polygon.h

00001 // polygon.h (A 2D polygon embeded in a <dim> dimensional space)
00002 //
00003 //  The WorldForge Project
00004 //  Copyright (C) 2002  The WorldForge Project
00005 //
00006 //  This program is free software; you can redistribute it and/or modify
00007 //  it under the terms of the GNU General Public License as published by
00008 //  the Free Software Foundation; either version 2 of the License, or
00009 //  (at your option) any later version.
00010 //
00011 //  This program is distributed in the hope that it will be useful,
00012 //  but WITHOUT ANY WARRANTY; without even the implied warranty of
00013 //  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00014 //  GNU General Public License for more details.
00015 //
00016 //  You should have received a copy of the GNU General Public License
00017 //  along with this program; if not, write to the Free Software
00018 //  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
00019 //
00020 //  For information about WorldForge and its authors, please contact
00021 //  the Worldforge Web Site at http://www.worldforge.org.
00022 //
00023 
00024 // Author: Ron Steinke
00025 
00026 #ifndef WFMATH_POLYGON_H
00027 #define WFMATH_POLYGON_H
00028 
00029 #include <wfmath/const.h>
00030 #include <wfmath/vector.h>
00031 #include <wfmath/point.h>
00032 #include <wfmath/rotmatrix.h>
00033 #include <wfmath/axisbox.h>
00034 #include <wfmath/rotbox.h>
00035 #include <wfmath/ball.h>
00036 #include <wfmath/intersect_decls.h>
00037 
00038 #include <vector>
00039 
00040 namespace WFMath {
00041 
00042 template<const int dim> class Polygon;
00043 
00044 template<const int dim>
00045 std::ostream& operator<<(std::ostream& os, const Polygon<dim>& r);
00046 template<const int dim>
00047 std::istream& operator>>(std::istream& is, Polygon<dim>& r);
00048 
00050 template<>
00051 class Polygon<2>
00052 {
00053  public:
00054   Polygon() {}
00055   Polygon(const Polygon& p) : m_points(p.m_points) {}
00056 
00057   ~Polygon() {}
00058 #ifndef WFMATH_NO_CLASS_FUNCTION_SPECIALIZATION
00059   friend std::ostream& operator<< <2>(std::ostream& os, const Polygon& p);
00060   friend std::istream& operator>> <2>(std::istream& is, Polygon& p);
00061 #endif
00062   Polygon& operator=(const Polygon& p)
00063         {m_points = p.m_points; return *this;}
00064 
00065   bool isEqualTo(const Polygon& p, double epsilon = WFMATH_EPSILON) const;
00066 
00067   bool operator==(const Polygon& p) const       {return isEqualTo(p);}
00068   bool operator!=(const Polygon& p) const       {return !isEqualTo(p);}
00069 
00070   bool isValid() const;
00071 
00072   // Descriptive characteristics
00073 
00074   int numCorners() const {return m_points.size();}
00075   Point<2> getCorner(int i) const
00076         {assert(i >= 0 && ((unsigned int) i) < m_points.size()); return m_points[i];}
00077 #ifndef WFMATH_NO_TEMPLATES_AS_TEMPLATE_PARAMETERS
00078   Point<2> getCenter() const {return Barycenter(m_points);}
00079 #endif
00080 
00081   // For a Polygon<2>, addCorner() and moveCorner() always succeed.
00082   // The return values are present for the sake of a unified template
00083   // interface, and the epsilon argument is ignored
00084 
00085   // Add before i'th corner, zero is beginning, numCorners() is end
00086   bool addCorner(int i, const Point<2>& p, double epsilon = WFMATH_EPSILON)
00087         {m_points.insert(m_points.begin() + i, p); return true;}
00088 
00089   // Remove the i'th corner
00090   void removeCorner(int i) {m_points.erase(m_points.begin() + i);}
00091 
00092   // Move the i'th corner to p
00093   bool moveCorner(int i, const Point<2>& p, double epsilon = WFMATH_EPSILON)
00094         {m_points[i] = p; return true;}
00095 
00096   // Remove all points
00097   void clear()  {m_points.clear();}
00098 
00099   const Point<2>& operator[](int i) const {return m_points[i];}
00100   Point<2>& operator[](int i)             {return m_points[i];}
00101 
00102   void resize(unsigned int size) {m_points.resize(size);}
00103 
00104   // Movement functions
00105 
00106   Polygon& shift(const Vector<2>& v);
00107   Polygon& moveCornerTo(const Point<2>& p, int corner)
00108         {return shift(p - getCorner(corner));}
00109 #ifndef WFMATH_NO_TEMPLATES_AS_TEMPLATE_PARAMETERS
00110   Polygon& moveCenterTo(const Point<2>& p)
00111         {return shift(p - getCenter());}
00112 #endif
00113 
00114   Polygon& rotateCorner(const RotMatrix<2>& m, int corner)
00115         {rotatePoint(m, getCorner(corner)); return *this;}
00116 #ifndef WFMATH_NO_TEMPLATES_AS_TEMPLATE_PARAMETERS
00117   Polygon& rotateCenter(const RotMatrix<2>& m)
00118         {rotatePoint(m, getCenter()); return *this;}
00119 #endif
00120   Polygon& rotatePoint(const RotMatrix<2>& m, const Point<2>& p);
00121 
00122   // Intersection functions
00123 
00124 #ifndef WFMATH_NO_TEMPLATES_AS_TEMPLATE_PARAMETERS
00125   AxisBox<2> boundingBox() const {return BoundingBox(m_points);}
00126   Ball<2> boundingSphere() const {return BoundingSphere(m_points);}
00127   Ball<2> boundingSphereSloppy() const {return BoundingSphereSloppy(m_points);}
00128 #endif
00129 
00130   Polygon toParentCoords(const Point<2>& origin,
00131       const RotMatrix<2>& rotation = RotMatrix<2>().identity()) const;
00132   Polygon toParentCoords(const AxisBox<2>& coords) const;
00133   Polygon toParentCoords(const RotBox<2>& coords) const;
00134 
00135   // toLocal is just like toParent, expect we reverse the order of
00136   // translation and rotation and use the opposite sense of the rotation
00137   // matrix
00138 
00139   Polygon toLocalCoords(const Point<2>& origin,
00140       const RotMatrix<2>& rotation = RotMatrix<2>().identity()) const;
00141   Polygon toLocalCoords(const AxisBox<2>& coords) const;
00142   Polygon toLocalCoords(const RotBox<2>& coords) const;
00143 
00144   friend bool Intersect<2>(const Polygon& r, const Point<2>& p, bool proper);
00145   friend bool Contains<2>(const Point<2>& p, const Polygon& r, bool proper);
00146 
00147   friend bool Intersect<2>(const Polygon& p, const AxisBox<2>& b, bool proper);
00148   friend bool Contains<2>(const Polygon& p, const AxisBox<2>& b, bool proper);
00149   friend bool Contains<2>(const AxisBox<2>& b, const Polygon& p, bool proper);
00150 
00151   friend bool Intersect<2>(const Polygon& p, const Ball<2>& b, bool proper);
00152   friend bool Contains<2>(const Polygon& p, const Ball<2>& b, bool proper);
00153   friend bool Contains<2>(const Ball<2>& b, const Polygon& p, bool proper);
00154 
00155   friend bool Intersect<2>(const Polygon& r, const Segment<2>& s, bool proper);
00156   friend bool Contains<2>(const Polygon& p, const Segment<2>& s, bool proper);
00157   friend bool Contains<2>(const Segment<2>& s, const Polygon& p, bool proper);
00158 
00159   friend bool Intersect<2>(const Polygon& p, const RotBox<2>& r, bool proper);
00160   friend bool Contains<2>(const Polygon& p, const RotBox<2>& r, bool proper);
00161   friend bool Contains<2>(const RotBox<2>& r, const Polygon& p, bool proper);
00162 
00163   friend bool Intersect<2>(const Polygon& p1, const Polygon& p2, bool proper);
00164   friend bool Contains<2>(const Polygon& outer, const Polygon& inner, bool proper);
00165 
00166  private:
00167   std::vector<Point<2> > m_points;
00168   typedef std::vector<Point<2> >::iterator theIter;
00169   typedef std::vector<Point<2> >::const_iterator theConstIter;
00170 
00171 };
00172 
00173 // Helper classes, to keep track of the orientation of
00174 // a 2D polygon in dim dimensions
00175 
00176 typedef enum {
00177   _WFMATH_POLY2REORIENT_NONE,
00178   _WFMATH_POLY2REORIENT_CLEAR_AXIS2,
00179   _WFMATH_POLY2REORIENT_CLEAR_BOTH_AXES,
00180   _WFMATH_POLY2REORIENT_MOVE_AXIS2_TO_AXIS1,
00181   _WFMATH_POLY2REORIENT_SCALE1_CLEAR2
00182 } _Poly2ReorientType;
00183 
00184 // Reorient a 2D polygon to match a change in the basis
00185 // used by _Poly2Orient
00186 class _Poly2Reorient
00187 {
00188  public:
00189   _Poly2Reorient(_Poly2ReorientType type, CoordType scale = 0.0)
00190         : m_type(type), m_scale(scale) {}
00191   ~_Poly2Reorient() {}
00192 
00193   void reorient(Polygon<2>& poly, int skip = -1) const;
00194 
00195  private:
00196   _Poly2ReorientType m_type;
00197   CoordType m_scale;
00198 };
00199 
00200 template<const int dim> class _Poly2Orient;
00201 
00202 struct _Poly2OrientIntersectData {
00203   int dim;
00204   Point<2> p1, p2;
00205   Vector<2> v1, v2, off;
00206   bool o1_is_line, o2_is_line;
00207 };
00208 
00209 // Finds the intersection of the two planes, returns the
00210 // dimension of the intersection space, the rest of the arguments
00211 // are various information returned depending on the dimension of
00212 // the intersection
00213 template<const int dim>
00214 int  _Intersect(const _Poly2Orient<dim> &, const _Poly2Orient<dim> &,
00215                 _Poly2OrientIntersectData &);
00216 
00217 // Keep track of the orientation of a 2D polygon in dim dimensions
00218 template<const int dim>
00219 class _Poly2Orient
00220 {
00221  public:
00222   _Poly2Orient() {}
00223   _Poly2Orient(const _Poly2Orient& p)   {operator=(p);}
00224   ~_Poly2Orient() {}
00225 
00226   _Poly2Orient& operator=(const _Poly2Orient& p);
00227 
00228   // Convert a point in the 2D polygon to a point in dim dimensional space
00229   Point<dim> convert(const Point<2>& p) const;
00230 
00231   // Try to convert a point from dim dimensions into 2D, expanding the
00232   // basis if necessary. Returns true on success. On failure, the
00233   // basis is unchanged.
00234   bool expand(const Point<dim>& pd, Point<2>& p2, double epsilon = WFMATH_EPSILON);
00235 
00236   // Reduce the basis to the minimum necessary to span the points in
00237   // poly (with the exception of skip). Returns _Poly2Reorient, which needs
00238   // to be used to reorient the points to match the new basis.
00239   _Poly2Reorient reduce(const Polygon<2>& poly, int skip = -1);
00240 
00241   void shift(const Vector<dim>& v) {if(m_origin.isValid()) m_origin += v;}
00242   void rotate(const RotMatrix<dim>& m, const Point<dim>& p);
00243   // Rotates about the point which corresponds to "p" in the oriented plane
00244   void rotate2(const RotMatrix<dim>& m, const Point<2>& p);
00245 
00246 //3D only
00247   void rotate(const Quaternion& q, const Point<3>& p);
00248   // Rotates about the point which corresponds to "p" in the oriented plane
00249   void rotate2(const Quaternion& q, const Point<2>& p);
00250 
00251   _Poly2Orient toParentCoords(const Point<dim>& origin,
00252       const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
00253         {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(origin, rotation);
00254                 p.m_axes[0] *= rotation; p.m_axes[1] *= rotation; return p;}
00255   _Poly2Orient toParentCoords(const AxisBox<dim>& coords) const
00256         {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(coords); return p;}
00257   _Poly2Orient toParentCoords(const RotBox<dim>& coords) const
00258         {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(coords);
00259                 p.m_axes[0] *= coords.orientation();
00260                 p.m_axes[1] *= coords.orientation(); return p;}
00261 
00262   // toLocal is just like toParent, expect we reverse the order of
00263   // translation and rotation and use the opposite sense of the rotation
00264   // matrix
00265 
00266   _Poly2Orient toLocalCoords(const Point<dim>& origin,
00267       const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
00268         {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(origin, rotation);
00269                 p.m_axes[0] = rotation * p.m_axes[0];
00270                 p.m_axes[1] = rotation * p.m_axes[1]; return p;}
00271   _Poly2Orient toLocalCoords(const AxisBox<dim>& coords) const
00272         {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(coords); return p;}
00273   _Poly2Orient toLocalCoords(const RotBox<dim>& coords) const
00274         {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(coords);
00275                 p.m_axes[0] = coords.orientation() * p.m_axes[0];
00276                 p.m_axes[1] = coords.orientation() * p.m_axes[1]; return p;}
00277 
00278   // 3D only
00279   _Poly2Orient<3> toParentCoords(const Point<3>& origin, const Quaternion& rotation) const
00280         {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(origin, rotation);
00281                 p.m_axes[0].rotate(rotation); p.m_axes[0].rotate(rotation); return p;}
00282   _Poly2Orient<3> toLocalCoords(const Point<3>& origin, const Quaternion& rotation) const
00283         {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(origin, rotation);
00284                 p.m_axes[0].rotate(rotation.inverse());
00285                 p.m_axes[0].rotate(rotation.inverse()); return p;}
00286 
00287   // Gives the offset from pd to the space spanned by
00288   // the basis, and puts the nearest point in p2.
00289   Vector<dim> offset(const Point<dim>& pd, Point<2>& p2) const;
00290 
00291   // Like offset, but returns true if the point is in the plane
00292   bool checkContained(const Point<dim>& pd, Point<2> & p2) const;
00293 
00294   // Check if the AxisBox intersects the spanned space, and if so
00295   // return a point in the intersection.
00296   bool checkIntersect(const AxisBox<dim>& b, Point<2>& p2, bool proper) const;
00297 
00298   friend int  _Intersect<dim>(const _Poly2Orient<dim> &, const _Poly2Orient<dim> &,
00299                               _Poly2OrientIntersectData &);
00300 
00301  private:
00302   // special case of the above when both axes are valid
00303   bool checkIntersectPlane(const AxisBox<dim>& b, Point<2>& p2, bool proper) const;
00304 
00305   Point<dim> m_origin;
00306   Vector<dim> m_axes[2]; // Normalized to unit length
00307 };
00308 
00310 template<const int dim>
00311 class Polygon
00312 {
00313  public:
00314   Polygon() {}
00315   Polygon(const Polygon& p) : m_orient(p.m_orient), m_poly(p.m_poly) {}
00316 
00317   ~Polygon() {}
00318 
00319   friend std::ostream& operator<< <dim>(std::ostream& os, const Polygon& p);
00320   friend std::istream& operator>> <dim>(std::istream& is, Polygon& p);
00321 
00322   Polygon& operator=(const Polygon& p)
00323         {m_orient = p.m_orient; m_poly = p.m_poly; return *this;}
00324 
00325   bool isEqualTo(const Polygon& p2, double epsilon = WFMATH_EPSILON) const;
00326 
00327   bool operator==(const Polygon& p) const       {return isEqualTo(p);}
00328   bool operator!=(const Polygon& p) const       {return !isEqualTo(p);}
00329 
00330   bool isValid() const {return m_poly.isValid();}
00331 
00332   // Descriptive characteristics
00333 
00334   int numCorners() const {return m_poly.numCorners();}
00335   Point<dim> getCorner(int i) const
00336         {assert(i >= 0 && i < m_poly.numCorners()); return m_orient.convert(m_poly[i]);}
00337   Point<dim> getCenter() const {return m_orient.convert(m_poly.getCenter());}
00338 
00339   // The failure of the following functions does not invalidate the
00340   // polygon, but merely leaves it unchaged.
00341 
00342   // Add before i'th corner, zero is beginning, numCorners() is end
00343   // Only succeeds if p lies in a plane with all current points
00344   bool addCorner(int i, const Point<dim>& p, double epsilon = WFMATH_EPSILON);
00345 
00346   // Remove the i'th corner
00347   void removeCorner(int i);
00348 
00349   // Move the i'th corner to p, only succeeds if new location
00350   // lies in the same plane as all the other points. Note that,
00351   // under certain circumstances, this plane may not contain the
00352   // original location of the point.
00353   bool moveCorner(int i, const Point<dim>& p, double epsilon = WFMATH_EPSILON);
00354 
00355   // Remove all points
00356   void clear()  {m_poly.clear(); m_orient = _Poly2Orient<dim>();}
00357 
00358   // Movement functions
00359 
00360   Polygon& shift(const Vector<dim>& v)
00361         {m_orient.shift(v); return *this;}
00362   Polygon& moveCornerTo(const Point<dim>& p, int corner)
00363         {return shift(p - getCorner(corner));}
00364   Polygon& moveCenterTo(const Point<dim>& p)
00365         {return shift(p - getCenter());}
00366 
00367   Polygon& rotateCorner(const RotMatrix<dim>& m, int corner)
00368         {m_orient.rotate2(m, m_poly[corner]); return *this;}
00369   Polygon& rotateCenter(const RotMatrix<dim>& m)
00370         {if(m_poly.numCorners() > 0)
00371                 m_orient.rotate2(m, m_poly.getCenter());
00372          return *this;}
00373   Polygon& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p)
00374         {m_orient.rotate(m, p); return *this;}
00375 
00376   // 3D rotation functions
00377   Polygon<3>& rotateCorner(const Quaternion& q, int corner)
00378         {m_orient.rotate2(q, m_poly[corner]); return *this;}
00379   Polygon<3>& rotateCenter(const Quaternion& q)
00380         {if(m_poly.numCorners() > 0)
00381                 m_orient.rotate2(q, m_poly.getCenter());
00382          return *this;}
00383   Polygon<3>& rotatePoint(const Quaternion& q, const Point<3>& p)
00384         {m_orient.rotate(q, p); return *this;}
00385 
00386   // Intersection functions
00387 
00388   AxisBox<dim> boundingBox() const;
00389   Ball<dim> boundingSphere() const;
00390   Ball<dim> boundingSphereSloppy() const;
00391 
00392   Polygon toParentCoords(const Point<dim>& origin,
00393       const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
00394         {Polygon p(*this); p.m_orient = m_orient.toParentCoords(origin, rotation); return p;}
00395   Polygon toParentCoords(const AxisBox<dim>& coords) const
00396         {Polygon p(*this); p.m_orient = m_orient.toParentCoords(coords); return p;}
00397   Polygon toParentCoords(const RotBox<dim>& coords) const
00398         {Polygon p(*this); p.m_orient = m_orient.toParentCoords(coords); return p;}
00399 
00400   // toLocal is just like toParent, expect we reverse the order of
00401   // translation and rotation and use the opposite sense of the rotation
00402   // matrix
00403 
00404   Polygon toLocalCoords(const Point<dim>& origin,
00405       const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
00406         {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(origin, rotation); return p;}
00407   Polygon toLocalCoords(const AxisBox<dim>& coords) const
00408         {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(coords); return p;}
00409   Polygon toLocalCoords(const RotBox<dim>& coords) const
00410         {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(coords); return p;}
00411 
00412   // 3D only
00413   Polygon<3> toParentCoords(const Point<3>& origin, const Quaternion& rotation) const
00414         {Polygon<3> p(*this); p.m_orient = m_orient.toParentCoords(origin, rotation); return p;}
00415   Polygon<3> toLocalCoords(const Point<3>& origin, const Quaternion& rotation) const
00416         {Polygon<3> p(*this); p.m_orient = m_orient.toLocalCoords(origin, rotation); return p;}
00417 
00418   friend bool Intersect<dim>(const Polygon& r, const Point<dim>& p, bool proper);
00419   friend bool Contains<dim>(const Point<dim>& p, const Polygon& r, bool proper);
00420 
00421   friend bool Intersect<dim>(const Polygon& p, const AxisBox<dim>& b, bool proper);
00422   friend bool Contains<dim>(const Polygon& p, const AxisBox<dim>& b, bool proper);
00423   friend bool Contains<dim>(const AxisBox<dim>& b, const Polygon& p, bool proper);
00424 
00425   friend bool Intersect<dim>(const Polygon& p, const Ball<dim>& b, bool proper);
00426   friend bool Contains<dim>(const Polygon& p, const Ball<dim>& b, bool proper);
00427   friend bool Contains<dim>(const Ball<dim>& b, const Polygon& p, bool proper);
00428 
00429   friend bool Intersect<dim>(const Polygon& r, const Segment<dim>& s, bool proper);
00430   friend bool Contains<dim>(const Polygon& p, const Segment<dim>& s, bool proper);
00431   friend bool Contains<dim>(const Segment<dim>& s, const Polygon& p, bool proper);
00432 
00433   friend bool Intersect<dim>(const Polygon& p, const RotBox<dim>& r, bool proper);
00434   friend bool Contains<dim>(const Polygon& p, const RotBox<dim>& r, bool proper);
00435   friend bool Contains<dim>(const RotBox<dim>& r, const Polygon& p, bool proper);
00436 
00437   friend bool Intersect<dim>(const Polygon& p1, const Polygon& p2, bool proper);
00438   friend bool Contains<dim>(const Polygon& outer, const Polygon& inner, bool proper);
00439 
00440  private:
00441 
00442   _Poly2Orient<dim> m_orient;
00443   Polygon<2> m_poly;
00444 };
00445 
00446 } // namespace WFMath
00447 
00448 #include <wfmath/polygon_funcs.h>
00449 
00450 #endif  // WFMATH_POLYGON_H

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