weights_cov If !=NULL, it must point to a vector of size()==number of elements, with normalized weights to take into account for the covariance.
elem_do_wrap2pi If !=NULL; it must point to an array of "bool" of size()==dimension of each element, stating if it's needed to do a wrap to [-pi,pi] to each dimension.
See also:
This method is used in mrpt::math::unscented_transform_gaussian

Definition at line 278 of file base/include/mrpt/math/utils.h.

References ASSERTDEB_, ASSERTMSG_, M_2PI, M_PI, and wrapToPi().

Referenced by transform_gaussian_unscented().

template<class VECTOR_OF_VECTOR >
CMatrixDouble mrpt::math::covVector ( const VECTOR_OF_VECTOR &  v  )  [inline]

Computes the covariance matrix from a list of values given as a vector of vectors, where each row is a sample.

Parameters:
v The set of data, as a vector of N vectors of M elements.
out_cov The output MxM matrix for the estimated covariance matrix.
See also:
math::mean,math::stddev, math::cov, meanAndCovVector

Definition at line 260 of file base/include/mrpt/math/utils.h.

References meanAndCovVector().

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.

An implicit constructor is used if a CPose2D is given.

See also:
createFromPoseY,createFromPoseAndVector
void BASE_IMPEXP mrpt::math::createFromPoseAndVector ( const 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
void BASE_IMPEXP 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
void BASE_IMPEXP mrpt::math::createFromPoseX ( const 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
void BASE_IMPEXP 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
void BASE_IMPEXP mrpt::math::createFromPoseY ( const 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
void BASE_IMPEXP mrpt::math::createFromPoseZ ( const 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
void BASE_IMPEXP mrpt::math::createPlaneFromPoseAndNormal ( const 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
void BASE_IMPEXP mrpt::math::createPlaneFromPoseXY ( const CPose3D &  pose,
TPlane &  plane 
)

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

See also:
createPlaneFromPoseXZ,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal
void BASE_IMPEXP mrpt::math::createPlaneFromPoseXZ ( const CPose3D &  pose,
TPlane &  plane 
)

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

See also:
createPlaneFromPoseXY,createPlaneFromPoseYZ,createPlaneFromPoseAndNormal
void BASE_IMPEXP mrpt::math::createPlaneFromPoseYZ ( const CPose3D &  pose,
TPlane &  plane 
)

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

See also:
createPlaneFromPoseXY,createPlaneFromPoseXZ,createPlaneFromPoseAndNormal
void BASE_IMPEXP mrpt::math::cross_correlation_FFT ( const CMatrixFloat &  A,
const CMatrixFloat &  B,
CMatrixFloat &  out_corr 
)

Correlation of two matrixes using 2D FFT.

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

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

It uses the simple implementation:

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

Definition at line 789 of file geometry.h.

References ASSERT_.

template<class T , class U , class V >
void mrpt::math::crossProduct3D ( const T &  v0,
const U &  v1,
V &  vOut 
) [inline]

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

It uses the simple implementation:

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

Definition at line 771 of file geometry.h.

Referenced by generateAxisBaseFromDirection().

template<class CONTAINER1 , class CONTAINER2 >
void mrpt::math::cumsum ( const CONTAINER1 &  in_data,
CONTAINER2 &  out_cumsum 
) [inline]

Referenced by condidenceIntervals().

void BASE_IMPEXP mrpt::math::dft2_complex ( const CMatrixFloat &  in_real,
const CMatrixFloat &  in_imag,
CMatrixFloat &  out_real,
CMatrixFloat &  out_imag 
)

Compute the 2D Discrete Fourier Transform (DFT) of a complex matrix, returning the real and imaginary parts separately.

Parameters:
in_real The N_1xN_2 matrix with the real part.
in_imag The N_1xN_2 matrix with the imaginary part.
out_real The N_1xN_2 output matrix which will store the real values (user has not to initialize the size of this matrix).
out_imag The N_1xN_2 output matrix which will store the imaginary values (user has not to initialize the size of this matrix). If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.
See also:
fft_real, idft2_complex,dft2_real
void BASE_IMPEXP mrpt::math::dft2_real ( const CMatrixFloat &  in_data,
CMatrixFloat &  out_real,
CMatrixFloat &  out_imag 
)

Compute the 2D Discrete Fourier Transform (DFT) of a real matrix, returning the real and imaginary parts separately.

Parameters:
in_data The N_1xN_2 matrix.
out_real The N_1xN_2 output matrix which will store the real values (user has not to initialize the size of this matrix).
out_imag The N_1xN_2 output matrix which will store the imaginary values (user has not to initialize the size of this matrix).
See also:
fft_real, ifft2_read, fft2_complex If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.
double mrpt::math::distance ( const TPlane &  pl,
const TPolygon3D &  po 
) [inline]

Gets the distance between a plane and a polygon.

Definition at line 604 of file geometry.h.

References distance().

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

Gets the distance between a polygon and a plane.

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 594 of file geometry.h.

References distance().

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.

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 584 of file geometry.h.

References distance().

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.

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

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

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

Definition at line 570 of file geometry.h.

References distance().

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.

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 563 of file geometry.h.

References distance().

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.

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

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

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.

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

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

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

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

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

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

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

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

Referenced by mrpt::math::CArray< T, N >::assign(), mrpt::slam::TDataAssociationResults::clear(), condidenceIntervals(), distance(), mrpt::utils::find_in_vector(), 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::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), mrpt::math::CBinaryRelation< T, U, UIsObject >::removeElement(), mrpt::math::CBinaryRelation< T, U, UIsObject >::removeElements(), mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration(), and mrpt::math::CBinaryRelation< T, U, UIsObject >::setRelationValue().

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 
) [inline]

Returns the distance between 2 points in 3D.

Definition at line 889 of file geometry.h.

References mrpt::utils::square().

template<typename T >
T mrpt::math::distanceBetweenPoints ( const T  x1,
const T  y1,
const T  x2,
const T  y2 
) [inline]

Returns the distance between 2 points in 2D.

Definition at line 883 of file geometry.h.

References mrpt::utils::square().

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.

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 
) [inline]

Returns the square distance between 2 points in 3D.

Definition at line 901 of file geometry.h.

References mrpt::utils::square().

template<typename T >
T mrpt::math::distanceSqrBetweenPoints ( const T  x1,
const T  y1,
const T  x2,
const T  y2 
) [inline]

Returns the square distance between 2 points in 2D.

Definition at line 895 of file geometry.h.

References mrpt::utils::square().

double BASE_IMPEXP mrpt::math::erf ( double  x  ) 

The error function of a Normal distribution.

Referenced by noncentralChi2CDF(), and mrpt::math::detail::noncentralChi2CDF_exact().

double BASE_IMPEXP mrpt::math::erfc ( double  x  ) 

The complementary error function of a Normal distribution.

class VECTORLIKE3 class MATRIXLIKE class USERPARAM void mrpt::math::estimateJacobian ( const VECTORLIKE &  x,
void(*)(const VECTORLIKE &x, const USERPARAM &y, VECTORLIKE3 &out)  functor,
const VECTORLIKE2 &  increments,
const USERPARAM &  userParam,
MATRIXLIKE &  out_Jacobian 
)

Definition at line 745 of file base/include/mrpt/math/utils.h.

References ASSERT_, MRPT_END, and MRPT_START.

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), mrpt::math::jacobians::jacob_numeric_estimate(), and mrpt::bayes::CKalmanFilterCapable< 7, 3, 3, 7 >::runOneKalmanIteration().

template<class VECTOR_OF_VECTORS , class VECTORLIKE >
void mrpt::math::extractColumnFromVectorOfVectors ( const size_t  colIndex,
const VECTOR_OF_VECTORS &  data,
VECTORLIKE &  out_column 
) [inline]

Extract a column from a vector of vectors, and store it in another vector.

  • Input data can be: std::vector<vector_double>, std::deque<std::list<double> >, std::list<CArrayDouble<5> >, etc. etc.
  • Output is the sequence: data[0][idx],data[1][idx],data[2][idx], etc..

For the sake of generality, this function does NOT check the limits in the number of column, unless it's implemented in the [] operator of each of the "rows".

Definition at line 503 of file base/include/mrpt/math/utils.h.

double BASE_IMPEXP mrpt::math::factorial ( unsigned int  n  ) 

Computes the factorial of an integer number and returns it as a double value (internally it uses logarithms for avoiding overflow).

uint64_t BASE_IMPEXP mrpt::math::factorial64 ( unsigned int  n  ) 

Computes the factorial of an integer number and returns it as a 64-bit integer number.

void BASE_IMPEXP mrpt::math::fft_real ( vector_float &  in_realData,
vector_float &  out_FFT_Re,
vector_float &  out_FFT_Im,
vector_float &  out_FFT_Mag 
)

Computes the FFT of a 2^N-size vector of real numbers, and returns the Re+Im+Magnitude parts.

See also:
fft2_real
template<class T >
CMatrixTemplateNumeric<T> mrpt::math::generateAxisBaseFromDirection ( T  dx,
T  dy,
T  dz 
) [inline]

Computes an axis base (a set of three 3D normal vectors) with the given vector being the first of them.

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)

(JLB @ 18-SEP-2007)

Definition at line 1025 of file geometry.h.

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

void BASE_IMPEXP mrpt::math::generateAxisBaseFromDirectionAndAxis ( const double(&)  vec[3],
char  coord,
CMatrixDouble &  matrix 
)

Creates a rotation matrix so that the coordinate given (0 for x, 1 for y, 2 for z) corresponds to the vector.

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).

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).

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 193 of file geometry.h.

References getAngle().

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).

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

Computes the angle between two planes.

Referenced by getAngle().

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).

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

template<typename VEC >
CConstVectorRowWrapper<VEC> mrpt::math::getAsRow ( const VEC &  v  )  [inline]

Definition at line 1182 of file CMatrixViews.h.

template<typename VEC >
CConstVectorColumnWrapper< VEC > mrpt::math::getAsRow ( VEC &  v  )  [inline]

Definition at line 1266 of file CMatrixViews.h.

template<typename MAT >
CConstMatrixColumnAccessorExtended<MAT> mrpt::math::getColumnAccessor ( const MAT &  m,
size_t  colIdx,
size_t  offset,
size_t  space = 1 
) [inline]

Definition at line 877 of file CMatrixViews.h.

template<typename MAT >
CConstMatrixColumnAccessor<MAT> mrpt::math::getColumnAccessor ( const MAT &  m,
size_t  colIdx 
) [inline]

Definition at line 827 of file CMatrixViews.h.

template<typename MAT >
CMatrixColumnAccessorExtended<MAT> mrpt::math::getColumnAccessor ( MAT &  m,
size_t  colIdx,
size_t  offset,
size_t  space = 1 
) [inline]

Definition at line 781 of file CMatrixViews.h.

template<typename MAT >
CMatrixColumnAccessor<MAT> mrpt::math::getColumnAccessor ( MAT &  m,
size_t  colIdx 
) [inline]

Definition at line 714 of file CMatrixViews.h.

Referenced by generateAxisBaseFromDirection().

double mrpt::math::getEpsilon (  )  [inline]

Gets the value of the geometric epsilon.

See also:
geometryEpsilon,setEpsilon

Definition at line 710 of file geometry.h.

References geometryEpsilon.

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.

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.

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.

Returns an estimation of the error.

See also:
spline, leastSquareLinearFit
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.

Returns an estimation of the error.

See also:
spline, leastSquareLinearFit
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.

Returns an estimation of the error.

See also:
spline, leastSquareLinearFit
template<typename MAT >
CConstMatrixRowAccessorExtended<MAT> mrpt::math::getRowAccessor ( const MAT &  m,
size_t  rowIdx,
size_t  offset,
size_t  space = 1 
) [inline]

Definition at line 1098 of file CMatrixViews.h.

template<typename MAT >
CConstMatrixRowAccessor<MAT> mrpt::math::getRowAccessor ( const MAT &  m,
size_t  rowIdx 
) [inline]

Definition at line 1048 of file CMatrixViews.h.

template<typename MAT >
CMatrixRowAccessorExtended<MAT> mrpt::math::getRowAccessor ( MAT &  m,
size_t  rowIdx,
size_t  offset,
size_t  space = 1 
) [inline]

Definition at line 1002 of file CMatrixViews.h.

template<typename MAT >
CMatrixRowAccessor<MAT> mrpt::math::getRowAccessor ( MAT &  m,
size_t  rowIdx 
) [inline]

Definition at line 935 of file CMatrixViews.h.

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

Gets the bisector of a 3D segment.

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

Gets the bisector of a 2D segment.

template<typename MAT >
CConstMatrixViewTranspose<MAT> mrpt::math::getTransposed ( const MAT &  m  )  [inline]

Definition at line 164 of file CMatrixViews.h.

template<typename MAT >
CMatrixViewTranspose<MAT> mrpt::math::getTransposed ( MAT &  m  )  [inline]

Definition at line 116 of file CMatrixViews.h.

template<class CONTAINER >
std::vector<double> mrpt::math::histogram ( const CONTAINER &  v,
double  limit_min,
double  limit_max,
size_t  number_bins,
bool  do_normalization = false,
std::vector< double > *  out_bin_centers = NULL 
) [inline]

Referenced by condidenceIntervals().

void BASE_IMPEXP mrpt::math::idft2_complex ( const CMatrixFloat &  in_real,
const CMatrixFloat &  in_imag,
CMatrixFloat &  out_real,
CMatrixFloat &  out_imag 
)

Compute the 2D inverse Discrete Fourier Transform (DFT).

Parameters:
in_real The N_1xN_2 input matrix with real values, where both dimensions MUST BE powers of 2.
in_imag The N_1xN_2 input matrix with imaginary values, where both dimensions MUST BE powers of 2.
out_real The N_1xN_2 output matrix for real part (user has not to initialize the size of this matrix).
out_imag The N_1xN_2 output matrix for imaginary part (user has not to initialize the size of this matrix).
See also:
fft_real, dft2_real,dft2_complex If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.
void BASE_IMPEXP mrpt::math::idft2_real ( const CMatrixFloat &  in_real,
const CMatrixFloat &  in_imag,
CMatrixFloat &  out_data 
)

Compute the 2D inverse Discrete Fourier Transform (DFT).

Parameters:
in_real The N_1xN_2 input matrix with real values.
in_imag The N_1xN_2 input matrix with imaginary values.
out_data The N_1xN_2 output matrix (user has not to initialize the size of this matrix). Note that the real and imaginary parts of the FFT will NOT be checked to assure that they represent the transformation of purely real data. If the dimensions of the matrix are powers of two, the fast fourier transform (FFT) is used instead of the general algorithm.
See also:
fft_real, fft2_real
template<class T >
T mrpt::math::interpolate ( const T &  x,
const std::vector< T > &  ys,
const T &  x0,
const T &  x1 
) [inline]

Interpolate a data sequence "ys" ranging from "x0" to "x1" (equally spaced), to obtain the approximation of the sequence at the point "x".

If the point "x" is out of the range [x0,x1], the closest extreme "ys" value is returned.

See also:
spline, interpolate2points

Definition at line 799 of file base/include/mrpt/math/utils.h.

References ASSERT_, MRPT_END, and MRPT_START.

double BASE_IMPEXP mrpt::math::interpolate2points ( const double  x,
const double  x0,
const double  y0,
const double  x1,
const double  y1,
bool  wrap2pi = false 
)

Linear interpolation/extrapolation: evaluates at "x" the line (x0,y0)-(x1,y1).

If wrap2pi is true, output is wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also:
spline, interpolate, leastSquareLinearFit
bool BASE_IMPEXP mrpt::math::intersect ( const TObject3D &  o1,
const TObject3D &  o2,
TObject3D &  obj 
)

Gets the intersection between any pair of 3D objects.

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

Gets the intersection between any pair of 2D objects.

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 
) [inline]

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 507 of file geometry.h.

References intersect().

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 
) [inline]

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 494 of file geometry.h.

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

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.

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

See also:
TObject3D
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.

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
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 470 of file geometry.h.

References intersect().

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 463 of file geometry.h.

References intersect().

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 456 of file geometry.h.

References intersect().

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

Gets the intersection between two 3D polygons.

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

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

See also:
TObject3D
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.

See also:
TObject3D
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.

See also:
TObject3D
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 429 of file geometry.h.

References intersect().

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 422 of file geometry.h.

References intersect().

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

Gets the intersection between two 2D polygons.

See also:
TObject2D
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.

See also:
TObject2D
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.

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

Gets the intersection between two 2D segments.

See also:
TObject2D
bool mrpt::math::intersect ( const TSegment2D &  s1,
const TLine2D &  r2,
TObject2D &  obj 
) [inline]

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

See also:
TObject2D

Definition at line 168 of file geometry.h.

References intersect().

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.

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

Gets the intersection between two 2D lines.

See also:
TObject2D
bool BASE_IMPEXP mrpt::math::intersect ( const TLine3D &  r1,
const TLine3D &  r2,
TObject3D &  obj 
)

Gets the intersection between two 3D lines.

See also:
TObject3D
bool mrpt::math::intersect ( const TLine3D &  r1,
const TPlane &  p2,
TObject3D &  obj 
) [inline]

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

See also:
TObject3D

Definition at line 146 of file geometry.h.

References intersect().

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

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

See also:
TObject3D

Definition at line 139 of file geometry.h.

References intersect().

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

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

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

Gets the intersection between two planes.

See also:
TObject3D
bool mrpt::math::intersect ( const TPlane &  p1,
const TSegment3D &  s2,
TObject3D &  obj 
) [inline]

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

See also:
TObject3D

Definition at line 122 of file geometry.h.

References intersect().

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.

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

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

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

Gets the intersection between two 3D segments.

See also:
TObject3D

Referenced by mrpt::opengl::CPolyhedron::getIntersection(), and intersect().

bool BASE_IMPEXP mrpt::math::isFinite ( double  f  ) 

Returns true if the number is non infinity.

bool BASE_IMPEXP mrpt::math::isFinite ( float  f  ) 

Returns true if the number is non infinity.

bool BASE_IMPEXP mrpt::math::isNaN ( double  f  ) 

Returns true if the number is NaN.

bool BASE_IMPEXP mrpt::math::isNaN ( float  f  ) 

Returns true if the number is NaN.

template<typename VECTORLIKE1 , typename MATRIXLIKE1 , typename VECTORLIKE2 , typename MATRIXLIKE2 >
double mrpt::math::KLD_Gaussians ( const VECTORLIKE1 &  mu0,
const MATRIXLIKE1 &  cov0,
const VECTORLIKE2 &  mu1,
const MATRIXLIKE2 &  cov1 
) [inline]

Kullback-Leibler divergence (KLD) between two independent multivariate Gaussians.

$ D_\mathrm{KL}(\mathcal{N}_0 \| \mathcal{N}_1) = { 1 \over 2 } ( \log_e ( { \det \Sigma_1 \over \det \Sigma_0 } ) + \mathrm{tr} ( \Sigma_1^{-1} \Sigma_0 ) + ( \mu_1 - \mu_0 )^\top \Sigma_1^{-1} ( \mu_1 - \mu_0 ) - N ) $

Definition at line 104 of file distributions.h.

References ASSERT_, MRPT_END, MRPT_START, multiply_HCHt_scalar(), and size().

template<class VECTORLIKE1 , class VECTORLIKE2 , class VECTORLIKE3 >
void mrpt::math::leastSquareLinearFit ( const VECTORLIKE1 &  ts,
VECTORLIKE2 &  outs,
const VECTORLIKE3 &  x,
const VECTORLIKE3 &  y,
bool  wrap2pi = false 
) [inline]

Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a sequence of points "ts" and returned at "outs".

If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also:
spline, getRegressionLine, getRegressionPlane

Definition at line 887 of file base/include/mrpt/math/utils.h.

References ASSERT_, minimum(), MRPT_END, MRPT_START, mrpt::math::CMatrixTemplate< T >::set_unsafe(), and wrapToPi().

template<typename NUMTYPE , class VECTORLIKE >
NUMTYPE mrpt::math::leastSquareLinearFit ( const NUMTYPE  t,
const VECTORLIKE &  x,
const VECTORLIKE &  y,
bool  wrap2pi = false 
) [inline]

Interpolates or extrapolates using a least-square linear fit of the set of values "x" and "y", evaluated at a single point "t".

The vectors x and y must have size >=2, and all values of "x" must be different. If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also:
spline
getRegressionLine, getRegressionPlane

Definition at line 837 of file base/include/mrpt/math/utils.h.

References ASSERT_, minimum(), MRPT_END, MRPT_START, mrpt::math::CMatrixTemplate< T >::set_unsafe(), and wrapToPi().

template<class T >
std::vector<T> mrpt::math::linspace ( T  first,
T  last,
size_t  count 
) [inline]

Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.

See also:
sequence

Definition at line 110 of file base/include/mrpt/math/utils.h.

References linspace().

template<typename T , typename K >
void mrpt::math::linspace ( T  first,
T  last,
size_t  count,
std::vector< K > &  out_vector 
) [inline]

Generates an equidistant sequence of numbers given the first one, the last one and the desired number of points.

See also:
sequence

Definition at line 90 of file base/include/mrpt/math/utils.h.

Referenced by linspace().

template<typename T , typename At , size_t N>
std::vector<T>& mrpt::math::loadVector ( std::vector< T > &  v,
At(&)  theArray[N] 
) [inline]

Assignment operator for initializing a std::vector from a C array (The vector will be automatically set to the correct size). 

         vector_double  v;
  const double numbers[] = { 1,2,3,5,6,7,8,9,10 };
  loadVector( v, numbers );
Note:
This operator performs the appropiate type castings, if required.

Definition at line 949 of file base/include/mrpt/math/utils.h.

References MRPT_COMPILE_TIME_ASSERT.

bool BASE_IMPEXP mrpt::math::loadVector ( utils::CFileStream &  f,
std::vector< double > &  d 
)

Loads one row of a text file as a numerical std::vector.

Returns:
false on EOF or invalid format. The body of the function is implemented in MATH.cpp
bool BASE_IMPEXP mrpt::math::loadVector ( utils::CFileStream &  f,
std::vector< int > &  d 
)

Loads one row of a text file as a numerical std::vector.

Returns:
false on EOF or invalid format. The body of the function is implemented in MATH.cpp
template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type mrpt::math::mahalanobisDistance ( const VECTORLIKE &  delta_mu,
const MATRIXLIKE &  cov 
) [inline]

Computes the mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point.

\[ d^2 = \sqrt( \Delta_\mu^\top \Sigma^{-1} \Delta_\mu ) \]

Definition at line 1063 of file base/include/mrpt/math/utils.h.

References mahalanobisDistance2().

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type mrpt::math::mahalanobisDistance ( const VECTORLIKE &  mean_diffs,
const MAT1 &  COV1,
const MAT2 &  COV2,
const MAT3 &  CROSS_COV12 
) [inline]

Computes the mahalanobis distance between two *non-independent* Gaussians (or independent if CROSS_COV12=NULL), given the two covariance matrices and the vector with the difference of their means.

\[ d = \sqrt{ \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12 )^{-1} \Delta_\mu } \]

Definition at line 1035 of file base/include/mrpt/math/utils.h.

References mahalanobisDistance().

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type mrpt::math::mahalanobisDistance ( const VECTORLIKE1 &  X,
const VECTORLIKE2 &  MU,
const MAT &  COV 
) [inline]

Computes the mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv

\[ d = \sqrt{ (X-MU)^\top \Sigma^{-1} (X-MU) } \]

.

Definition at line 994 of file base/include/mrpt/math/utils.h.

References mahalanobisDistance2().

Referenced by mahalanobisDistance().

template<class VECTORLIKE , class MATRIXLIKE >
MATRIXLIKE::value_type mrpt::math::mahalanobisDistance2 ( const VECTORLIKE &  delta_mu,
const MATRIXLIKE &  cov 
) [inline]

Computes the squared mahalanobis distance between a point and a Gaussian, given the covariance matrix and the vector with the difference between the mean and the point.

\[ d^2 = \Delta_\mu^\top \Sigma^{-1} \Delta_\mu \]

Definition at line 1049 of file base/include/mrpt/math/utils.h.

References ASSERTDEB_, and mrpt::math::detail::multiply_HCHt_scalar().

template<class VECTORLIKE , class MAT1 , class MAT2 , class MAT3 >
VECTORLIKE::value_type mrpt::math::mahalanobisDistance2 ( const VECTORLIKE &  mean_diffs,
const MAT1 &  COV1,
const MAT2 &  COV2,
const MAT3 &  CROSS_COV12 
) [inline]

Computes the squared mahalanobis distance between two *non-independent* Gaussians, given the two covariance matrices and the vector with the difference of their means.

\[ d^2 = \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12 )^{-1} \Delta_\mu \]

Definition at line 1008 of file base/include/mrpt/math/utils.h.

References ASSERT_, MRPT_END, MRPT_START, mrpt::math::detail::multiply_HCHt_scalar(), and size().

template<class VECTORLIKE1 , class VECTORLIKE2 , class MAT >
VECTORLIKE1::value_type mrpt::math::mahalanobisDistance2 ( const VECTORLIKE1 &  X,
const VECTORLIKE2 &  MU,
const MAT &  COV 
) [inline]

Computes the squared mahalanobis distance of a vector X given the mean MU and the covariance *inverse* COV_inv

\[ d^2 = (X-MU)^\top \Sigma^{-1} (X-MU) \]

.

Definition at line 971 of file base/include/mrpt/math/utils.h.

References ASSERT_, MRPT_END, MRPT_START, mrpt::math::detail::multiply_HCHt_scalar(), and size().

Referenced by mahalanobisDistance().

template<typename T , class VECLIKE , class MATRIXLIKE >
void mrpt::math::mahalanobisDistance2AndLogPDF ( const VECLIKE &  diff_mean,
const MATRIXLIKE &  cov,
T &  maha2_out,
T &  log_pdf_out 
) [inline]

Computes both, the logarithm of the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian.

See also:
productIntegralTwoGaussians, mahalanobisDistance2, normalPDF, mahalanobisDistance2AndPDF

Definition at line 1144 of file base/include/mrpt/math/utils.h.

References ASSERTDEB_, M_2PI, MRPT_END, MRPT_START, and multiply_HCHt_scalar().

Referenced by mahalanobisDistance2AndPDF().

template<typename T , class VECLIKE , class MATRIXLIKE >
void mrpt::math::mahalanobisDistance2AndPDF ( const VECLIKE &  diff_mean,
const MATRIXLIKE &  cov,
T &  maha2_out,
T &  pdf_out 
) [inline]

Computes both, the PDF and the square Mahalanobis distance between a point (given by its difference wrt the mean) and a Gaussian.

See also:
productIntegralTwoGaussians, mahalanobisDistance2, normalPDF

Definition at line 1168 of file base/include/mrpt/math/utils.h.

References mahalanobisDistance2AndLogPDF().

template<size_t N, typename T >
std::vector<T> mrpt::math::make_vector ( const T  val1,
  ... 
) [inline]

A versatile template to build vectors on-the-fly in a style close to MATLAB's v=[a b c d .

..] The first argument of the template is the vector length, and the second the type of the numbers. Some examples:

    vector_double  = make_vector<4,double>(1.0,3.0,4.0,5.0);
    vector_float   = make_vector<2,float>(-8.12, 3e4);

Definition at line 1190 of file base/include/mrpt/math/utils.h.

References MRPT_COMPILE_TIME_ASSERT.

template<class MATRIX >
mrpt::math::MAT_TYPE_COVARIANCE_OF ( MATRIX   )  const [inline]

Computes the covariance matrix from a list of samples in an NxM matrix, where each row is a sample, so the covariance is MxM.

Parameters:
v The set of data, as a NxM matrix.
out_cov The output MxM matrix for the estimated covariance matrix.
See also:
math::mean,math::stddev, math::cov

Definition at line 1165 of file ops_matrices.h.

References meanAndCov().

template<class MAT1 , class MAT2 >
mrpt::math::MAT_TYPE_PRODUCT_OF ( MAT1  ,
MAT2   
) const [inline]

Matrix multiplication operator: A * B -> RES The meaning of the lengthy macros in the declaration is:

  • MAT_TYPE_PRODUCT_OF: Return type is the correct one for A*B, e.g.

NxM * MxK -> NxK, DYN*DYN -> DYN.

  • RET_MAT_ASSERT_MRPTMATRIX: Assure that the compiler will use this "operator*" only with MRPT matrices.

Referenced by mrpt::math::detail::multiply_HCHt().

template<class MAT >
mrpt::math::MAT_TYPE_TRANSPOSE_OF ( MAT   )  const [inline]

unary transpose operator ~

Definition at line 1070 of file ops_matrices.h.

std::string BASE_IMPEXP mrpt::math::MATLAB_plotCovariance2D ( const CMatrixFloat &  cov22,
const CVectorFloat &  mean,
const float &  stdCount,
const std::string &  style = std::string("b"),
const size_t &  nEllipsePoints = 30 
)

Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('float' version).

Generates a string with the MATLAB commands required to plot an confidence interval (ellipse) for a 2D Gaussian ('double' version).

Parameters:
cov22 The 2x2 covariance matrix
mean The 2-length vector with the mean
stdCount How many "quantiles" to get into the area of the ellipse: 2: 95%, 3:99.97%,...
style A matlab style string, for colors, line styles,...
nEllipsePoints The number of points in the ellipse to generate
cov22 The 2x2 covariance matrix
mean The 2-length vector with the mean
stdCount How many "quantiles" to get into the area of the ellipse: 2: 95%, 3:99.97%,...
style A matlab style string, for colors, line styles,...
nEllipsePoints The number of points in the ellipse to generate
template<class CONTAINER >
CONTAINER::value_type mrpt::math::maximum ( const CONTAINER &  v,
size_t *  maxIndex = NULL 
) [inline]

Referenced by condidenceIntervals(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), weightedHistogram(), and weightedHistogramLog().

template<class CONTAINER >
double mrpt::math::mean ( const CONTAINER &  v  )  [inline]

Referenced by condidenceIntervals(), mrpt::random::CRandomGenerator::drawGaussian1DMatrix(), mrpt::random::CRandomGenerator::drawGaussian1DVector(), mrpt::random::CRandomGenerator::drawGaussianMultivariate(), mrpt::random::CRandomGenerator::drawGaussianMultivariateMany(), mrpt::random::matrixRandomNormal(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), and mrpt::random::vectorRandomNormal().

class MAT_OUT void mrpt::math::meanAndCov ( const MAT_IN &  v,
vector_double &  out_mean,
MAT_OUT &  out_cov 
)

Definition at line 1120 of file ops_matrices.h.

References ASSERTMSG_, and mrpt::utils::square().

Referenced by MAT_TYPE_COVARIANCE_OF().

template<class VECTOR_OF_VECTOR , class VECTORLIKE , class MATRIXLIKE >
void mrpt::math::meanAndCovVector ( const VECTOR_OF_VECTOR &  v,
VECTORLIKE &  out_mean,
MATRIXLIKE &  out_cov 
) [inline]

Computes the mean vector and covariance from a list of values given as a vector of vectors, where each row is a sample.

Parameters:
v The set of data, as a vector of N vectors of M elements.
out_mean The output M-vector for the estimated mean.
out_cov The output MxM matrix for the estimated covariance matrix.
See also:
math::mean,math::stddev, math::cov

Definition at line 215 of file base/include/mrpt/math/utils.h.

References ASSERTMSG_, and mrpt::utils::square().

Referenced by covVector().

template<class VECTORLIKE >
void mrpt::math::meanAndStd ( const VECTORLIKE &  v,
double &  out_mean,
double &  out_std,
bool  unbiased = true 
) [inline]
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.

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.
template<class CONTAINER >
CONTAINER::value_type mrpt::math::minimum ( const CONTAINER &  v,
size_t *  minIndex = NULL 
) [inline]

Referenced by leastSquareLinearFit(), mrpt::slam::PF_implementation< PARTICLE_TYPE >::PF_SLAM_implementation_pfAuxiliaryPFStandardAndOptimal(), weightedHistogram(), and weightedHistogramLog().

template<class CONTAINER >
void mrpt::math::minimum_maximum ( const CONTAINER &  v,
typename CONTAINER::mrpt_autotype::value_type &  out_min,
typename CONTAINER::mrpt_autotype::value_type &  out_max,
size_t *  minIndex = static_cast< size_t * >(NULL),
size_t *  maxIndex = static_cast< size_t * >(NULL) 
) [inline]

Referenced by condidenceIntervals().

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

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

double BASE_IMPEXP mrpt::math::minimumDistanceFromPointToSegment ( 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, and returns that minimum distance.

template<class MAT1 , class MAT2 >
MAT1::value_type mrpt::math::multiply_HCHt_scalar ( const MAT1 &  H,
const MAT2 &  C 
) [inline]

Just like s=H.multiply_HCHt_scalar(C), but defined in mrpt::math for backward compatibility.

Definition at line 1048 of file ops_matrices.h.

References mrpt::math::detail::multiply_HCHt_scalar().

Referenced by KLD_Gaussians(), mahalanobisDistance2AndLogPDF(), and normalPDF().

template<>
bool mrpt::math::myStaticCast ( double  val  )  [inline]

Definition at line 43 of file CMatrixTemplate.h.

template<typename U >
U mrpt::math::myStaticCast ( double  val  )  [inline]

Definition at line 43 of file CMatrixTemplate.h.

template<class T >
double mrpt::math::noncentralChi2CDF ( unsigned int  degreesOfFreedom,
T  noncentrality,
T  arg 
) [inline]

Cumulative non-central chi square distribution (approximate).

Computes approximate values of the cumulative density of a chi square distribution with degreesOfFreedom, and noncentrality parameter noncentrality at the given argument arg, i.e. the probability that a random number drawn from the distribution is below arg It uses the approximate transform into a normal distribution due to Wilson and Hilferty (see Abramovitz, Stegun: "Handbook of Mathematical Functions", formula 26.3.32). The algorithm's running time is independent of the inputs. The accuracy is only about 0.1 for few degrees of freedom, but reaches about 0.001 above dof = 5.

Note:
Function code from the Vigra project (http://hci.iwr.uni-heidelberg.de/vigra/); code under "MIT X11 License", GNU GPL-compatible.

Definition at line 164 of file distributions.h.

References erf(), and mrpt::utils::square().

Referenced by chi2CDF().

template<class CONTAINER >
CONTAINER::value_type mrpt::math::norm ( const CONTAINER &  v  )  [inline]

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute().

template<class CONTAINER >
CONTAINER::value_type mrpt::math::norm_inf ( const CONTAINER &  v,
size_t *  maxIndex = NULL 
) [inline]

Referenced by mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute().

double BASE_IMPEXP mrpt::math::normalCDF ( double  p  ) 

Evaluates the Gaussian cumulative density function.

The employed approximation is that from W. J. Cody freely available in http://www.netlib.org/specfun/erf

template<class T >
void mrpt::math::normalize ( const std::vector< T > &  v,
std::vector< T > &  out_v 
) [inline]

Normalize a vector, such as its norm is the unity.

If the vector has a null norm, the output is a null vector.

Definition at line 191 of file base/include/mrpt/math/utils.h.

References mrpt::utils::square().

template<typename VECTORLIKE , typename MATRIXLIKE >
MATRIXLIKE::value_type mrpt::math::normalPDF ( const VECTORLIKE &  d,
const MATRIXLIKE &  cov 
) [inline]

Evaluates the multivariate normal (Gaussian) distribution at a given point given its distance vector "d" from the Gaussian mean.

Definition at line 84 of file distributions.h.

References ASSERTDEB_, M_2PI, MRPT_END, MRPT_START, and multiply_HCHt_scalar().

template<class VECTORLIKE1 , class VECTORLIKE2 , class MATRIXLIKE >
MATRIXLIKE::value_type mrpt::math::normalPDF ( const VECTORLIKE1 &  x,
const VECTORLIKE2 &  mu,
const MATRIXLIKE &  cov,
const bool  scaled_pdf = false 
) [inline]

Evaluates the multivariate normal (Gaussian) distribution at a given point "x".

Parameters:
x A vector or column or row matrix with the point at which to evaluate the pdf.
mu A vector or column or row matrix with the Gaussian mean.
cov The covariance matrix of the Gaussian.
scaled_pdf If set to true, the PDF will be scaled to be in the range [0,1].

Definition at line 63 of file distributions.h.

References ASSERTDEB_, M_2PI, MAT_TYPE_SAMESIZE_OF, MRPT_END, MRPT_START, multiply_HCHt_scalar(), size(), and UNINITIALIZED_MATRIX.

double BASE_IMPEXP mrpt::math::normalPDF ( double  x,
double  mu,
double  std 
)

Evaluates the univariate normal (Gaussian) distribution at a given point "x".

double BASE_IMPEXP mrpt::math::normalQuantile ( double  p  ) 

Evaluates the Gaussian distribution quantile for the probability value p=[0,1].

The employed approximation is that from Peter J. Acklam (pjacklam@online.no), freely available in http://home.online.no/~pjacklam.

template<class T >
std::vector<T> mrpt::math::ones ( size_t  count  )  [inline]

Generates a vector of all ones of the given length.

Definition at line 130 of file base/include/mrpt/math/utils.h.

bool mrpt::math::operator!= ( const TSegment3D &  s1,
const TSegment3D &  s2 
) [inline]

Definition at line 785 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

bool mrpt::math::operator!= ( const TSegment2D &  s1,
const TSegment2D &  s2 
) [inline]

Definition at line 777 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

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

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

Definition at line 625 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::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 613 of file lightweight_geom_data.h.

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

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

Exact comparison between 3D points.

Definition at line 601 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 TPoint2D &  p1,
const TPoint2D &  p2 
) [inline]

Exact comparison between 2D points.

Definition at line 589 of file lightweight_geom_data.h.

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

template<class T , std::size_t N>
bool mrpt::math::operator!= ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 295 of file CArray.h.

template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric<T,N> mrpt::math::operator* ( const CArrayNumeric< T, N > &  A,
const VECTORLIKE &  B 
) [inline]

Dot product: ARRAY <- ARRAY .

* VECTORorARRAY

Definition at line 462 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric<T,N> mrpt::math::operator+ ( const CArrayNumeric< T, N > &  A,
const VECTORLIKE &  B 
) [inline]

Operator ARRAY <- ARRAY + VECTORorARRAY.

Definition at line 444 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

TPoint3D mrpt::math::operator- ( const TPoint3D &  p1  )  [inline]

Unary minus operator for 3D points.

Definition at line 577 of file lightweight_geom_data.h.

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

template<typename T , std::size_t N, class VECTORLIKE >
CArrayNumeric<T,N> mrpt::math::operator- ( const CArrayNumeric< T, N > &  A,
const VECTORLIKE &  B 
) [inline]

Operator ARRAY <- ARRAY - VECTORorARRAY.

Definition at line 453 of file CArray.h.

References ASSERT_, and mrpt::math::CArray< T, N >::size().

template<class T >
CMatrixTemplateNumeric<T> mrpt::math::operator/ ( const CMatrixTemplateNumeric< T > &  m1,
const CMatrixTemplateNumeric< T > &  m2 
) [inline]

Binary matrix division operator A/B = A*inv(B).

Definition at line 1054 of file ops_matrices.h.

template<class T , std::size_t N>
bool mrpt::math::operator< ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 291 of file CArray.h.

template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const CMatrixFixedNumeric< double, NROWS, NCOLS > &  M 
) [inline]

Write operator for writing into a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 83 of file ops_matrices.h.

template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const CMatrixFixedNumeric< float, NROWS, NCOLS > &  M 
) [inline]

Write operator for writing into a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 76 of file ops_matrices.h.

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

TObject3D binary output.

mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TPlane &  p 
) [inline]

TPlane binary output.

Definition at line 2409 of file lightweight_geom_data.h.

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

mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TLine3D &  l 
) [inline]

TLine3D binary output.

Definition at line 2396 of file lightweight_geom_data.h.

References mrpt::math::TLine3D::director, and mrpt::math::TLine3D::pBase.

mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TSegment3D &  s 
) [inline]

TSegment3D binary output.

Definition at line 2383 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TObject2D &  o 
)

TObject2D binary input.

mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TLine2D &  l 
) [inline]

TLine2D binary output.

Definition at line 2361 of file lightweight_geom_data.h.

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

mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TSegment2D &  s 
) [inline]

TSegment2D binary output.

Definition at line 2348 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TPose3D &  o 
)

TPose3D binary output.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TPose2D &  o 
)

TPose2D binary output.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator<< ( mrpt::utils::CStream &  out,
const mrpt::math::TPoint3D &  o 
)

TPoint3D binary output.

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

TPoint2D binary output.

template<typename T , size_t N>
std::ostream& mrpt::math::operator<< ( std::ostream &  ostrm,
const CArray< T, N > &  a 
) [inline]

Textual output stream function.

Use only for text output, for example: "std::cout << mat;"

Definition at line 473 of file CArray.h.

template<class T , std::size_t N>
bool mrpt::math::operator<= ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 303 of file CArray.h.

template<class T , size_t NROWS, size_t NCOLS>
bool mrpt::math::operator== ( const CMatrixFixedNumeric< T, NROWS, NCOLS > &  M1,
const CMatrixFixedNumeric< T, NROWS, NCOLS > &  M2 
) [inline]

Equal comparison (==).

Definition at line 91 of file ops_matrices.h.

bool mrpt::math::operator== ( const TSegment3D &  s1,
const TSegment3D &  s2 
) [inline]

Definition at line 781 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

bool mrpt::math::operator== ( const TSegment2D &  s1,
const TSegment2D &  s2 
) [inline]

Definition at line 773 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

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

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

Definition at line 619 of file lightweight_geom_data.h.

References mrpt::math::TPose3D::pitch, mrpt::math::TPose3D::roll, wrapTo2Pi(), mrpt::math::TPose3D::x, mrpt::math::TPose3D::y, mrpt::math::TPose3D::yaw, and mrpt::math::TPose3D::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 607 of file lightweight_geom_data.h.

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

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

Exact comparison between 3D points.

Definition at line 595 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 TPoint2D &  p1,
const TPoint2D &  p2 
) [inline]

Exact comparison between 2D points.

Definition at line 583 of file lightweight_geom_data.h.

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

template<class T , std::size_t N>
bool mrpt::math::operator== ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 287 of file CArray.h.

References mrpt::math::CArray< T, N >::begin(), and mrpt::math::CArray< T, N >::end().

template<class T , std::size_t N>
bool mrpt::math::operator> ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 299 of file CArray.h.

template<class T , std::size_t N>
bool mrpt::math::operator>= ( const CArray< T, N > &  x,
const CArray< T, N > &  y 
) [inline]

Definition at line 307 of file CArray.h.

template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
CMatrixFixedNumeric< double, NROWS, NCOLS > &  M 
) [inline]

Read operator from a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 66 of file ops_matrices.h.

References ASSERTMSG_, mrpt::format(), mrpt::math::CMatrixTemplate< T >::getColCount(), mrpt::math::CMatrixTemplate< T >::getRowCount(), mrpt::utils::CStream::ReadObject(), and mrpt::math::CMatrixTemplate< T >::size().

template<size_t NROWS, size_t NCOLS>
mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
CMatrixFixedNumeric< float, NROWS, NCOLS > &  M 
) [inline]

Read operator from a CStream.

The format is compatible with that of CMatrix & CMatrixD

Definition at line 57 of file ops_matrices.h.

References ASSERTMSG_, mrpt::format(), mrpt::math::CMatrixTemplate< T >::getColCount(), mrpt::math::CMatrixTemplate< T >::getRowCount(), mrpt::utils::CStream::ReadObject(), and mrpt::math::CMatrixTemplate< T >::size().

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

TObject3D binary input.

mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TPlane &  p 
) [inline]

TPlane binary input.

Definition at line 2403 of file lightweight_geom_data.h.

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

mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TLine3D &  l 
) [inline]

TLine3D binary input.

Definition at line 2390 of file lightweight_geom_data.h.

References mrpt::math::TLine3D::director, and mrpt::math::TLine3D::pBase.

mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TSegment3D &  s 
) [inline]

TSegment3D binary input.

Definition at line 2377 of file lightweight_geom_data.h.

References mrpt::math::TSegment3D::point1, and mrpt::math::TSegment3D::point2.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TObject2D &  o 
)

TObject2D binary input.

mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TLine2D &  l 
) [inline]

TLine2D binary input.

Definition at line 2355 of file lightweight_geom_data.h.

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

mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TSegment2D &  s 
) [inline]

TSegment2D binary input.

Definition at line 2342 of file lightweight_geom_data.h.

References mrpt::math::TSegment2D::point1, and mrpt::math::TSegment2D::point2.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TPose3D &  o 
)

TPose3D binary input.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TPose2D &  o 
)

TPose2D binary input.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TPoint3D &  o 
)

TPoint3D binary input.

BASE_IMPEXP mrpt::utils::CStream& mrpt::math::operator>> ( mrpt::utils::CStream &  in,
mrpt::math::TPoint2D &  o 
)

TPoint2D binary input.

template<class T >
CMatrixTemplateNumeric<T> mrpt::math::operator^ ( const CMatrixTemplateNumeric< T > &  m,
const unsigned int  pow 
) [inline]

binary power operator

Definition at line 1061 of file ops_matrices.h.

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.

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

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

See also:
pointIntoPolygon2D

Definition at line 932 of file geometry.h.

References mrpt::utils::sign(), and wrapToPi().

template<typename T , class VECLIKE , class MATLIKE1 , class MATLIKE2 >
void mrpt::math::productIntegralAndMahalanobisTwoGaussians ( const VECLIKE &  mean_diffs,
const MATLIKE1 &  COV1,
const MATLIKE2 &  COV2,
T &  maha2_out,
T &  intprod_out,
const MATLIKE1 *  CROSS_COV12 = NULL 
) [inline]

Computes both, the integral of the product of two Gaussians and their square Mahalanobis distance.

See also:
productIntegralTwoGaussians, mahalanobisDistance2

Definition at line 1117 of file base/include/mrpt/math/utils.h.

References ASSERT_, and M_2PI.

template<typename T , size_t DIM>
T mrpt::math::productIntegralTwoGaussians ( const std::vector< T > &  mean_diffs,
const CMatrixFixedNumeric< T, DIM, DIM > &  COV1,
const CMatrixFixedNumeric< T, DIM, DIM > &  COV2 
) [inline]

Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2".

\[ D = \frac{1}{(2 \pi)^{0.5 N} \sqrt{} } \exp( \Delta_\mu^\top (\Sigma_1 + \Sigma_2)^{-1} \Delta_\mu) \]

Definition at line 1095 of file base/include/mrpt/math/utils.h.

References ASSERT_, M_2PI, and UNINITIALIZED_MATRIX.

template<typename T >
T mrpt::math::productIntegralTwoGaussians ( const std::vector< T > &  mean_diffs,
const CMatrixTemplateNumeric< T > &  COV1,
const CMatrixTemplateNumeric< T > &  COV2 
) [inline]

Computes the integral of the product of two Gaussians, with means separated by "mean_diffs" and covariances "COV1" and "COV2".

\[ D = \frac{1}{(2 \pi)^{0.5 N} \sqrt{} } \exp( \Delta_\mu^\top (\Sigma_1 + \Sigma_2 - 2 \Sigma_12)^{-1} \Delta_\mu) \]

Definition at line 1072 of file base/include/mrpt/math/utils.h.

References ASSERT_, and M_2PI.

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

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

Definition at line 392 of file geometry.h.

References project2D().

template<class T >
void mrpt::math::project2D ( const T &  obj,
const TLine2D &  newXLine,
const TPoint2D &  newOrigin,
T &  newObj 
) [inline]

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.

Definition at line 383 of file geometry.h.

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

template<class T >
void mrpt::math::project2D ( const T &  obj,
const TLine2D &  newXLine,
T &  newObj 
) [inline]

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.

Definition at line 374 of file geometry.h.

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

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

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

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

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

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

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

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

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

Definition at line 353 of file geometry.h.

References mrpt::math::TSegment2D::point1, mrpt::math::TSegment2D::point2, and project2D().

void mrpt::math::project2D ( const TPoint2D &  point,
const CPose2D &  newXpose,
TPoint2D &  newPoint 
) [inline]

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

Definition at line 347 of file geometry.h.

Referenced by project2D().

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

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

Definition at line 338 of file geometry.h.

References project3D().

template<class T >
void mrpt::math::project3D ( const T &  obj,
const TPlane &  newXYPlane,
const TPoint3D &  newOrigin,
T &  newObj 
) [inline]

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 328 of file geometry.h.

References project3D().

template<class T >
void mrpt::math::project3D ( const T &  obj,
const TPlane &  newXYPlane,
T &  newObj 
) [inline]

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 319 of file geometry.h.

References project3D().

void BASE_IMPEXP mrpt::math::project3D ( const TObject3D &  object,
const CPose3D &  newXYPose,
TObject3D &  newObject 
)

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

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

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

void BASE_IMPEXP mrpt::math::project3D ( const TPlane &  plane,
const CPose3D &  newXYpose,
TPlane &  newPlane 
)

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

void BASE_IMPEXP mrpt::math::project3D ( const TLine3D &  line,
const CPose3D &  newXYpose,
TLine3D &  newLine 
)

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

void mrpt::math::project3D ( const TSegment3D &  segment,
const CPose3D &  newXYpose,
TSegment3D &  newSegment 
) [inline]

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

Definition at line 295 of file geometry.h.

References mrpt::math::TSegment3D::point1, mrpt::math::TSegment3D::point2, and project3D().

void mrpt::math::project3D ( const TPoint3D &  point,
const CPose3D &  newXYpose,
TPoint3D &  newPoint 
) [inline]

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

Definition at line 289 of file geometry.h.

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

Referenced by project3D().

template<class T >
void BASE_IMPEXP mrpt::math::qr_decomposition ( CMatrixTemplateNumeric< T > &  A,
CMatrixTemplateNumeric< T > &  R,
CMatrixTemplateNumeric< T > &  Q,
CVectorTemplate< T > &  c,
int &  sing 
) [inline]

Matrix QR decomposition.

A = QR, where R is upper triangular and Q is orthogonal, that is, ~QQ = 1 If A is a LxM dimension matrix, this function only return the LxL upper triangular matrix R instead of LxM pseudo-upper triangular matrix (been L<=M) This function has been extracted from "Numerical Recipes in C". /param A is the original matrix to decompose /param c,Q. The orthogonal matrix Q is represented as a product of n-1 Householder matrices Q1,...Qn-1, where Qj = 1 - u[j] x u[j]/c[j] The i'th component of u[j] is zero for i = 1,...,j-1 while the nonzero components are returned in Q(i,j) for i=j,...,n /param R is the upper triangular matrix /param sign returns as true (1) is singularity is encountered during the decomposition, but the decomposition is still complete in this case; otherwise it returns false (0)

template<typename NUMTYPE >
void BASE_IMPEXP mrpt::math::ransac_detect_2D_lines ( const std::vector< NUMTYPE > &  x,
const std::vector< NUMTYPE > &  y,
std::vector< std::pair< size_t, TLine2D > > &  out_detected_lines,
const double  threshold,
const size_t  min_inliers_for_valid_line = 5 
) [inline]

Fit a number of 2-D lines to a given point cloud, automatically determining the number of existing lines by means of the provided threshold and minimum number of supporting inliers.

Parameters:
out_detected_lines The output list of pairs: number of supporting inliers, detected line.
threshold The maximum distance between a point and a temptative line such as the point is considered an inlier.
min_inliers_for_valid_line The minimum number of supporting inliers to consider a line as valid.
template<class POINTSMAP >
void mrpt::math::ransac_detect_3D_planes ( const POINTSMAP *  points_map,
vector< pair< size_t, TPlane > > &  out_detected_planes,
const double  threshold,
const size_t  min_inliers_for_valid_plane 
) [inline]

A stub for ransac_detect_3D_planes() with the points given as a mrpt::slam::CPointsMap.

Definition at line 76 of file ransac_applications.h.

References ransac_detect_3D_planes().

template<typename NUMTYPE >
void BASE_IMPEXP mrpt::math::ransac_detect_3D_planes ( const std::vector< NUMTYPE > &  x,
const std::vector< NUMTYPE > &  y,
const std::vector< NUMTYPE > &  z,
std::vector< std::pair< size_t, TPlane > > &  out_detected_planes,
const double  threshold,
const size_t  min_inliers_for_valid_plane = 10 
) [inline]

Fit a number of 3-D planes to a given point cloud, automatically determining the number of existing planes by means of the provided threshold and minimum number of supporting inliers.

Parameters:
out_detected_planes The output list of pairs: number of supporting inliers, detected plane.
threshold The maximum distance between a point and a temptative plane such as the point is considered an inlier.
min_inliers_for_valid_plane The minimum number of supporting inliers to consider a plane as valid.

Referenced by ransac_detect_3D_planes().

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 wether 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.

template<class MATRIX >
mrpt::math::RET_MAT_ASSERT_MRPTMATRIX ( MATRIX   )  const [inline]

Unary inversion operator.

Definition at line 1084 of file ops_matrices.h.

References UNINITIALIZED_MATRIX.

template<class MATRIX >
mrpt::math::RET_TYPE_ASSERT_MRPTMATRIX ( MATRIX  ,
std::ostream   
) [inline]

Textual output stream function.

Use only for text output, for example: "std::cout << mat;"

Definition at line 104 of file ops_matrices.h.

template<class MATRIXLIKE1 , class MATRIXLIKE2 >
mrpt::math::RET_VOID_ASSERT_MRPTMATRICES ( MATRIXLIKE1  ,
MATRIXLIKE2   
) const [inline]

Efficiently compute the inverse of a 4x4 homogeneous matrix by only transposing the rotation 3x3 part and solving the translation with dot products.

This is a generic template which works with: MATRIXLIKE: CMatrixTemplateNumeric, CMatrixFixedNumeric

template<class T >
T mrpt::math::round2up ( T  val  )  [inline]

Round up to the nearest power of two of a given number.

Definition at line 522 of file base/include/mrpt/math/utils.h.

References THROW_EXCEPTION.

template<class T >
T mrpt::math::round_10power ( T  val,
int  power10 
) [inline]

Round a decimal number up to the given 10'th power (eg, to 1000,100,10, and also fractions) power10 means round up to: 1 -> 10, 2 -> 100, 3 -> 1000, .

.. -1 -> 0.1, -2 -> 0.01, ...

Definition at line 538 of file base/include/mrpt/math/utils.h.

References mrpt::utils::round_long().

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.

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.

template<class T , T STEP>
std::vector<T> mrpt::math::sequence ( T  first,
size_t  length 
) [inline]

Generates a sequence of values [first,first+STEP,first+2*STEP,.

..]

See also:
linspace

Definition at line 119 of file base/include/mrpt/math/utils.h.

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

Changes the value of the geometric epsilon.

See also:
geometryEpsilon,getEpsilon

Definition at line 703 of file geometry.h.

References geometryEpsilon.

template<class MATRIXLIKE >
size_t mrpt::math::size ( const MATRIXLIKE &  m,
int  dim 
) [inline]

Returns the size of the matrix in the i'th dimension: 1=rows, 2=columns (MATLAB-compatible function)

Note:
Template argument MATRIXLIKE can be: CMatrixTemplate, CMatrixTemplateNumeric, CMatrixFixedNumeric

Definition at line 534 of file utils_defs.h.

References THROW_EXCEPTION_CUSTOM_MSG1.

Referenced by mrpt::math::CVectorTemplate< KFTYPE >::abs(), mrpt::math::CVectorTemplate< KFTYPE >::deconcatenate(), mrpt::math::CVectorTemplate< KFTYPE >::extract_array(), mrpt::math::CVectorTemplate< KFTYPE >::extract_vector(), mrpt::math::detail::extractColFromMatrix(), mrpt::math::detail::extractRowFromMatrix(), mrpt::math::CVectorTemplate< KFTYPE >::find_max(), mrpt::math::CVectorTemplate< KFTYPE >::find_min(), mrpt::math::CVectorTemplate< KFTYPE >::find_min_max(), mrpt::poses::CPose3DQuat::fromString(), mrpt::poses::CPose3D::fromString(), mrpt::poses::CPose2D::fromString(), mrpt::poses::CPoint3D::fromString(), mrpt::poses::CPoint2D::fromString(), mrpt::vision::CMatchedFeatureList::get_type(), mrpt::vision::CFeatureList::get_type(), mrpt::math::CPolygon::GetVertex_x(), mrpt::math::CPolygon::GetVertex_y(), mrpt::vision::CFeature::TDescriptors::hasDescriptorLogPolarImg(), mrpt::vision::CFeature::TDescriptors::hasDescriptorPolarImg(), mrpt::math::CVectorTemplate< KFTYPE >::insert_array(), mrpt::math::CVectorTemplate< KFTYPE >::insert_vector(), mrpt::math::detail::insertColToMatrix(), mrpt::math::detail::insertMatrixInto(), mrpt::math::detail::insertMatrixTransposeInto(), mrpt::math::detail::insertRowToMatrix(), KLD_Gaussians(), mrpt::math::CVectorTemplate< KFTYPE >::likeMatrix(), mahalanobisDistance2(), mrpt::math::CVectorTemplate< KFTYPE >::mean(), mrpt::math::detail::multiply_HCHt_scalar(), normalPDF(), mrpt::math::CVectorTemplate< KFTYPE >::operator*(), mrpt::math::CVectorTemplate< KFTYPE >::operator+(), mrpt::math::CVectorTemplate< KFTYPE >::operator+=(), mrpt::math::CVectorTemplate< KFTYPE >::operator-(), mrpt::math::CVectorTemplate< KFTYPE >::operator/(), mrpt::math::CVectorTemplate< KFTYPE >::operator~(), mrpt::math::CVectorTemplate< KFTYPE >::saveToTextFile(), mrpt::math::detail::trace(), and mrpt::math::CPolygon::verticesCount().

double BASE_IMPEXP mrpt::math::spline ( const double  t,
const std::vector< double > &  x,
const std::vector< double > &  y,
bool  wrap2pi = false 
)

Interpolates the value of a function in a point "t" given 4 SORTED points where "t" is between the two middle points If wrap2pi is true, output "y" values are wrapped to ]-pi,pi] (It is assumed that input "y" values already are in the correct range).

See also:
leastSquareLinearFit
bool BASE_IMPEXP mrpt::math::splitInConvexComponents ( const TPolygon3D &  poly,
vector< TPolygon3D > &  components 
)

Splits a 3D polygon into convex components.

Exceptions:
std::logic_error if the polygon can't be fit into a plane.
bool BASE_IMPEXP mrpt::math::splitInConvexComponents ( const TPolygon2D &  poly,
vector< TPolygon2D > &  components 
)

Splits a 2D polygon into convex components.

template<class CONTAINER >
CONTAINER::value_type mrpt::math::squareNorm ( const CONTAINER &  v  )  [inline]
template<class VECTORLIKE >
double mrpt::math::stddev ( const VECTORLIKE &  v,
bool  unbiased = true 
) [inline]
template<class CONTAINER >
CONTAINER::value_type mrpt::math::sum ( const CONTAINER &  v  )  [inline]

Referenced by mrpt::math::detail::chol(), mrpt::math::CLevenbergMarquardtTempl< VECTORTYPE, USERPARAM >::execute(), mrpt::math::CVectorTemplate< KFTYPE >::mean(), ANNsampStat::mean(), mrpt::math::detail::noncentralChi2CDF_exact(), ANNsampStat::operator+=(), ANNsampStat::reset(), and ANNsampStat::stdDev().

template<class CONTAINER , typename RET >
RET mrpt::math::sumRetType ( const CONTAINER &  v  )  [inline]
bool mrpt::math::traceRay ( const 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 753 of file geometry.h.

References mrpt::math::TPolygonWithPlane::getPlanes(), and traceRay().

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

Fast ray tracing method using polygons' properties.

See also:
CRenderizable::rayTrace

Referenced by traceRay().

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void mrpt::math::transform_gaussian_linear ( const VECTORLIKE1 &  x_mean,
const MATLIKE1 &  x_cov,
void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)  functor,
const USERPARAM &  fixed_param,
VECTORLIKE2 &  y_mean,
MATLIKE2 &  y_cov,
const VECTORLIKE1 &  x_increments 
) [inline]

First order uncertainty propagation estimator of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant. The Jacobians are estimated numerically using the vector of small increments "x_increments".

See also:
The example in MRPT/samples/unscented_transform_test
transform_gaussian_unscented, transform_gaussian_montecarlo

Definition at line 145 of file transform_gaussian.h.

References mrpt::math::jacobians::jacob_numeric_estimate(), MAT_TYPE_JACOBIAN_OF, MRPT_END, and MRPT_START.

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void mrpt::math::transform_gaussian_montecarlo ( const VECTORLIKE1 &  x_mean,
const MATLIKE1 &  x_cov,
void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)  functor,
const USERPARAM &  fixed_param,
VECTORLIKE2 &  y_mean,
MATLIKE2 &  y_cov,
const size_t  num_samples = 1000,
std::vector< VECTORLIKE3 > *  out_samples_y = NULL 
) [inline]

Simple Montecarlo-base estimation of the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant.

Parameters:
out_samples_y If !=NULL, this vector will contain, upon return, the sequence of random samples generated and propagated through the functor().
See also:
The example in MRPT/samples/unscented_transform_test
transform_gaussian_unscented, transform_gaussian_linear

Definition at line 116 of file transform_gaussian.h.

References covariancesAndMean(), mrpt::random::CRandomGenerator::drawGaussianMultivariateMany(), MRPT_END, MRPT_START, and mrpt::random::randomGenerator.

template<class VECTORLIKE1 , class MATLIKE1 , class USERPARAM , class VECTORLIKE2 , class VECTORLIKE3 , class MATLIKE2 >
void mrpt::math::transform_gaussian_unscented ( const VECTORLIKE1 &  x_mean,
const MATLIKE1 &  x_cov,
void(*)(const VECTORLIKE1 &x, const USERPARAM &fixed_param, VECTORLIKE3 &y)  functor,
const USERPARAM &  fixed_param,
VECTORLIKE2 &  y_mean,
MATLIKE2 &  y_cov,
const bool *  elem_do_wrap2pi = NULL,
const double  alpha = 1e-3,
const double  K = 0,
const double  beta = 2.0 
) [inline]

Scaled unscented transformation (SUT) for estimating the Gaussian distribution of a variable Y=f(X) for an arbitrary function f() provided by the user.

The user must supply the function in "functor" which takes points in the X space and returns the mapped point in Y, optionally using an extra, constant parameter ("fixed_param") which remains constant.

The parameters alpha, K and beta are the common names of the SUT method, and the default values are those recommended in most papers.

Parameters:
elem_do_wrap2pi If !=NULL; it must point to an array of "bool" of size()==dimension of each element, stating if it's needed to do a wrap to [-pi,pi] to each dimension.
See also:
The example in MRPT/samples/unscented_transform_test
transform_gaussian_montecarlo, transform_gaussian_linear

Definition at line 57 of file transform_gaussian.h.

References covariancesAndMeanWeighted(), MAT_TYPE_SAMESIZE_OF, MRPT_END, and MRPT_START.

void mrpt::math::unwrap2PiSequence ( vector_double &  x  ) 

Modify a sequence of angle values such as no consecutive values have a jump larger than PI in absolute value.

See also:
wrapToPi
template<class T >
void BASE_IMPEXP mrpt::math::UpdateCholesky ( CMatrixTemplateNumeric< T > &  chol,
CVectorTemplate< T > &  r1Modification 
) [inline]

If R = CHOL(A) is the original Cholesky factorization of A, then R1 = CHOLUPDATE(R,X) returns the upper triangular Cholesky factor of A + X*X', where X is a column vector of appropriate length.

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 805 of file geometry.h.

References geometryEpsilon.

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 813 of file geometry.h.

References geometryEpsilon.

template<class VECTORLIKE1 , class VECTORLIKE2 >
void mrpt::math::weightedHistogram ( const VECTORLIKE1 &  values,
const VECTORLIKE1 &  weights,
float  binWidth,
VECTORLIKE2 &  out_binCenters,
VECTORLIKE2 &  out_binValues 
) [inline]

Computes the weighted histogram for a vector of values and their corresponding weights.

Parameters:
values [IN] The N values
weights [IN] The weights for the corresponding N values (don't need to be normalized)
binWidth [IN] The desired width of the bins
out_binCenters [OUT] The centers of the M bins generated to cover from the minimum to the maximum value of "values" with the given "binWidth"
out_binValues [OUT] The ratio of values at each given bin, such as the whole vector sums up the unity.
See also:
weightedHistogramLog

Definition at line 395 of file base/include/mrpt/math/utils.h.

References ASSERT_, ASSERTDEB_, maximum(), minimum(), MRPT_END, MRPT_START, and mrpt::utils::round().

template<class VECTORLIKE1 , class VECTORLIKE2 >
void mrpt::math::weightedHistogramLog ( const VECTORLIKE1 &  values,
const VECTORLIKE1 &  log_weights,
float  binWidth,
VECTORLIKE2 &  out_binCenters,
VECTORLIKE2 &  out_binValues 
) [inline]

Computes the weighted histogram for a vector of values and their corresponding log-weights.

Parameters:
values [IN] The N values
weights [IN] The log-weights for the corresponding N values (don't need to be normalized)
binWidth [IN] The desired width of the bins
out_binCenters [OUT] The centers of the M bins generated to cover from the minimum to the maximum value of "values" with the given "binWidth"
out_binValues [OUT] The ratio of values at each given bin, such as the whole vector sums up the unity.
See also:
weightedHistogram

Definition at line 449 of file base/include/mrpt/math/utils.h.

References ASSERT_, ASSERTDEB_, maximum(), minimum(), MRPT_END, MRPT_START, and mrpt::utils::round().

template<class T >
T mrpt::math::wrapTo2Pi ( T  a  )  [inline]

Modifies the given angle to translate it into the [0,2pi[ range.

Note:
Take care of not instancing this template for integer numbers, since it only works for float, double and long double.
See also:
wrapToPi, wrapTo2Pi, unwrap2PiSequence

Definition at line 160 of file base/include/mrpt/math/utils.h.

References wrapTo2PiInPlace().

Referenced by operator!=(), operator==(), and wrapToPi().

template<class T >
void mrpt::math::wrapTo2PiInPlace ( T &  a  )  [inline]

Modifies the given angle to translate it into the [0,2pi[ range.

Note:
Take care of not instancing this template for integer numbers, since it only works for float, double and long double.
See also:
wrapToPi, wrapTo2Pi, unwrap2PiSequence

Definition at line 148 of file base/include/mrpt/math/utils.h.

References M_2PI.

Referenced by wrapTo2Pi().

template<class T >
T mrpt::math::wrapToPi ( T  a  )  [inline]

Modifies the given angle to translate it into the ]-pi,pi] range.

Note:
Take care of not instancing this template for integer numbers, since it only works for float, double and long double.
See also:
wrapTo2Pi, wrapToPiInPlace, unwrap2PiSequence

Definition at line 171 of file base/include/mrpt/math/utils.h.

References M_PI, and wrapTo2Pi().

Referenced by covariancesAndMeanWeighted(), leastSquareLinearFit(), pointIntoQuadrangle(), and wrapToPiInPlace().

template<class T >
void mrpt::math::wrapToPiInPlace ( T &  a  )  [inline]

Modifies the given angle to translate it into the ]-pi,pi] range.

Note:
Take care of not instancing this template for integer numbers, since it only works for float, double and long double.
See also:
wrapToPi,wrapTo2Pi, unwrap2PiSequence

Definition at line 181 of file base/include/mrpt/math/utils.h.

References wrapToPi().

template<class T >
std::vector<T> mrpt::math::zeros ( size_t  count  )  [inline]

Generates a vector of all zeros of the given length.

Definition at line 137 of file base/include/mrpt/math/utils.h.

Variable Documentation

class BASE_IMPEXP mrpt::math::CMatrix

Definition at line 95 of file math_frwds.h.

class BASE_IMPEXP mrpt::math::CMatrixD

Definition at line 96 of file math_frwds.h.

Referenced by mrpt::utils::CProbabilityDensityFunction< CPose2D, 3 >::MRPT_DECLARE_DEPRECATED_FUNCTION().

class BASE_IMPEXP mrpt::math::CMatrixTemplateNumeric

Definition at line 86 of file math_frwds.h.

const unsigned char mrpt::math::GEOMETRIC_TYPE_LINE = 2

Object type identifier for TLine2D or TLine3D.

See also:
TObject2D,TObject3D

Definition at line 1228 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::generate2DObject(), mrpt::math::TObject3D::isLine(), mrpt::math::TObject2D::isLine(), mrpt::math::TObject3D::operator=(), and mrpt::math::TObject2D::operator=().

const unsigned char mrpt::math::GEOMETRIC_TYPE_PLANE = 4

Object type identifier for TPlane.

See also:
TObject3D

Definition at line 1238 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::generate2DObject(), mrpt::math::TObject3D::isPlane(), and mrpt::math::TObject3D::operator=().

const unsigned char mrpt::math::GEOMETRIC_TYPE_POINT = 0

Object type identifier for TPoint2D or TPoint3D.

See also:
TObject2D,TObject3D

Definition at line 1218 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::generate2DObject(), mrpt::math::TObject3D::isPoint(), mrpt::math::TObject2D::isPoint(), mrpt::math::TObject3D::operator=(), and mrpt::math::TObject2D::operator=().

const unsigned char mrpt::math::GEOMETRIC_TYPE_POLYGON = 3

Object type identifier for TPolygon2D or TPolygon3D.

See also:
TObject2D,TObject3D

Definition at line 1233 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::destroy(), mrpt::math::TObject2D::destroy(), mrpt::math::TObject3D::generate2DObject(), mrpt::math::TObject3D::isPolygon(), mrpt::math::TObject2D::isPolygon(), mrpt::math::TObject3D::operator=(), and mrpt::math::TObject2D::operator=().

const unsigned char mrpt::math::GEOMETRIC_TYPE_SEGMENT = 1

Object type identifier for TSegment2D or TSegment3D.

See also:
TObject2D,TObject3D

Definition at line 1223 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::generate2DObject(), mrpt::math::TObject3D::isSegment(), mrpt::math::TObject2D::isSegment(), mrpt::math::TObject3D::operator=(), and mrpt::math::TObject2D::operator=().

const unsigned char mrpt::math::GEOMETRIC_TYPE_UNDEFINED = 255

Object type identifier for empty TObject2D or TObject3D.

See also:
TObject2D,TObject3D

Definition at line 1243 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::destroy(), mrpt::math::TObject2D::destroy(), and mrpt::math::TObject3D::operator=().

double BASE_IMPEXP mrpt::math::geometryEpsilon

Global epsilon to overcome small precision errors.

Referenced by getEpsilon(), setEpsilon(), vectorsAreParallel2D(), and vectorsAreParallel3D().

struct BASE_IMPEXP mrpt::math::TLine3D

Definition at line 630 of file lightweight_geom_data.h.

struct BASE_IMPEXP mrpt::math::TObject3D

Definition at line 632 of file lightweight_geom_data.h.

class BASE_IMPEXP mrpt::math::TPolygon3D

Definition at line 631 of file lightweight_geom_data.h.

Referenced by mrpt::math::TObject3D::operator=(), and mrpt::math::TObject3D::TObject3D().

struct BASE_IMPEXP mrpt::math::TSegment3D

Definition at line 629 of file lightweight_geom_data.h.

Referenced by mrpt::opengl::CSetOfLines::appendLine(), and mrpt::opengl::CSetOfLines::setLineByIndex().

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