lightweight_geom_data.h

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/* +---------------------------------------------------------------------------+
   |          The Mobile Robot Programming Toolkit (MRPT) C++ library          |
   |                                                                           |
   |                   http://mrpt.sourceforge.net/                            |
   |                                                                           |
   |   Copyright (C) 2005-2010  University of Malaga                           |
   |                                                                           |
   |    This software was written by the Machine Perception and Intelligent    |
   |      Robotics Lab, University of Malaga (Spain).                          |
   |    Contact: Jose-Luis Blanco  <jlblanco@ctima.uma.es>                     |
   |                                                                           |
   |  This file is part of the MRPT project.                                   |
   |                                                                           |
   |     MRPT is free software: you can redistribute it and/or modify          |
   |     it under the terms of the GNU General Public License as published by  |
   |     the Free Software Foundation, either version 3 of the License, or     |
   |     (at your option) any later version.                                   |
   |                                                                           |
   |   MRPT is distributed in the hope that it will be useful,                 |
   |     but WITHOUT ANY WARRANTY; without even the implied warranty of        |
   |     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         |
   |     GNU General Public License for more details.                          |
   |                                                                           |
   |     You should have received a copy of the GNU General Public License     |
   |     along with MRPT.  If not, see <http://www.gnu.org/licenses/>.         |
   |                                                                           |
   +---------------------------------------------------------------------------+ */
#ifndef LIGHTWEIGHT_GEOM_DATA_H
#define LIGHTWEIGHT_GEOM_DATA_H

#include <mrpt/utils/utils_defs.h>
#include <mrpt/utils/stl_extensions.h>
#include <mrpt/math/utils.h>

namespace mrpt  {
        namespace poses {
                class CPoseOrPoint;
                class CPoint2D;
                class CPoint3D;
                class CPose2D;
                class CPose3D;
        }
        namespace utils { class CStream; }
}

namespace mrpt  {
namespace math  {
        using namespace mrpt::utils; // For "square"

        struct TPoint2D;
        struct TPose2D;
        struct TPoint3D;
        struct TPose3D;

        //Pragma defined to ensure no structure packing
#pragma pack(push,1)
        //Set of typedefs for lightweight geometric items.
        /**
          * Lightweight 2D point. Allows coordinate access using [] operator.
          * \sa mrpt::poses::CPoint2D
          */
//#define TOBJECTS_USE_UNIONS
        struct MRPTDLLIMPEXP TPoint2D   {
                /**
                  * X coordinate.
                  */
                double x;
                /**
                  * Y coordinate.
                  */
                double y;
                /**
                  * Constructor from TPose2D, discarding phi.
                  * \sa TPose2D
                  */
                explicit TPoint2D(const TPose2D &p);
                /**
                  * Constructor from TPoint3D, discarding z.
                  * \sa TPoint3D
                  */
                explicit TPoint2D(const TPoint3D &p);
                /**
                  * Constructor from TPose3D, discarding z and the angular coordinates.
                  * \sa TPose3D
                  */
                explicit TPoint2D(const TPose3D &p);
                /**
                  * Constructor from CPoseOrPoint, losing information
                  * \sa CPoseOrPoint,CPoint3D,CPose2D,CPose3D
                  */
                explicit TPoint2D(const mrpt::poses::CPoseOrPoint &p);
                /**
                  * Implicit constructor from heavyweight type.
                  * \sa CPoint2D
                  */
                TPoint2D(const mrpt::poses::CPoint2D &p);
                /**
                  * Constructor from coordinates.
                  */
                inline TPoint2D(double xx,double yy):x(xx),y(yy)        {}
                /**
                  * Default fast constructor. Initializes to garbage.
                  */
                inline TPoint2D()       {}
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline double &operator[](size_t i)     {
                        return (&x)[i];
                }
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline const double &operator[](size_t i) const {
                        return (&x)[i];
                }
                /**
                  * Transformation into vector.
                  */
                void getAsVector(vector_double &v) const        {
                        v.resize(2);
                        v[0]=x; v[1]=y;
                }

                bool operator<(const TPoint2D &p) const;
        };

        /**
          * Lightweight 2D pose. Allows coordinate access using [] operator.
          * \sa mrpt::poses::CPose2D
          */
        struct MRPTDLLIMPEXP TPose2D    {
                /**
                  * X coordinate.
                  */
                double x;
                /**
                  * Y coordinate.
                  */
                double y;
                /**
                  * Phi coordinate.
                  */
                double phi;
                /**
                  * Implicit constructor from TPoint2D. Zeroes the phi coordinate.
                  * \sa TPoint2D
                  */
                TPose2D(const TPoint2D &p);
                /**
                  * Constructor from TPoint3D, losing information. Zeroes the phi coordinate.
                  * \sa TPoint3D
                  */
                explicit TPose2D(const TPoint3D &p);
                /**
                  * Constructor from TPose3D, losing information. The phi corresponds to the original pose's yaw.
                  * \sa TPose3D
                  */
                explicit TPose2D(const TPose3D &p);
                /**
                  * Implicit constructor from heavyweight type.
                  * \sa mrpt::poses::CPose2D
                  */
                TPose2D(const mrpt::poses::CPose2D &p);
                /**
                  * Constructor from coordinates.
                  */
                inline TPose2D(double xx,double yy,double pphi):x(xx),y(yy),phi(pphi)   {}
                /**
                  * Default fast constructor. Initializes to garbage.
                  */
                inline TPose2D()        {}
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline double &operator[](size_t i)     {
                        return (&x)[i];
                }
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline const double &operator[](size_t i) const {
                        return (&x)[i];
                }
                /**
                  * Transformation into vector.
                  */
                void getAsVector(vector_double &v) const        {
                        v.resize(3);
                        v[0]=x; v[1]=y; v[2]=phi;
                }
        };

        /**
          * Lightweight 3D point. Allows coordinate access using [] operator.
          * \sa mrpt::poses::TPoint3D
          */
        struct MRPTDLLIMPEXP TPoint3D   {
                /**
                  * X coordinate.
                  */
                double x;
                /**
                  * Y coordinate.
                  */
                double y;
                /**
                  * Z coordinate.
                  */
                double z;
                /**
                  * Implicit constructor from TPoint2D. Zeroes the z.
                  * \sa TPoint2D
                  */
                TPoint3D(const TPoint2D &p);
                /**
                  * Constructor from TPose2D, losing information. Zeroes the z.
                  * \sa TPose2D
                  */
                explicit TPoint3D(const TPose2D &p);
                /**
                  * Constructor from TPose3D, losing information.
                  * \sa TPose3D
                  */
                explicit TPoint3D(const TPose3D &p);
                /**
                  * Implicit constructor from heavyweight type.
                  * \sa mrpt::poses::CPoint3D
                  */
                TPoint3D(const mrpt::poses::CPoint3D &p);
                /**
                  * Constructor from heavyweight 3D pose.
                  * \sa mrpt::poses::CPose3D.
                  */
                explicit TPoint3D(const mrpt::poses::CPose3D &p);
                /**
                  * Constructor from coordinates.
                  */
                inline TPoint3D(double xx,double yy,double zz):x(xx),y(yy),z(zz)        {}
                /**
                  * Default fast constructor. Initializes to garbage.
                  */
                inline TPoint3D()       {}
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline double &operator[](size_t i)     {
                        return (&x)[i];
                }
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline const double &operator[](size_t i) const {
                        return (&x)[i];
                }
                /**
                  * Point-to-point distance.
                  */
                inline double distanceTo(const TPoint3D &p) const       {
                        return sqrt(square(p.x-x)+square(p.y-y)+square(p.z-z));
                }
                /**
                  * Point-to-point distance, squared.
                  */
                inline double sqrDistanceTo(const TPoint3D &p) const    {
                        return square(p.x-x)+square(p.y-y)+square(p.z-z);
                }
                /**
                  * Point norm.
                  */
                inline double norm() const      {
                        return sqrt(square(x)+square(y)+square(z));
                }
                /**
                  * Point scale.
                  */
                inline void operator *=(const double f) {
                        x*=f;y*=f;z*=f;
                }
                /**
                  * Transformation into vector.
                  */
                void getAsVector(vector_double &v) const {
                        v.resize(3);
                        v[0]=x; v[1]=y; v[2]=z;
                }
                /**
                  * Translation.
                  */
                inline const TPoint3D &operator+=(const TPoint3D &p)    {
                        x+=p.x;
                        y+=p.y;
                        z+=p.z;
                        return *this;
                }
                /**
                  * Difference between points.
                  */
                inline const TPoint3D &operator-=(const TPoint3D &p)    {
                        x-=p.x;
                        y-=p.y;
                        z-=p.z;
                        return *this;
                }
                /**
                  * Point sum.
                  */
                inline TPoint3D operator+(const TPoint3D &p)    {
                        return TPoint3D(x+p.x,y+p.y,z+p.z);
                }
                /**
                  * Poinst substraction.
                  */
                inline TPoint3D operator-(const TPoint3D &p)    {
                        return TPoint3D(x-p.x,y-p.y,z-p.z);
                }

                bool operator<(const TPoint3D &p) const;
        };

        /**
          * Lightweight 3D pose (three spatial coordinates, plus three angular coordinates). Allows coordinate access using [] operator.
          * \sa mrpt::poses::CPose3D
          */
        struct MRPTDLLIMPEXP TPose3D    {
                /**
                  * X coordinate.
                  */
                double x;
                /**
                  * Y coordinate.
                  */
                double y;
                /**
                  * Z coordinate.
                  */
                double z;
                /**
                  * Yaw coordinate (rotation angle over Z axis).
                  */
                double yaw;
                /**
                  * Pitch coordinate (rotation angle over Y axis).
                  */
                double pitch;
                /**
                  * Roll coordinate (rotation angle over X coordinate).
                  */
                double roll;
                /**
                  * Implicit constructor from TPoint2D. Zeroes all the unprovided information.
                  * \sa TPoint2D
                  */
                TPose3D(const TPoint2D &p);
                /**
                  * Implicit constructor from TPose2D. Gets the yaw from the 2D pose's phi, zeroing all the unprovided information.
                  * \sa TPose2D
                  */
                TPose3D(const TPose2D &p);
                /**
                  * Implicit constructor from TPoint3D. Zeroes angular information.
                  * \sa TPoint3D
                  */
                TPose3D(const TPoint3D &p);
                /**
                  * Implicit constructor from heavyweight type.
                  * \sa mrpt::poses::CPose3D
                  */
                TPose3D(const mrpt::poses::CPose3D &p);
                /**
                  * Constructor from coordinates.
                  */
                TPose3D(double _x,double _y,double _z,double _yaw,double _pitch,double _roll):x(_x),y(_y),z(_z),yaw(_yaw),pitch(_pitch),roll(_roll)     {}
                /**
                  * Default fast constructor. Initializes to garbage.
                  */
                inline TPose3D()        {}
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline double &operator[](size_t i)     {
                        return (&x)[i];
                }
                /**
                  * Unsafe coordinate access using operator[]. Intended for loops.
                  */
                inline const double &operator[](size_t i) const {
                        return (&x)[i];
                }
                /**
                  * Pose's spatial coordinates norm.
                  */
                double norm() const {
                        return sqrt(square(x)+square(y)+square(z));
                }
                /**
                  * Gets the pose as a vector of doubles.
                  */
                void getAsVector(vector_double &v) const {
                        v.resize(6);
                        v[0]=x; v[1]=y; v[2]=z; v[3]=yaw; v[4]=pitch; v[5]=roll;
                }
        };
#pragma pack(pop)
        /**
          * Unary minus operator for 3D points.
          */
        inline TPoint3D operator-(const TPoint3D &p1)   {
                return TPoint3D(-p1.x,-p1.y,-p1.z);
        }
        /**
          * Sum operator for 3D points.
          */
        inline TPoint3D operator+(const TPoint3D &p1,const TPoint3D &p2) {
                return TPoint3D(p1.x+p2.x,p1.y+p2.y,p1.z+p2.z);
        }
        /**
          * Substract operator for 3D points.
          */
        inline TPoint3D operator-(const TPoint3D &p1,const TPoint3D &p2) {
                return TPoint3D(p1.x-p2.x,p1.y-p2.y,p1.z-p2.z);
        }
        /**
          * Exact comparison between 2D points.
          */
        inline bool operator==(const TPoint2D &p1,const TPoint2D &p2)   {
                return (p1.x==p2.x)&&(p1.y==p2.y);
        }
        /**
          * Exact comparison between 2D points.
          */
        inline bool operator!=(const TPoint2D &p1,const TPoint2D &p2)   {
                return (p1.x!=p2.x)||(p1.y!=p2.y);
        }
        /**
          * Exact comparison between 3D points.
          */
        inline bool operator==(const TPoint3D &p1,const TPoint3D &p2)   {
                return (p1.x==p2.x)&&(p1.y==p2.y)&&(p1.z==p2.z);
        }
        /**
          * Exact comparison between 3D points.
          */
        inline bool operator!=(const TPoint3D &p1,const TPoint3D &p2)   {
                return (p1.x!=p2.x)||(p1.y!=p2.y)||(p1.z!=p2.z);
        }
        /**
          * Exact comparison between 2D poses, taking possible cycles into account.
          */
        inline bool operator==(const TPose2D &p1,const TPose2D &p2)     {
                return (p1.x==p2.x)&&(p1.y==p2.y)&&(mrpt::math::wrapTo2Pi(p1.phi)==mrpt::math::wrapTo2Pi(p2.phi));
        }
        /**
          * Exact comparison between 2D poses, taking possible cycles into account.
          */
        inline bool operator!=(const TPose2D &p1,const TPose2D &p2)     {
                return (p1.x!=p2.x)||(p1.y!=p2.y)||(mrpt::math::wrapTo2Pi(p1.phi)!=mrpt::math::wrapTo2Pi(p2.phi));
        }
        /**
          * Exact comparison between 3D poses, taking possible cycles into account.
          */
        inline bool operator==(const TPose3D &p1,const TPose3D &p2)     {
                return (p1.x==p2.x)&&(p1.y==p2.y)&&(p1.z==p2.z)&&(mrpt::math::wrapTo2Pi(p1.yaw)==mrpt::math::wrapTo2Pi(p2.yaw))&&(mrpt::math::wrapTo2Pi(p1.pitch)==mrpt::math::wrapTo2Pi(p2.pitch))&&(mrpt::math::wrapTo2Pi(p1.roll)==mrpt::math::wrapTo2Pi(p2.roll));
        }
        /**
          * Exact comparison between 3D poses, taking possible cycles into account.
          */
        inline bool operator!=(const TPose3D &p1,const TPose3D &p2)     {
                return (p1.x!=p2.x)||(p1.y!=p2.y)||(p1.z!=p2.z)||(mrpt::math::wrapTo2Pi(p1.yaw)!=mrpt::math::wrapTo2Pi(p2.yaw))||(mrpt::math::wrapTo2Pi(p1.pitch)!=mrpt::math::wrapTo2Pi(p2.pitch))||(mrpt::math::wrapTo2Pi(p1.roll)!=mrpt::math::wrapTo2Pi(p2.roll));
        }
        //Forward declarations
        struct MRPTDLLIMPEXP TSegment3D;
        struct MRPTDLLIMPEXP TLine3D;
        class MRPTDLLIMPEXP TPolygon3D;
        struct MRPTDLLIMPEXP TObject3D;

        //Pragma defined to ensure no structure packing
#pragma pack(push,1)
        /**
          * 2D segment, consisting of two points.
          * \sa TSegment3D,TLine2D,TPolygon2D,TPoint2D
          */
        struct MRPTDLLIMPEXP TSegment2D {
        public:
                /**
                  * Origin point.
                  */
                TPoint2D point1;
                /**
                  * Destiny point.
                  */
                TPoint2D point2;
                /**
                  * Segment length.
                  */
                double length() const;
                /**
                  * Distance to point.
                  */
                double distance(const TPoint2D &point) const;
                /**
                  * Check whether a point is inside a segment.
                  */
                bool contains(const TPoint2D &point) const;
                /**
                  * Unsafe point access using [] operator, intended for loops.
                  */
                inline TPoint2D &operator[](size_t i)   {
                        return (&point1)[i];
                }
                /**
                  * Unsafe point access using [] operator, intended for loops.
                  */
                inline const TPoint2D &operator[](size_t i) const       {
                        return (&point1)[i];
                }
                /**
                  * Project into 3D space, setting the z to 0.
                  */
                void generate3DObject(TSegment3D &s) const;
                /**
                  * Segment's central point.
                  */
                inline void getCenter(TPoint2D &p) const        {
                        p.x=(point1.x+point2.x)/2;
                        p.y=(point1.y+point2.y)/2;
                }
                /**
                  * Constructor from both points.
                  */
                TSegment2D(const TPoint2D &p1,const TPoint2D &p2):point1(p1),point2(p2) {}
                /**
                  * Fast default constructor. Initializes to garbage.
                  */
                TSegment2D()    {}
                /**
                  * Explicit constructor from 3D object, discarding the z.
                  */
                explicit TSegment2D(const TSegment3D &s);

                bool operator<(const TSegment2D &s) const;
        };
        /**
          * 3D segment, consisting of two points.
          * \sa TSegment2D,TLine3D,TPlane,TPolygon3D,TPoint3D
          */
        struct MRPTDLLIMPEXP TSegment3D {
        public:
                /**
                  * Origin point.
                  */
                TPoint3D point1;
                /**
                  * Destiny point.
                  */
                TPoint3D point2;
                /**
                  * Segment length.
                  */
                double length() const;
                /**
                  * Distance to point.
                  */
                double distance(const TPoint3D &point) const;
                /**
                  * Check whether a point is inside the segment.
                  */
                bool contains(const TPoint3D &point) const;
                /**
                  * Unsafe point access using [] operator, intended for loops.
                  */
                inline TPoint3D &operator[](size_t i)   {
                        return (&point1)[i];
                }
                /**
                  * Unsafe point access using [] operator, intended for loops.
                  */
                inline const TPoint3D &operator[](size_t i) const       {
                        return (&point1)[i];
                }
                /**
                  * Projection into 2D space, discarding the z.
                  */
                inline void generate2DObject(TSegment2D &s) const       {
                        s=TSegment2D(*this);
                }
                /**
                  * Segment's central point.
                  */
                inline void getCenter(TPoint3D &p) const        {
                        p.x=(point1.x+point2.x)/2;
                        p.y=(point1.y+point2.y)/2;
                        p.z=(point1.z+point2.z)/2;
                }
                /**
                  * Constructor from both points.
                  */
                TSegment3D(const TPoint3D &p1,const TPoint3D &p2):point1(p1),point2(p2) {}
                /**
                  * Fast default constructor. Initializes to garbage.
                  */
                TSegment3D()    {}
                /**
                  * Constructor from 2D object. Sets the z to zero.
                  */
                TSegment3D(const TSegment2D &s):point1(s.point1),point2(s.point2)       {}

                bool operator<(const TSegment3D &s) const;
        };
#pragma pack(pop)

        inline bool operator==(const TSegment2D &s1,const TSegment2D &s2)       {
                return (s1.point1==s2.point1)&&(s1.point2==s2.point2);
        }

        inline bool operator!=(const TSegment2D &s1,const TSegment2D &s2)       {
                return (s1.point1!=s1.point1)||(s1.point2!=s2.point2);
        }

        inline bool operator==(const TSegment3D &s1,const TSegment3D &s2)       {
                return (s1.point1==s2.point1)&&(s1.point2==s2.point2);
        }

        inline bool operator!=(const TSegment3D &s1,const TSegment3D &s2)       {
                return (s1.point1!=s1.point1)||(s1.point2!=s2.point2);
        }

        /**
          * 2D line without bounds, represented by its equation \f$Ax+By+C=0\f$.
          * \sa TLine3D,TSegment2D,TPolygon2D,TPoint2D
          */
        struct MRPTDLLIMPEXP TLine2D    {
        public:
                /**
                  * Line coefficients, stored as an array: \f$\left[A,B,C\right]\f$.
                  */
                double coefs[3];
                /**
                  * Evaluate point in the line's equation.
                  */
                double evaluatePoint(const TPoint2D &point) const;
                /**
                  * Check whether a point is inside the line.
                  */
                bool contains(const TPoint2D &point) const;
                /**
                  * Distance from a given point.
                  */
                double distance(const TPoint2D &point) const;
                /**
                  * Get line's normal vector.
                  */
                void getNormalVector(double (&vector)[2]) const;
                /**
                  * Unitarize line's normal vector.
                  */
                void unitarize();
                /**
                  * Get line's normal vector after unitarizing line.
                  */
                inline void getUnitaryNormalVector(double (&vector)[2]) {
                        unitarize();
                        getNormalVector(vector);
                }
                /**
                  * Get line's director vector.
                  */
                void getDirectorVector(double (&vector)[2]) const;
                /**
                  * Unitarize line and then get director vector.
                  */
                inline void getUnitaryDirectorVector(double (&vector)[2])       {
                        unitarize();
                        getDirectorVector(vector);
                }
                /**
                  * Project into 3D space, setting the z to 0.
                  */
                void generate3DObject(TLine3D &l) const;
                /**
                  * Get a pose2D whose X axis corresponds to the line.
                  * \sa mrpt::poses::CPose2D.
                  */
                void getAsPose2D(mrpt::poses::CPose2D &outPose) const;
                /**
                  * Get a pose2D whose X axis corresponds to the line, forcing the base point to one given.
                  * \throw logic_error if the point is not inside the line.
                  * \sa mrpt::poses::CPose2D.
                  */
                void getAsPose2DForcingOrigin(const TPoint2D &origin,mrpt::poses::CPose2D &outPose) const;
                /**
                  * Constructor from two points, through which the line will pass.
                  * \throw logic_error if both points are the same
                  */
                TLine2D(const TPoint2D &p1,const TPoint2D &p2) throw(std::logic_error);
                /**
                  * Constructor from a segment.
                  */
                explicit TLine2D(const TSegment2D &s);
                /**
                  * Fast default constructor. Initializes to garbage.
                  */
                TLine2D()       {}
                /**
                  * Constructor from line's coefficients.
                  */
                inline TLine2D(double A,double B,double C)      {
                        coefs[0]=A;
                        coefs[1]=B;
                        coefs[2]=C;
                }
                /**
                  * Construction from 3D object, discarding the Z.
                  * \throw std::logic_error if the line is normal to the XY plane.
                  */
                explicit TLine2D(const TLine3D &l);
        };

        /**
          * 3D line, represented by a base point and a director vector.
          * \sa TLine2D,TSegment3D,TPlane,TPolygon3D,TPoint3D
          */
        struct MRPTDLLIMPEXP TLine3D    {
        public:
                /**
                  * Base point.
                  */
                TPoint3D pBase;
                /**
                  * Director vector.
                  */
                double director[3];
                /**
                  * Check whether a point is inside the line.
                  */
                bool contains(const TPoint3D &point) const;
                /**
                  * Distance between the line and a point.
                  */
                double distance(const TPoint3D &point) const;
                /**
                  * Unitarize director vector.
                  */
                void unitarize();
                /**
                  * Get director vector.
                  */
                inline void getDirectorVector(double (&vector)[3]) const        {
                        for (size_t i=0;i<3;i++) vector[i]=director[i];
                }
                /**
                  * Unitarize and then get director vector.
                  */
                inline void getUnitaryDirectorVector(double (&vector)[3])       {
                        unitarize();
                        getDirectorVector(vector);
                }
                /**
                  * Project into 2D space, discarding the Z coordinate.
                  * \throw std::logic_error if the line's director vector is orthogonal to the XY plane.
                  */
                inline void generate2DObject(TLine2D &l) const  {
                        l=TLine2D(*this);
                }
                /**
                  * Constructor from two points, through which the line will pass.
                  * \throw std::logic_error if both points are the same.
                  */
                TLine3D(const TPoint3D &p1,const TPoint3D &p2) throw(std::logic_error);
                /**
                  * Constructor from 3D segment.
                  */
                explicit TLine3D(const TSegment3D &s);
                /**
                  * Fast default constructor. Initializes to garbage.
                  */
                TLine3D()       {}
                /**
                  * Implicit constructor from 2D object. Zeroes the z.
                  */
                TLine3D(const TLine2D &l);
        };

        /**
          * 3D Plane, represented by its equation \f$Ax+By+Cz+D=0\f$
          * \sa TSegment3D,TLine3D,TPolygon3D,TPoint3D
          */
        struct MRPTDLLIMPEXP TPlane     {
        public:
                /**
                  * Plane coefficients, stored as an array: \f$\left[A,B,C,D\right]\f$
                  */
                double coefs[4];
                /**
                  * Evaluate a point in the plane's equation.
                  */
                double evaluatePoint(const TPoint3D &point) const;
                /**
                  * Check whether a point is contained into the plane.
                  */
                bool contains(const TPoint3D &point) const;
                /**
                  * Check whether a segment is fully contained into the plane.
                  */
                bool contains(const TSegment3D &segment)        {
                        return contains(segment.point1)&&contains(segment.point2);
                }
                /**
                  * Check whether a line is fully contained into the plane.
                  */
                bool contains(const TLine3D &line) const;
                /**
                  * Distance to 3D point.
                  */
                double distance(const TPoint3D &point) const;
                /**
                  * Distance to 3D line. Will be zero if the line is not parallel to the plane.
                  */
                double distance(const TLine3D &line) const;
                /**
                  * Get plane's normal vector.
                  */
                void getNormalVector(double (&vec)[3]) const;
                /**
                  * Unitarize normal vector.
                  */
                void unitarize();
                /**
                  * Unitarize, then get normal vector.
                  */
                inline void getUnitaryNormalVector(double (&vec)[3])    {
                        unitarize();
                        getNormalVector(vec);
                }
                /**
                  * Gets a pose whose XY plane corresponds to this plane.
                  */
                void getAsPose3D(mrpt::poses::CPose3D &outPose);
                /**
                  * Gets a pose whose XY plane corresponds to this, forcing an exact point as its spatial coordinates.
                  * \throw std::logic_error if the point is not inside the plane.
                  */
                void getAsPose3DForcingOrigin(const TPoint3D &newOrigin,mrpt::poses::CPose3D &pose);
                /**
                  * Gets a plane which contains these three points.
                  * \throw std::logic_error if the points are linearly dependants.
                  */
                TPlane(const TPoint3D &p1,const TPoint3D &p2,const TPoint3D &p3) throw(std::logic_error);
                /**
                  * Gets a plane which contains this point and this line.
                  * \throw std::logic_error if the point is inside the line.
                  */
                TPlane(const TPoint3D &p1,const TLine3D &r2) throw(std::logic_error);
                /**
                  * Gets a plane which contains the two lines.
                  * \throw std::logic_error if the lines do not cross.
                  */
                TPlane(const TLine3D &r1,const TLine3D &r2) throw(std::logic_error);
                /**
                  * Fast default constructor. Initializes to garbage.
                  */
                TPlane()        {}
                /**
                  * Constructor from plane coefficients.
                  */
                inline TPlane(double A,double B,double C,double D)      {
                        coefs[0]=A;
                        coefs[1]=B;
                        coefs[2]=C;
                        coefs[3]=D;
                }
                /**
                  * Constructor from an array of coefficients.
                  */
                inline TPlane(const double (&vec)[4])   {
                        for (size_t i=0;i<4;i++) coefs[i]=vec[i];
                }
        };

        /**
          * 2D polygon, inheriting from std::vector<TPoint2D>.
          * \sa TPolygon3D,TSegment2D,TLine2D,TPoint2D, CPolygon
          */
        class MRPTDLLIMPEXP TPolygon2D:public std::vector<TPoint2D>     {
        public:
                /**
                  * Distance to a point.
                  */
                double distance(const TPoint2D &point) const;
                /**
                  * Check whether a point is inside the polygon.
                  */
                bool contains(const TPoint2D &point) const;
                /**
                  * Gets as set of segments, instead of points.
                  */
                void getAsSegmentList(std::vector<TSegment2D> &v) const;
                /**
                  * Projects into 3D space, zeroing the z.
                  */
                void generate3DObject(TPolygon3D &p) const;
                /**
                  * Polygon's central point.
                  */
                void getCenter(TPoint2D &p) const;
                /**
                  * Checks whether is convex.
                  */
                bool isConvex() const;
                /**
                  * Erase repeated vertices.
                  * \sa removeRedundantVertices
                  */
                void removeRepeatedVertices();
                /**
                  * Erase every redundant vertex from the polygon, saving space.
                  * \sa removeRepeatedVertices
                  */
                void removeRedundantVertices();
                /**
                  * Gets plot data, ready to use on a 2D plot.
                  * \sa mrpt::gui::CDisplayWindowPlots
                  */
                void getPlotData(std::vector<double> &x,std::vector<double> &y) const;
                /**
                  * Default constructor.
                  */
                TPolygon2D():std::vector<TPoint2D>()    {}
                /**
                  * Constructor for a given number of vertices, intializing them as garbage.
                  */
                explicit TPolygon2D(size_t N):std::vector<TPoint2D>(N)  {}
                /**
                  * Implicit constructor from a vector of 2D points.
                  */
                TPolygon2D(const std::vector<TPoint2D> &v):std::vector<TPoint2D>(v)     {}
                /**
                  * Constructor from a 3D object.
                  */
                explicit TPolygon2D(const TPolygon3D &p);
                /**
                  * Static method to create a regular polygon, given its size and radius.
                  * \throw std::logic_error if radius is near zero or the number of edges is less than three.
                  */
                static void createRegularPolygon(size_t numEdges,double radius,TPolygon2D &poly);
                /**
                  * Static method to create a regular polygon from its size and radius. The center will correspond to the given pose.
                  * \throw std::logic_error if radius is near zero or the number of edges is less than three.
                  */
                static inline void createRegularPolygon(size_t numEdges,double radius,TPolygon2D &poly,const mrpt::poses::CPose2D &pose);
        };

        /**
          * 3D polygon, inheriting from std::vector<TPoint3D>
          * \sa TPolygon2D,TSegment3D,TLine3D,TPlane,TPoint3D
          */
        class MRPTDLLIMPEXP TPolygon3D:public std::vector<TPoint3D>     {
        public:
                /**
                  * Distance to point.
                  */
                double distance(const TPoint3D &point) const;
                /**
                  * Check whether a point is inside the polygon.
                  */
                bool contains(const TPoint3D &point) const;
                /**
                  * Gets as set of segments, instead of set of points.
                  */
                void getAsSegmentList(std::vector<TSegment3D> &v) const;
                /**
                  * Gets a plane which contains the polygon. Returns false if the polygon is skew and cannot be fit inside a plane.
                  */
                bool getPlane(TPlane &p) const;
                /**
                  * Gets the best fitting plane, disregarding whether the polygon actually fits inside or not.
                  * \sa getBestFittingPlane
                  */
                void getBestFittingPlane(TPlane &p) const;
                /**
                  * Projects into a 2D space, discarding the z.
                  * \get getPlane,isSkew
                  */
                inline void generate2DObject(TPolygon2D &p) const       {
                        p=TPolygon2D(*this);
                }
                /**
                  * Get polygon's central point.
                  */
                void getCenter(TPoint3D &p) const;
                /**
                  * Check whether the polygon is skew. Returns true if there doesn't exist a plane in which the polygon can fit.
                  * \sa getBestFittingPlane
                  */
                bool isSkew() const;
                /**
                  * Remove polygon's repeated vertices.
                  */
                void removeRepeatedVertices();
                /**
                  * Erase every redundant vertex, thus saving space.
                  */
                void removeRedundantVertices();
                /**
                  * Default constructor. Creates a polygon with no vertices.
                  */
                TPolygon3D():std::vector<TPoint3D>()    {}
                /**
                  * Constructor for a given size. Creates a polygon with a fixed number of vertices, which are initialized to garbage.
                  */
                explicit TPolygon3D(size_t N):std::vector<TPoint3D>(N)  {}
                /**
                  * Implicit constructor from a 3D points vector.
                  */
                TPolygon3D(const std::vector<TPoint3D> &v):std::vector<TPoint3D>(v)     {}
                /**
                  * Constructor from a 2D object. Zeroes the z.
                  */
                TPolygon3D(const TPolygon2D &p);
                /**
                  * Static method to create a regular polygon, given its size and radius.
                  * \throw std::logic_error if number of edges is less than three, or radius is near zero.
                  */
                static void createRegularPolygon(size_t numEdges,double radius,TPolygon3D &poly);
                /**
                  * Static method to create a regular polygon, given its size and radius. The center will be located on the given pose.
                  * \throw std::logic_error if number of edges is less than three, or radius is near zero.
                  */
                static inline void createRegularPolygon(size_t numEdges,double radius,TPolygon3D &poly,const mrpt::poses::CPose3D &pose);
        };

        /**
          * Object type identifier for TPoint2D or TPoint3D.
          * \sa TObject2D,TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_POINT=0;
        /**
          * Object type identifier for TSegment2D or TSegment3D.
          * \sa TObject2D,TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_SEGMENT=1;
        /**
          * Object type identifier for TLine2D or TLine3D.
          * \sa TObject2D,TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_LINE=2;
        /**
          * Object type identifier for TPolygon2D or TPolygon3D.
          * \sa TObject2D,TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_POLYGON=3;
        /**
          * Object type identifier for TPlane.
          * \sa TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_PLANE=4;
        /**
          * Object type identifier for empty TObject2D or TObject3D.
          * \sa TObject2D,TObject3D
          */
        const unsigned char GEOMETRIC_TYPE_UNDEFINED=255;

        /**
          * Standard type for storing any lightweight 2D type. Do not inherit from this class.
          * \sa TPoint2D,TSegment2D,TLine2D,TPolygon2D
          */
#ifdef TOBJECTS_USE_UNIONS
        struct MRPTDLLIMPEXP TObject2D  {
        private:
                /**
                  * Object type identifier.
                  */
                unsigned char type;
                /**
                  * Union type storing pointers to every allowed type.
                  */
                union   {
                        TPoint2D *point;
                        TSegment2D *segment;
                        TLine2D *line;
                        TPolygon2D *polygon;
                }       data;
                /**
                  * Destroys the object, releasing the pointer to the content (if any).
                  */
                void destroy()  {
                        switch(type)    {
                                case GEOMETRIC_TYPE_POINT:
                                        delete data.point;
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        delete data.segment;
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        delete data.line;
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        delete data.polygon;
                                        break;
                        }
                        type=GEOMETRIC_TYPE_UNDEFINED;
                }
        public:
                /**
                  * Implicit constructor from point.
                  */
                TObject2D(const TPoint2D &p):type(GEOMETRIC_TYPE_POINT) {
                        data.point=new TPoint2D(p);
                }
                /**
                  * Implicit constructor from segment.
                  */
                TObject2D(const TSegment2D &s):type(GEOMETRIC_TYPE_SEGMENT)     {
                        data.segment=new TSegment2D(s);
                }
                /**
                  * Implicit constructor from line.
                  */
                TObject2D(const TLine2D &r):type(GEOMETRIC_TYPE_LINE)   {
                        data.line=new TLine2D(r);
                }
                /**
                  * Implicit constructor from polygon.
                  */
                TObject2D(const TPolygon2D &p):type(GEOMETRIC_TYPE_POLYGON)     {
                        data.polygon=new TPolygon2D(p);
                }
                /**
                  * Implicit constructor from polygon.
                  */
                TObject2D():type(GEOMETRIC_TYPE_UNDEFINED)      {}
                /**
                  * Object destruction.
                  */
                ~TObject2D()    {
                        destroy();
                }
                /**
                  * Checks whether content is a point.
                  */
                inline bool isPoint() const     {
                        return type==GEOMETRIC_TYPE_POINT;
                }
                /**
                  * Checks whether content is a segment.
                  */
                inline bool isSegment() const   {
                        return type==GEOMETRIC_TYPE_SEGMENT;
                }
                /**
                  * Checks whether content is a line.
                  */
                inline bool isLine() const      {
                        return type==GEOMETRIC_TYPE_LINE;
                }
                /**
                  * Checks whether content is a polygon.
                  */
                inline bool isPolygon() const   {
                        return type==GEOMETRIC_TYPE_POLYGON;
                }
                /**
                  * Gets content type.
                  */
                inline unsigned char getType() const    {
                        return type;
                }
                /**
                  * Gets the content as a point, returning false if the type is inadequate.
                  */
                inline bool getPoint(TPoint2D &p) const {
                        if (isPoint())  {
                                p=*(data.point);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a segment, returning false if the type is inadequate.
                  */
                inline bool getSegment(TSegment2D &s) const     {
                        if (isSegment())        {
                                s=*(data.segment);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a line, returning false if the type is inadequate.
                  */
                inline bool getLine(TLine2D &r) const   {
                        if (isLine())   {
                                r=*(data.line);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a polygon, returning false if the type is inadequate.
                  */
                inline bool getPolygon(TPolygon2D &p) const     {
                        if (isPolygon())        {
                                p=*(data.polygon);
                                return true;
                        }       else return false;
                }
                /**
                  * Assign another TObject2D. Pointers are not shared.
                  */
                void operator=(const TObject2D &obj)    {
                        if (this==&obj) return;
                        destroy();
                        switch (type=obj.type)  {
                                case GEOMETRIC_TYPE_POINT:
                                        data.point=new TPoint2D(*(obj.data.point));
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        data.segment=new TSegment2D(*(obj.data.segment));
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        data.line=new TLine2D(*(obj.data.line));
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        data.polygon=new TPolygon2D(*(obj.data.polygon));
                                        break;
                        }
                }
                /**
                  * Assign a point to this object.
                  */
                inline void operator=(const TPoint2D &p)        {
                        destroy();
                        type=GEOMETRIC_TYPE_POINT;
                        data.point=new TPoint2D(p);
                }
                /**
                  * Assign a segment to this object.
                  */
                inline void operator=(const TSegment2D &s)      {
                        destroy();
                        type=GEOMETRIC_TYPE_SEGMENT;
                        data.segment=new TSegment2D(s);
                }
                /**
                  * Assign a line to this object.
                  */
                inline void operator=(const TLine2D &l) {
                        destroy();
                        type=GEOMETRIC_TYPE_LINE;
                        data.line=new TLine2D(l);
                }
                /**
                  * Assign a polygon to this object.
                  */
                inline void operator=(const TPolygon2D &p)      {
                        destroy();
                        type=GEOMETRIC_TYPE_POLYGON;
                        data.polygon=new TPolygon2D(p);
                }
                /**
                  * Project into 3D space.
                  */
                void generate3DObject(TObject3D &obj) const;
                /**
                  * Constructor from another TObject2D.
                  */
                TObject2D(const TObject2D &obj):type(GEOMETRIC_TYPE_UNDEFINED)  {
                        operator=(obj);
                }
                /**
                  * Static method to retrieve all the points in a vector of TObject2D.
                  */
                static void getPoints(const std::vector<TObject2D> &objs,std::vector<TPoint2D> &pnts);
                /**
                  * Static method to retrieve all the segments in a vector of TObject2D.
                  */
                static void getSegments(const std::vector<TObject2D> &objs,std::vector<TSegment2D> &sgms);
                /**
                  * Static method to retrieve all the lines in a vector of TObject2D.
                  */
                static void getLines(const std::vector<TObject2D> &objs,std::vector<TLine2D> &lins);
                /**
                  * Static method to retrieve all the polygons in a vector of TObject2D.
                  */
                static void getPolygons(const std::vector<TObject2D> &objs,std::vector<TPolygon2D> &polys);
                /**
                  * Static method to retrieve all the points in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getPoints(const std::vector<TObject2D> &objs,std::vector<TPoint2D> &pnts,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the segments in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getSegments(const std::vector<TObject2D> &objs,std::vector<TSegment2D> &sgms,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the lines in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getLines(const std::vector<TObject2D> &objs,std::vector<TLine2D> &lins,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the polygons in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getPolygons(const std::vector<TObject2D> &objs,std::vector<TPolygon2D> &polys,std::vector<TObject2D> &remainder);
        };
        /**
          * Standard object for storing any 3D lightweight object. Do not inherit from this class.
          * \sa TPoint3D,TSegment3D,TLine3D,TPlane,TPolygon3D
          */
        struct MRPTDLLIMPEXP TObject3D  {
        private:
                /**
                  * Object type identifier.
                  */
                unsigned char type;
                /**
                  * Union containing pointer to actual data.
                  */
                union   {
                        TPoint3D *point;
                        TSegment3D *segment;
                        TLine3D *line;
                        TPolygon3D *polygon;
                        TPlane *plane;
                }       data;
                /**
                  * Destroys the object and releases the pointer, if any.
                  */
                void destroy()  {
                        switch (type)   {
                                case GEOMETRIC_TYPE_POINT:
                                        delete data.point;
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        delete data.segment;
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        delete data.line;
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        delete data.polygon;
                                        break;
                                case GEOMETRIC_TYPE_PLANE:
                                        delete data.plane;
                                        break;
                                case GEOMETRIC_TYPE_UNDEFINED:
                                        break;
                                default:
                                        THROW_EXCEPTION("Invalid TObject2D object");
                        }
                        type=GEOMETRIC_TYPE_UNDEFINED;
                }
        public:
                /**
                  * Constructor from point.
                  */
                TObject3D(const TPoint3D &p):type(GEOMETRIC_TYPE_POINT) {
                        data.point=new TPoint3D(p);
                }
                /**
                  * Constructor from segment.
                  */
                TObject3D(const TSegment3D &s):type(GEOMETRIC_TYPE_SEGMENT)     {
                        data.segment=new TSegment3D(s);
                }
                /**
                  * Constructor from line.
                  */
                TObject3D(const TLine3D &r):type(GEOMETRIC_TYPE_LINE)   {
                        data.line=new TLine3D(r);
                }
                /**
                  * Constructor from polygon.
                  */
                TObject3D(const TPolygon3D &p):type(GEOMETRIC_TYPE_POLYGON)     {
                        data.polygon=new TPolygon3D(p);
                }
                /**
                  * Constructor from plane.
                  */
                TObject3D(const TPlane &p):type(GEOMETRIC_TYPE_PLANE)   {
                        data.plane=new TPlane(p);
                }
                /**
                  * Empty constructor.
                  */
                TObject3D():type(GEOMETRIC_TYPE_UNDEFINED)      {}
                /**
                  * Destructor.
                  */
                ~TObject3D()    {
                        destroy();
                }
                /**
                  * Checks whether content is a point.
                  */
                inline bool isPoint() const     {
                        return type==GEOMETRIC_TYPE_POINT;
                }
                /**
                  * Checks whether content is a segment.
                  */
                inline bool isSegment() const   {
                        return type==GEOMETRIC_TYPE_SEGMENT;
                }
                /**
                  * Checks whether content is a line.
                  */
                inline bool isLine() const      {
                        return type==GEOMETRIC_TYPE_LINE;
                }
                /**
                  * Checks whether content is a polygon.
                  */
                inline bool isPolygon() const   {
                        return type==GEOMETRIC_TYPE_POLYGON;
                }
                /**
                  * Checks whether content is a plane.
                  */
                inline bool isPlane() const     {
                        return type==GEOMETRIC_TYPE_PLANE;
                }
                /**
                  * Gets object type.
                  */
                inline unsigned char getType() const    {
                        return type;
                }
                /**
                  * Gets the content as a point, returning false if the type is not adequate.
                  */
                inline bool getPoint(TPoint3D &p) const {
                        if (isPoint())  {
                                p=*(data.point);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a segment, returning false if the type is not adequate.
                  */
                inline bool getSegment(TSegment3D &s) const     {
                        if (isSegment())        {
                                s=*(data.segment);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a line, returning false if the type is not adequate.
                  */
                inline bool getLine(TLine3D &r) const   {
                        if (isLine())   {
                                r=*(data.line);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a polygon, returning false if the type is not adequate.
                  */
                inline bool getPolygon(TPolygon3D &p) const     {
                        if (isPolygon())        {
                                p=*(data.polygon);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a plane, returning false if the type is not adequate.
                  */
                inline bool getPlane(TPlane &p) const   {
                        if (isPlane())  {
                                p=*(data.plane);
                                return true;
                        }       else return false;
                }
                /**
                  * Assigns another object, creating a new pointer if needed.
                  */
                void operator=(const TObject3D &obj)    {
                        if (this==&obj) return;
                        destroy();
                        switch (type=obj.type)  {
                                case GEOMETRIC_TYPE_POINT:
                                        data.point=new TPoint3D(*(obj.data.point));
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        data.segment=new TSegment3D(*(obj.data.segment));
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        data.line=new TLine3D(*(obj.data.line));
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        data.polygon=new TPolygon3D(*(obj.data.polygon));
                                        break;
                                case GEOMETRIC_TYPE_PLANE:
                                        data.plane=new TPlane(*(obj.data.plane));
                                        break;
                                case GEOMETRIC_TYPE_UNDEFINED:
                                        break;
                                default:
                                        THROW_EXCEPTION("Invalid TObject3D object");
                        }
                }
                /**
                  * Assigns a point to this object.
                  */
                inline void operator=(const TPoint3D &p)        {
                        destroy();
                        type=GEOMETRIC_TYPE_POINT;
                        data.point=new TPoint3D(p);
                }
                /**
                  * Assigns a segment to this object.
                  */
                inline void operator=(const TSegment3D &s)      {
                        destroy();
                        type=GEOMETRIC_TYPE_SEGMENT;
                        data.segment=new TSegment3D(s);
                }
                /**
                  * Assigns a line to this object.
                  */
                inline void operator=(const TLine3D &l) {
                        destroy();
                        type=GEOMETRIC_TYPE_LINE;
                        data.line=new TLine3D(l);
                }
                /**
                  * Assigns a polygon to this object.
                  */
                inline void operator=(const TPolygon3D &p)      {
                        destroy();
                        type=GEOMETRIC_TYPE_POLYGON;
                        data.polygon=new TPolygon3D(p);
                }
                /**
                  * Assigns a plane to this object.
                  */
                inline void operator=(const TPlane &p)  {
                        destroy();
                        type=GEOMETRIC_TYPE_PLANE;
                        data.plane=new TPlane(p);
                }
                /**
                  * Projects into 2D space.
                  * \throw std::logic_error if the 3D object loses its properties when projecting into 2D space (for example, it's a plane or a vertical line).
                  */
                inline void generate2DObject(TObject2D &obj) const      {
                        switch (type)   {
                                case GEOMETRIC_TYPE_POINT:
                                        obj=TPoint2D(*(data.point));
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        obj=TSegment2D(*(data.segment));
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        obj=TLine2D(*(data.line));
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        obj=TPolygon2D(*(data.polygon));
                                        break;
                                case GEOMETRIC_TYPE_PLANE:
                                        throw std::logic_error("Too many dimensions");
                                default:
                                        obj=TObject2D();
                                        break;
                        }
                }
                /**
                  * Constructs from another object.
                  */
                TObject3D(const TObject3D &obj):type(GEOMETRIC_TYPE_UNDEFINED)  {
                        operator=(obj);
                }
                /**
                  * Static method to retrieve every point included in a vector of objects.
                  */
                static void getPoints(const std::vector<TObject3D> &objs,std::vector<TPoint3D> &pnts);
                /**
                  * Static method to retrieve every segment included in a vector of objects.
                  */
                static void getSegments(const std::vector<TObject3D> &objs,std::vector<TSegment3D> &sgms);
                /**
                  * Static method to retrieve every line included in a vector of objects.
                  */
                static void getLines(const std::vector<TObject3D> &objs,std::vector<TLine3D> &lins);
                /**
                  * Static method to retrieve every plane included in a vector of objects.
                  */
                static void getPlanes(const std::vector<TObject3D> &objs,std::vector<TPlane> &plns);
                /**
                  * Static method to retrieve every polygon included in a vector of objects.
                  */
                static void getPolygons(const std::vector<TObject3D> &objs,std::vector<TPolygon3D> &polys);
                /**
                  * Static method to retrieve every point included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPoints(const std::vector<TObject3D> &objs,std::vector<TPoint3D> &pnts,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every segment included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getSegments(const std::vector<TObject3D> &objs,std::vector<TSegment3D> &sgms,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every line included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getLines(const std::vector<TObject3D> &objs,std::vector<TLine3D> &lins,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every plane included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPlanes(const std::vector<TObject3D> &objs,std::vector<TPlane> &plns,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every polygon included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPolygons(const std::vector<TObject3D> &objs,std::vector<TPolygon3D> &polys,std::vector<TObject3D> &remainder);
        };
#else
        struct MRPTDLLIMPEXP TObject2D  {
        private:
                /**
                  * Object type identifier.
                  */
                unsigned char type;
                /**
                  * Union type storing pointers to every allowed type.
                  */
                struct  {
                        TPoint2D point;
                        TSegment2D segment;
                        TLine2D line;
                        TPolygon2D *polygon;
                }       data;
                /**
                  * Destroys the object, releasing the pointer to the content (if any).
                  */
                inline void destroy()   {
                        if (type==GEOMETRIC_TYPE_POLYGON) delete data.polygon;
                        type=GEOMETRIC_TYPE_UNDEFINED;
                }
        public:
                /**
                  * Implicit constructor from point.
                  */
                inline TObject2D(const TPoint2D &p):type(GEOMETRIC_TYPE_POINT)  {
                        data.point=p;
                }
                /**
                  * Implicit constructor from segment.
                  */
                inline TObject2D(const TSegment2D &s):type(GEOMETRIC_TYPE_SEGMENT)      {
                        data.segment=s;
                }
                /**
                  * Implicit constructor from line.
                  */
                inline TObject2D(const TLine2D &r):type(GEOMETRIC_TYPE_LINE)    {
                        data.line=r;
                }
                /**
                  * Implicit constructor from polygon.
                  */
                inline TObject2D(const TPolygon2D &p):type(GEOMETRIC_TYPE_POLYGON)      {
                        data.polygon=new TPolygon2D(p);
                }
                /**
                  * Implicit constructor from polygon.
                  */
                TObject2D():type(GEOMETRIC_TYPE_UNDEFINED)      {}
                /**
                  * Object destruction.
                  */
                ~TObject2D()    {
                        destroy();
                }
                /**
                  * Checks whether content is a point.
                  */
                inline bool isPoint() const     {
                        return type==GEOMETRIC_TYPE_POINT;
                }
                /**
                  * Checks whether content is a segment.
                  */
                inline bool isSegment() const   {
                        return type==GEOMETRIC_TYPE_SEGMENT;
                }
                /**
                  * Checks whether content is a line.
                  */
                inline bool isLine() const      {
                        return type==GEOMETRIC_TYPE_LINE;
                }
                /**
                  * Checks whether content is a polygon.
                  */
                inline bool isPolygon() const   {
                        return type==GEOMETRIC_TYPE_POLYGON;
                }
                /**
                  * Gets content type.
                  */
                inline unsigned char getType() const    {
                        return type;
                }
                /**
                  * Gets the content as a point, returning false if the type is inadequate.
                  */
                inline bool getPoint(TPoint2D &p) const {
                        if (isPoint())  {
                                p=data.point;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a segment, returning false if the type is inadequate.
                  */
                inline bool getSegment(TSegment2D &s) const     {
                        if (isSegment())        {
                                s=data.segment;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a line, returning false if the type is inadequate.
                  */
                inline bool getLine(TLine2D &r) const   {
                        if (isLine())   {
                                r=data.line;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a polygon, returning false if the type is inadequate.
                  */
                inline bool getPolygon(TPolygon2D &p) const     {
                        if (isPolygon())        {
                                p=*(data.polygon);
                                return true;
                        }       else return false;
                }
                /**
                  * Assign another TObject2D. Pointers are not shared.
                  */
                void operator=(const TObject2D &obj)    {
                        if (this==&obj) return;
                        destroy();
                        switch (type=obj.type)  {
                                case GEOMETRIC_TYPE_POINT:
                                        data.point=obj.data.point;
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        data.segment=obj.data.segment;
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        data.line=obj.data.line;
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        data.polygon=new TPolygon2D(*(obj.data.polygon));
                                        break;
                        }
                }
                /**
                  * Assign a point to this object.
                  */
                inline void operator=(const TPoint2D &p)        {
                        destroy();
                        type=GEOMETRIC_TYPE_POINT;
                        data.point=p;
                }
                /**
                  * Assign a segment to this object.
                  */
                inline void operator=(const TSegment2D &s)      {
                        destroy();
                        type=GEOMETRIC_TYPE_SEGMENT;
                        data.segment=s;
                }
                /**
                  * Assign a line to this object.
                  */
                inline void operator=(const TLine2D &l) {
                        destroy();
                        type=GEOMETRIC_TYPE_LINE;
                        data.line=l;
                }
                /**
                  * Assign a polygon to this object.
                  */
                inline void operator=(const TPolygon2D &p)      {
                        destroy();
                        type=GEOMETRIC_TYPE_POLYGON;
                        data.polygon=new TPolygon2D(p);
                }
                /**
                  * Project into 3D space.
                  */
                void generate3DObject(TObject3D &obj) const;
                /**
                  * Constructor from another TObject2D.
                  */
                TObject2D(const TObject2D &obj):type(GEOMETRIC_TYPE_UNDEFINED)  {
                        operator=(obj);
                }
                /**
                  * Static method to retrieve all the points in a vector of TObject2D.
                  */
                static void getPoints(const std::vector<TObject2D> &objs,std::vector<TPoint2D> &pnts);
                /**
                  * Static method to retrieve all the segments in a vector of TObject2D.
                  */
                static void getSegments(const std::vector<TObject2D> &objs,std::vector<TSegment2D> &sgms);
                /**
                  * Static method to retrieve all the lines in a vector of TObject2D.
                  */
                static void getLines(const std::vector<TObject2D> &objs,std::vector<TLine2D> &lins);
                /**
                  * Static method to retrieve all the polygons in a vector of TObject2D.
                  */
                static void getPolygons(const std::vector<TObject2D> &objs,std::vector<TPolygon2D> &polys);
                /**
                  * Static method to retrieve all the points in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getPoints(const std::vector<TObject2D> &objs,std::vector<TPoint2D> &pnts,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the segments in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getSegments(const std::vector<TObject2D> &objs,std::vector<TSegment2D> &sgms,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the lines in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getLines(const std::vector<TObject2D> &objs,std::vector<TLine2D> &lins,std::vector<TObject2D> &remainder);
                /**
                  * Static method to retrieve all the polygons in a vector of TObject2D, returning the remainder objects in another parameter.
                  */
                static void getPolygons(const std::vector<TObject2D> &objs,std::vector<TPolygon2D> &polys,std::vector<TObject2D> &remainder);
        };
        /**
          * Standard object for storing any 3D lightweight object. Do not inherit from this class.
          * \sa TPoint3D,TSegment3D,TLine3D,TPlane,TPolygon3D
          */
        struct MRPTDLLIMPEXP TObject3D  {
        private:
                /**
                  * Object type identifier.
                  */
                unsigned char type;
                /**
                  * Union containing pointer to actual data.
                  */
                struct  {
                        TPoint3D point;
                        TSegment3D segment;
                        TLine3D line;
                        TPolygon3D *polygon;
                        TPlane plane;
                }       data;
                /**
                  * Destroys the object and releases the pointer, if any.
                  */
                void destroy()  {
                        if (type==GEOMETRIC_TYPE_POLYGON) delete data.polygon;
                        type=GEOMETRIC_TYPE_UNDEFINED;
                }
        public:
                /**
                  * Constructor from point.
                  */
                TObject3D(const TPoint3D &p):type(GEOMETRIC_TYPE_POINT) {
                        data.point=p;
                }
                /**
                  * Constructor from segment.
                  */
                TObject3D(const TSegment3D &s):type(GEOMETRIC_TYPE_SEGMENT)     {
                        data.segment=s;
                }
                /**
                  * Constructor from line.
                  */
                TObject3D(const TLine3D &r):type(GEOMETRIC_TYPE_LINE)   {
                        data.line=r;
                }
                /**
                  * Constructor from polygon.
                  */
                TObject3D(const TPolygon3D &p):type(GEOMETRIC_TYPE_POLYGON)     {
                        data.polygon=new TPolygon3D(p);
                }
                /**
                  * Constructor from plane.
                  */
                TObject3D(const TPlane &p):type(GEOMETRIC_TYPE_PLANE)   {
                        data.plane=p;
                }
                /**
                  * Empty constructor.
                  */
                TObject3D():type(GEOMETRIC_TYPE_UNDEFINED)      {}
                /**
                  * Destructor.
                  */
                ~TObject3D()    {
                        destroy();
                }
                /**
                  * Checks whether content is a point.
                  */
                inline bool isPoint() const     {
                        return type==GEOMETRIC_TYPE_POINT;
                }
                /**
                  * Checks whether content is a segment.
                  */
                inline bool isSegment() const   {
                        return type==GEOMETRIC_TYPE_SEGMENT;
                }
                /**
                  * Checks whether content is a line.
                  */
                inline bool isLine() const      {
                        return type==GEOMETRIC_TYPE_LINE;
                }
                /**
                  * Checks whether content is a polygon.
                  */
                inline bool isPolygon() const   {
                        return type==GEOMETRIC_TYPE_POLYGON;
                }
                /**
                  * Checks whether content is a plane.
                  */
                inline bool isPlane() const     {
                        return type==GEOMETRIC_TYPE_PLANE;
                }
                /**
                  * Gets object type.
                  */
                inline unsigned char getType() const    {
                        return type;
                }
                /**
                  * Gets the content as a point, returning false if the type is not adequate.
                  */
                inline bool getPoint(TPoint3D &p) const {
                        if (isPoint())  {
                                p=data.point;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a segment, returning false if the type is not adequate.
                  */
                inline bool getSegment(TSegment3D &s) const     {
                        if (isSegment())        {
                                s=data.segment;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a line, returning false if the type is not adequate.
                  */
                inline bool getLine(TLine3D &r) const   {
                        if (isLine())   {
                                r=data.line;
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a polygon, returning false if the type is not adequate.
                  */
                inline bool getPolygon(TPolygon3D &p) const     {
                        if (isPolygon())        {
                                p=*(data.polygon);
                                return true;
                        }       else return false;
                }
                /**
                  * Gets the content as a plane, returning false if the type is not adequate.
                  */
                inline bool getPlane(TPlane &p) const   {
                        if (isPlane())  {
                                p=data.plane;
                                return true;
                        }       else return false;
                }
                /**
                  * Assigns another object, creating a new pointer if needed.
                  */
                void operator=(const TObject3D &obj)    {
                        if (this==&obj) return;
                        destroy();
                        switch (type=obj.type)  {
                                case GEOMETRIC_TYPE_POINT:
                                        data.point=obj.data.point;
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        data.segment=obj.data.segment;
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        data.line=obj.data.line;
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        data.polygon=new TPolygon3D(*(obj.data.polygon));
                                        break;
                                case GEOMETRIC_TYPE_PLANE:
                                        data.plane=obj.data.plane;
                                        break;
                                case GEOMETRIC_TYPE_UNDEFINED:
                                        break;
                                default:
                                        THROW_EXCEPTION("Invalid TObject3D object");
                        }
                }
                /**
                  * Assigns a point to this object.
                  */
                inline void operator=(const TPoint3D &p)        {
                        destroy();
                        type=GEOMETRIC_TYPE_POINT;
                        data.point=p;
                }
                /**
                  * Assigns a segment to this object.
                  */
                inline void operator=(const TSegment3D &s)      {
                        destroy();
                        type=GEOMETRIC_TYPE_SEGMENT;
                        data.segment=s;
                }
                /**
                  * Assigns a line to this object.
                  */
                inline void operator=(const TLine3D &l) {
                        destroy();
                        type=GEOMETRIC_TYPE_LINE;
                        data.line=l;
                }
                /**
                  * Assigns a polygon to this object.
                  */
                inline void operator=(const TPolygon3D &p)      {
                        destroy();
                        type=GEOMETRIC_TYPE_POLYGON;
                        data.polygon=new TPolygon3D(p);
                }
                /**
                  * Assigns a plane to this object.
                  */
                inline void operator=(const TPlane &p)  {
                        destroy();
                        type=GEOMETRIC_TYPE_PLANE;
                        data.plane=p;
                }
                /**
                  * Projects into 2D space.
                  * \throw std::logic_error if the 3D object loses its properties when projecting into 2D space (for example, it's a plane or a vertical line).
                  */
                inline void generate2DObject(TObject2D &obj) const      {
                        switch (type)   {
                                case GEOMETRIC_TYPE_POINT:
                                        obj=TPoint2D(data.point);
                                        break;
                                case GEOMETRIC_TYPE_SEGMENT:
                                        obj=TSegment2D(data.segment);
                                        break;
                                case GEOMETRIC_TYPE_LINE:
                                        obj=TLine2D(data.line);
                                        break;
                                case GEOMETRIC_TYPE_POLYGON:
                                        obj=TPolygon2D(*(data.polygon));
                                        break;
                                case GEOMETRIC_TYPE_PLANE:
                                        throw std::logic_error("Too many dimensions");
                                default:
                                        obj=TObject2D();
                                        break;
                        }
                }
                /**
                  * Constructs from another object.
                  */
                TObject3D(const TObject3D &obj):type(GEOMETRIC_TYPE_UNDEFINED)  {
                        operator=(obj);
                }
                /**
                  * Static method to retrieve every point included in a vector of objects.
                  */
                static void getPoints(const std::vector<TObject3D> &objs,std::vector<TPoint3D> &pnts);
                /**
                  * Static method to retrieve every segment included in a vector of objects.
                  */
                static void getSegments(const std::vector<TObject3D> &objs,std::vector<TSegment3D> &sgms);
                /**
                  * Static method to retrieve every line included in a vector of objects.
                  */
                static void getLines(const std::vector<TObject3D> &objs,std::vector<TLine3D> &lins);
                /**
                  * Static method to retrieve every plane included in a vector of objects.
                  */
                static void getPlanes(const std::vector<TObject3D> &objs,std::vector<TPlane> &plns);
                /**
                  * Static method to retrieve every polygon included in a vector of objects.
                  */
                static void getPolygons(const std::vector<TObject3D> &objs,std::vector<TPolygon3D> &polys);
                /**
                  * Static method to retrieve every point included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPoints(const std::vector<TObject3D> &objs,std::vector<TPoint3D> &pnts,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every segment included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getSegments(const std::vector<TObject3D> &objs,std::vector<TSegment3D> &sgms,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every line included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getLines(const std::vector<TObject3D> &objs,std::vector<TLine3D> &lins,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every plane included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPlanes(const std::vector<TObject3D> &objs,std::vector<TPlane> &plns,std::vector<TObject3D> &remainder);
                /**
                  * Static method to retrieve every polygon included in a vector of objects, returning the remaining objects in another argument.
                  */
                static void getPolygons(const std::vector<TObject3D> &objs,std::vector<TPolygon3D> &polys,std::vector<TObject3D> &remainder);
        };

#endif
        //Streaming functions
        /**
          * TPoint2D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator>>(mrpt::utils::CStream& in,mrpt::math::TPoint2D &o);
        /**
          * TPoint2D binary output.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator<<(mrpt::utils::CStream& out,const mrpt::math::TPoint2D &o);

        /**
          * TPoint3D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator>>(mrpt::utils::CStream& in,mrpt::math::TPoint3D &o);
        /**
          * TPoint3D binary output.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator<<(mrpt::utils::CStream& out,const mrpt::math::TPoint3D &o);

        /**
          * TPose2D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator>>(mrpt::utils::CStream& in,mrpt::math::TPose2D &o);
        /**
          * TPose2D binary output.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator<<(mrpt::utils::CStream& out,const mrpt::math::TPose2D &o);

        /**
          * TPose3D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator>>(mrpt::utils::CStream& in,mrpt::math::TPose3D &o);
        /**
          * TPose3D binary output.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream& operator<<(mrpt::utils::CStream& out,const mrpt::math::TPose3D &o);

        /**
          * TSegment2D binary input.
          */
        inline mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TSegment2D &s)     {
                return in>>s.point1>>s.point2;
        }
        /**
          * TSegment2D binary output.
          */
        inline mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TSegment2D &s)      {
                return out<<s.point1<<s.point2;
        }

        /**
          * TLine2D binary input.
          */
        inline mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TLine2D &l)        {
                return in>>l.coefs[0]>>l.coefs[1]>>l.coefs[2];
        }
        /**
          * TLine2D binary output.
          */
        inline mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TLine2D &l) {
                return out<<l.coefs[0]<<l.coefs[1]<<l.coefs[2];
        }

        /**
          * TObject2D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TObject2D &o);
        /**
          * TObject2D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TObject2D &o);

        /**
          * TSegment3D binary input.
          */
        inline mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TSegment3D &s)     {
                return in>>s.point1>>s.point2;
        }
        /**
          * TSegment3D binary output.
          */
        inline mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TSegment3D &s)      {
                return out<<s.point1<<s.point2;
        }

        /**
          * TLine3D binary input.
          */
        inline mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TLine3D &l)        {
                return in>>l.pBase>>l.director[0]>>l.director[1]>>l.director[2];
        }
        /**
          * TLine3D binary output.
          */
        inline mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TLine3D &l) {
                return out<<l.pBase<<l.director[0]<<l.director[1]<<l.director[2];
        }

        /**
          * TPlane binary input.
          */
        inline mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TPlane &p) {
                return in>>p.coefs[0]>>p.coefs[1]>>p.coefs[2]>>p.coefs[3];
        }
        /**
          * TPlane binary output.
          */
        inline mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TPlane &p)  {
                return out<<p.coefs[0]<<p.coefs[1]<<p.coefs[2]<<p.coefs[3];
        }

        /**
          * TObject3D binary input.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream &operator>>(mrpt::utils::CStream &in,mrpt::math::TObject3D &o);
        /**
          * TObject3D binary output.
          */
        MRPTDLLIMPEXP mrpt::utils::CStream &operator<<(mrpt::utils::CStream &out,const mrpt::math::TObject3D &o);

        }       //end of namespace math

        namespace utils
        {
                using namespace ::mrpt::math;

                // Specialization must occur in the same namespace
                MRPT_DECLARE_TTYPENAME(TPoint2D)
                MRPT_DECLARE_TTYPENAME(TPoint3D)
                MRPT_DECLARE_TTYPENAME(TPose2D)
                MRPT_DECLARE_TTYPENAME(TPose3D)
                MRPT_DECLARE_TTYPENAME(TSegment2D)
                MRPT_DECLARE_TTYPENAME(TLine2D)
                MRPT_DECLARE_TTYPENAME(TPolygon2D)
                MRPT_DECLARE_TTYPENAME(TObject2D)
                MRPT_DECLARE_TTYPENAME(TSegment3D)
                MRPT_DECLARE_TTYPENAME(TLine3D)
                MRPT_DECLARE_TTYPENAME(TPlane)
                MRPT_DECLARE_TTYPENAME(TPolygon3D)
                MRPT_DECLARE_TTYPENAME(TObject3D)

        } // end of namespace utils

}       //end of namespace
#endif

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