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csgeom/math3d_d.h

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00001 /*
00002     Copyright (C) 1998,1999,2000 by Jorrit Tyberghein
00003     Largely rewritten by Ivan Avramovic <ivan@avramovic.com>
00004     Converted to double by Thomas Hieber
00005 
00006     This library is free software; you can redistribute it and/or
00007     modify it under the terms of the GNU Library General Public
00008     License as published by the Free Software Foundation; either
00009     version 2 of the License, or (at your option) any later version.
00010 
00011     This library 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 GNU
00014     Library General Public License for more details.
00015 
00016     You should have received a copy of the GNU Library General Public
00017     License along with this library; if not, write to the Free
00018     Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
00019 */
00020 
00021 #ifndef __CS_MATH3D_D_H__
00022 #define __CS_MATH3D_D_H__
00023 
00024 #include "cstypes.h"
00025 
00032 #ifndef ABS
00033 #define ABS(x) ((x)<0?-(x):(x))
00034 #endif
00035 
00036 class csDVector3;
00037 class csDMatrix3;
00038 class csVector3;
00039 
00040 inline double dSqr (double d)
00041 {
00042   return d * d;
00043 }
00044 
00048 class csDVector3
00049 {
00050 public:
00052   double x;
00054   double y;
00056   double z;
00057 
00063   csDVector3 () {}
00064 
00070   csDVector3 (double m) : x(m), y(m), z(m) {}
00071 
00073   csDVector3 (double ix, double iy, double iz = 0) { x = ix; y = iy; z = iz; }
00074 
00076   csDVector3 (const csDVector3& v) { x = v.x; y = v.y; z = v.z; }
00077 
00079   csDVector3 (const csVector3&);
00080 
00082   inline friend
00083   csDVector3 operator+ (const csDVector3& v1, const csDVector3& v2)
00084   { return csDVector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); }
00085 
00087   inline friend
00088   csDVector3 operator- (const csDVector3& v1, const csDVector3& v2)
00089   { return csDVector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); }
00090 
00092   inline friend double operator* (const csDVector3& v1, const csDVector3& v2)
00093   { return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; }
00094 
00096   inline friend
00097   csDVector3 operator% (const csDVector3& v1, const csDVector3& v2)
00098   {
00099     return csDVector3 (v1.y*v2.z-v1.z*v2.y,
00100                        v1.z*v2.x-v1.x*v2.z,
00101                        v1.x*v2.y-v1.y*v2.x);
00102   }
00103 
00105   void Cross (const csDVector3 & px, const csDVector3 & py)
00106   {
00107     x = px.y*py.z - px.z*py.y;
00108     y = px.z*py.x - px.x*py.z;
00109     z = px.x*py.y - px.y*py.x;
00110   }
00111 
00113   inline friend csDVector3 operator* (const csDVector3& v, double f)
00114   { return csDVector3(v.x*f, v.y*f, v.z*f); }
00115 
00117   inline friend csDVector3 operator* (double f, const csDVector3& v)
00118   { return csDVector3(v.x*f, v.y*f, v.z*f); }
00119 
00121   inline friend csDVector3 operator/ (const csDVector3& v, double f)
00122   { f = 1.0f/f; return csDVector3(v.x*f, v.y*f, v.z*f); }
00123 
00125   inline friend bool operator== (const csDVector3& v1, const csDVector3& v2)
00126   { return v1.x==v2.x && v1.y==v2.y && v1.z==v2.z; }
00127 
00129   inline friend bool operator!= (const csDVector3& v1, const csDVector3& v2)
00130   { return v1.x!=v2.x || v1.y!=v2.y || v1.z!=v2.z; }
00131 
00133   inline friend
00134   csDVector3 operator>> (const csDVector3& v1, const csDVector3& v2)
00135   { return v2*(v1*v2)/(v2*v2); }
00136 
00138   inline friend
00139   csDVector3 operator<< (const csDVector3& v1, const csDVector3& v2)
00140   { return v1*(v1*v2)/(v1*v1); }
00141 
00143   inline friend bool operator< (const csDVector3& v, double f)
00144   { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }
00145 
00147   inline friend bool operator> (double f, const csDVector3& v)
00148   { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }
00149 
00151   inline double operator[](int n) const {return !n?x:n&1?y:z;}
00152 
00154   inline double & operator[](int n){return !n?x:n&1?y:z;}
00155 
00157   inline csDVector3& operator+= (const csDVector3& v)
00158   {
00159     x += v.x;
00160     y += v.y;
00161     z += v.z;
00162 
00163     return *this;
00164   }
00165 
00167   inline csDVector3& operator-= (const csDVector3& v)
00168   {
00169     x -= v.x;
00170     y -= v.y;
00171     z -= v.z;
00172 
00173     return *this;
00174   }
00175 
00177   inline csDVector3& operator*= (double f)
00178   { x *= f; y *= f; z *= f; return *this; }
00179 
00181   inline csDVector3& operator/= (double f)
00182   { x /= f; y /= f; z /= f; return *this; }
00183 
00185   inline csDVector3 operator+ () const { return *this; }
00186 
00188   inline csDVector3 operator- () const { return csDVector3(-x,-y,-z); }
00189 
00191   inline void Set (double sx, double sy, double sz) { x = sx; y = sy; z = sz; }
00192 
00194   double Norm () const;
00195 
00197   double SquaredNorm () const;
00198 
00204   csDVector3 Unit () const { return (*this)/(this->Norm()); }
00205 
00207   inline static double Norm (const csDVector3& v) { return v.Norm(); }
00208 
00210   inline static csDVector3 Unit (const csDVector3& v) { return v.Unit(); }
00211 
00213   void Normalize();
00214 };
00215 
00216 
00220 class csDMatrix3
00221 {
00222 public:
00223   double m11, m12, m13;
00224   double m21, m22, m23;
00225   double m31, m32, m33;
00226 
00227 public:
00229   csDMatrix3 ();
00230 
00232   csDMatrix3 (double m11, double m12, double m13,
00233             double m21, double m22, double m23,
00234             double m31, double m32, double m33);
00235 
00237   inline csDVector3 Row1() const { return csDVector3 (m11,m12,m13); }
00238 
00240   inline csDVector3 Row2() const { return csDVector3 (m21,m22,m23); }
00241 
00243   inline csDVector3 Row3() const { return csDVector3 (m31,m32,m33); }
00244 
00246   inline csDVector3 Col1() const { return csDVector3 (m11,m21,m31); }
00247 
00249   inline csDVector3 Col2() const { return csDVector3 (m12,m22,m32); }
00250 
00252   inline csDVector3 Col3() const { return csDVector3 (m13,m23,m33); }
00253 
00255   inline void Set (double m11, double m12, double m13,
00256                    double m21, double m22, double m23,
00257                    double m31, double m32, double m33)
00258   {
00259     csDMatrix3::m11 = m11; csDMatrix3::m12 = m12; csDMatrix3::m13 = m13;
00260     csDMatrix3::m21 = m21; csDMatrix3::m22 = m22; csDMatrix3::m23 = m23;
00261     csDMatrix3::m31 = m31; csDMatrix3::m32 = m32; csDMatrix3::m33 = m33;
00262   }
00263 
00265   csDMatrix3& operator+= (const csDMatrix3& m);
00266 
00268   csDMatrix3& operator-= (const csDMatrix3& m);
00269 
00271   csDMatrix3& operator*= (const csDMatrix3& m);
00272 
00274   csDMatrix3& operator*= (double s);
00275 
00277   csDMatrix3& operator/= (double s);
00278 
00280   inline csDMatrix3 operator+ () const { return *this; }
00282   inline csDMatrix3 operator- () const
00283   {
00284    return csDMatrix3(-m11,-m12,-m13,
00285                     -m21,-m22,-m23,
00286                     -m31,-m32,-m33);
00287   }
00288 
00290   void Transpose ();
00291 
00293   csDMatrix3 GetTranspose () const;
00294 
00296   inline csDMatrix3 GetInverse () const
00297   {
00298     csDMatrix3 C(
00299              (m22*m33 - m23*m32), -(m12*m33 - m13*m32),  (m12*m23 - m13*m22),
00300             -(m21*m33 - m23*m31),  (m11*m33 - m13*m31), -(m11*m23 - m13*m21),
00301              (m21*m32 - m22*m31), -(m11*m32 - m12*m31),  (m11*m22 - m12*m21) );
00302     double s = (double)1./(m11*C.m11 + m12*C.m21 + m13*C.m31);
00303 
00304     C *= s;
00305 
00306     return C;
00307   }
00308 
00310   void Invert() { *this = GetInverse (); }
00311 
00313   double Determinant () const;
00314 
00316   void Identity ();
00317 
00319   friend csDMatrix3 operator+ (const csDMatrix3& m1, const csDMatrix3& m2);
00321   friend csDMatrix3 operator- (const csDMatrix3& m1, const csDMatrix3& m2);
00323   friend csDMatrix3 operator* (const csDMatrix3& m1, const csDMatrix3& m2);
00324 
00326   inline friend csDVector3 operator* (const csDMatrix3& m, const csDVector3& v)
00327   {
00328    return csDVector3 (m.m11*v.x + m.m12*v.y + m.m13*v.z,
00329                      m.m21*v.x + m.m22*v.y + m.m23*v.z,
00330                      m.m31*v.x + m.m32*v.y + m.m33*v.z);
00331   }
00332 
00334   friend csDMatrix3 operator* (const csDMatrix3& m, double f);
00336   friend csDMatrix3 operator* (double f, const csDMatrix3& m);
00338   friend csDMatrix3 operator/ (const csDMatrix3& m, double f);
00340   friend bool operator== (const csDMatrix3& m1, const csDMatrix3& m2);
00342   friend bool operator!= (const csDMatrix3& m1, const csDMatrix3& m2);
00344   friend bool operator< (const csDMatrix3& m, double f);
00346   friend bool operator> (double f, const csDMatrix3& m);
00347 };
00348 
00349 
00355 class csDPlane
00356 {
00357 public:
00359   csDVector3 norm;
00360 
00362   double DD;
00363 
00365   csDPlane () : norm(0,0,1), DD(0) {}
00366 
00368   csDPlane (const csDVector3& plane_norm, double d=0) :
00369   norm(plane_norm), DD(d) {}
00370 
00372   csDPlane (double a, double b, double c, double d=0) : norm(a,b,c), DD(d) {}
00373 
00375   inline csDVector3& Normal () { return norm; }
00377   inline const csDVector3& Normal () const { return norm; }
00378 
00380   inline double A () const { return norm.x; }
00382   inline double B () const { return norm.y; }
00384   inline double C () const { return norm.z; }
00386   inline double D () const { return DD; }
00387 
00389   inline double& A () { return norm.x; }
00391   inline double& B () { return norm.y; }
00393   inline double& C () { return norm.z; }
00395   inline double& D () { return DD; }
00396 
00398   inline void Set (double a, double b, double c, double d)
00399    { norm.x = a; norm.y = b; norm.z = c; DD = d; }
00400 
00402   inline double Classify (const csDVector3& pt) const { return norm*pt+DD; }
00403 
00405   static double Classify (double A, double B, double C, double D,
00406                          const csDVector3& pt)
00407   { return A*pt.x + B*pt.y + C*pt.z + D; }
00408 
00414   inline double Distance (const csDVector3& pt) const
00415   { return ABS (Classify (pt)); }
00416 
00418   void Invert () { norm = -norm;  DD = -DD; }
00419 
00421   void Normalize ()
00422   {
00423     double f = norm.Norm ();
00424     if (f) { norm /= f;  DD /= f; }
00425   }
00426 
00427 };
00428 
00433 class csDMath3
00434 {
00435 public:
00443   static int WhichSide3D (const csDVector3& p,
00444                           const csDVector3& v1, const csDVector3& v2)
00445   {
00446     // double s = p * (v1%v2); (original expression: expanded to the below:)
00447     double s = p.x*(v1.y*v2.z-v1.z*v2.y) + p.y*(v1.z*v2.x-v1.x*v2.z) +
00448               p.z*(v1.x*v2.y-v1.y*v2.x);
00449     if (s < 0) return 1;
00450     else if (s > 0) return -1;
00451     else return 0;
00452   }
00453 
00459   static bool Visible (const csDVector3& p, const csDVector3& t1,
00460                        const csDVector3& t2, const csDVector3& t3);
00461 
00467   static bool Visible (const csDVector3& p, const csDPlane& pl)
00468   { return pl.Classify (p) <= 0; }
00469 
00479   static void Between (const csDVector3& v1, const csDVector3& v2,
00480                        csDVector3& v, double pct, double wid);
00481 
00488   static void SetMinMax (const csDVector3& v,
00489                          csDVector3& min, csDVector3& max)
00490   {
00491     if (v.x > max.x) max.x = v.x; else if (v.x < min.x ) min.x = v.x;
00492     if (v.y > max.y) max.y = v.y; else if (v.y < min.y ) min.y = v.y;
00493     if (v.z > max.z) max.z = v.z; else if (v.z < min.z ) min.z = v.z;
00494   }
00495 
00501   inline static double Area3 (const csDVector3 &a, const csDVector3 &b,
00502                              const csDVector3 &c)
00503   {
00504     csDVector3 v1 = b - a;
00505     csDVector3 v2 = c - a;
00506     return ((v1.y * v2.z + v1.z * v2.x + v1.x * v2.y) -
00507             (v1.y * v2.x + v1.x * v2.z + v1.z * v2.y));
00508   }
00509 
00515   inline static void CalcNormal (csDVector3& norm,     const csDVector3& v1,
00516                                  const csDVector3& v2, const csDVector3& v3)
00517   {
00518     norm = (v1-v2)%(v1-v3);
00519   }
00520 
00526   static void CalcNormal (csDVector3& norm,
00527                           const csDVector3& v, const csDVector3& u)
00528   { norm = u%v; /* NOT v%u - vertexes are defined clockwise */ }
00529 
00536   static void CalcPlane (const csDVector3& v1, const csDVector3& v2,
00537          const csDVector3& v3, csDVector3& normal, double& D)
00538   {
00539     normal = (v1-v2)%(v1-v3);
00540     D = - (normal * v1);
00541   }
00542 
00549   static bool PlanesEqual (const csDPlane& p1, const csDPlane& p2)
00550   {
00551     return ( ( p1.norm - p2.norm) < (double).001 ) &&
00552              (  ABS (p1.DD-p2.DD) < (double).001 );
00553   }
00554 
00560   static bool PlanesClose (const csDPlane& p1, const csDPlane& p2);
00561 };
00562 
00567 class csDSquaredDist
00568 {
00569 public:
00571   static double PointPoint (const csDVector3& p1, const csDVector3& p2)
00572   { return dSqr (p1.x - p2.x) + dSqr (p1.y - p2.y) + dSqr (p1.z - p2.z); }
00573 
00575   static double PointLine (const csDVector3& p,
00576                           const csDVector3& l1, const csDVector3& l2);
00577 
00579   static double PointPlane (const csDVector3& p, const csDPlane& plane)
00580   { double r = plane.Classify (p);  return r * r; }
00581 
00588   static double PointPoly (const csDVector3& p, csDVector3 *V, int n,
00589                           const csDPlane& plane, double sqdist = -1);
00590 };
00591 
00597 class csDIntersect3
00598 {
00599 public:
00604   static void Plane (
00605     const csDVector3& u, const csDVector3& v, // segment
00606     const csDVector3& normal, const csDVector3& a, // plane
00607     csDVector3& isect);                    // intersection point
00608 
00617   static bool Plane (
00618     const csDVector3& u, const csDVector3& v, // segment
00619     double A, double B, double C, double D, // plane Ax+By+Cz+D=0
00620     csDVector3& isect,                     // intersection point
00621     double& dist);                       // distance from u to isect
00622 
00631   static bool Plane (
00632     const csDVector3& u, const csDVector3& v, // segment
00633     const csDPlane& p,                     // plane Ax+By+Cz+D=0
00634     csDVector3& isect,                     // intersection point
00635     double& dist);                       // distance from u to isect
00636 
00642   static bool Planes(const csDPlane& p1, const csDPlane& p2,
00643                      const csDPlane& p3, csDVector3& isect);
00644 
00651   static double Z0Plane (
00652     const csDVector3& u, const csDVector3& v, // segment
00653     csDVector3& isect);                    // intersection point
00654 
00661   static double ZPlane (double zval,      // plane z = zval
00662     const csDVector3& u, const csDVector3& v, // segment
00663     csDVector3& isect);                    // intersection point
00664 
00669   static double XFrustum (
00670     double A, const csDVector3& u, const csDVector3& v, csDVector3& isect);
00671 
00676   static double YFrustum (
00677     double B, const csDVector3& u, const csDVector3& v, csDVector3& isect);
00678 };
00679 
00682 #endif // __CS_MATH3D_D_H__

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