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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 "csextern.h"
00025 
00026 #include "cstypes.h"
00027 
00035 #ifndef ABS
00036 #define ABS(x) ((x)<0?-(x):(x))
00037 #endif
00038 
00039 class csDVector3;
00040 class csDMatrix3;
00041 class csVector3;
00042 
00043 inline double dSqr (double d)
00044 {
00045   return d * d;
00046 }
00047 
00051 class CS_CRYSTALSPACE_EXPORT csDVector3
00052 {
00053 public:
00055   double x;
00057   double y;
00059   double z;
00060 
00066   csDVector3 () {}
00067 
00073   csDVector3 (double m) : x(m), y(m), z(m) {}
00074 
00076   csDVector3 (double ix, double iy, double iz = 0) { x = ix; y = iy; z = iz; }
00077 
00079   csDVector3 (const csDVector3& v) { x = v.x; y = v.y; z = v.z; }
00080 
00082   csDVector3 (const csVector3&);
00083 
00085   inline friend
00086   csDVector3 operator+ (const csDVector3& v1, const csDVector3& v2)
00087   { return csDVector3(v1.x+v2.x, v1.y+v2.y, v1.z+v2.z); }
00088 
00090   inline friend
00091   csDVector3 operator- (const csDVector3& v1, const csDVector3& v2)
00092   { return csDVector3(v1.x-v2.x, v1.y-v2.y, v1.z-v2.z); }
00093 
00095   inline friend double operator* (const csDVector3& v1, const csDVector3& v2)
00096   { return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; }
00097 
00099   inline friend
00100   csDVector3 operator% (const csDVector3& v1, const csDVector3& v2)
00101   {
00102     return csDVector3 (v1.y*v2.z-v1.z*v2.y,
00103                        v1.z*v2.x-v1.x*v2.z,
00104                        v1.x*v2.y-v1.y*v2.x);
00105   }
00106 
00108   void Cross (const csDVector3 & px, const csDVector3 & py)
00109   {
00110     x = px.y*py.z - px.z*py.y;
00111     y = px.z*py.x - px.x*py.z;
00112     z = px.x*py.y - px.y*py.x;
00113   }
00114 
00116   inline friend csDVector3 operator* (const csDVector3& v, double f)
00117   { return csDVector3(v.x*f, v.y*f, v.z*f); }
00118 
00120   inline friend csDVector3 operator* (double f, const csDVector3& v)
00121   { return csDVector3(v.x*f, v.y*f, v.z*f); }
00122 
00124   inline friend csDVector3 operator/ (const csDVector3& v, double f)
00125   { f = 1.0f/f; return csDVector3(v.x*f, v.y*f, v.z*f); }
00126 
00128   inline friend bool operator== (const csDVector3& v1, const csDVector3& v2)
00129   { return v1.x==v2.x && v1.y==v2.y && v1.z==v2.z; }
00130 
00132   inline friend bool operator!= (const csDVector3& v1, const csDVector3& v2)
00133   { return v1.x!=v2.x || v1.y!=v2.y || v1.z!=v2.z; }
00134 
00136   inline friend
00137   csDVector3 operator>> (const csDVector3& v1, const csDVector3& v2)
00138   { return v2*(v1*v2)/(v2*v2); }
00139 
00141   inline friend
00142   csDVector3 operator<< (const csDVector3& v1, const csDVector3& v2)
00143   { return v1*(v1*v2)/(v1*v1); }
00144 
00146   inline friend bool operator< (const csDVector3& v, double f)
00147   { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }
00148 
00150   inline friend bool operator> (double f, const csDVector3& v)
00151   { return ABS(v.x)<f && ABS(v.y)<f && ABS(v.z)<f; }
00152 
00154   inline double operator[](int n) const {return !n?x:n&1?y:z;}
00155 
00157   inline double & operator[](int n){return !n?x:n&1?y:z;}
00158 
00160   inline csDVector3& operator+= (const csDVector3& v)
00161   {
00162     x += v.x;
00163     y += v.y;
00164     z += v.z;
00165 
00166     return *this;
00167   }
00168 
00170   inline csDVector3& operator-= (const csDVector3& v)
00171   {
00172     x -= v.x;
00173     y -= v.y;
00174     z -= v.z;
00175 
00176     return *this;
00177   }
00178 
00180   inline csDVector3& operator*= (double f)
00181   { x *= f; y *= f; z *= f; return *this; }
00182 
00184   inline csDVector3& operator/= (double f)
00185   { x /= f; y /= f; z /= f; return *this; }
00186 
00188   inline csDVector3 operator+ () const { return *this; }
00189 
00191   inline csDVector3 operator- () const { return csDVector3(-x,-y,-z); }
00192 
00194   inline void Set (double sx, double sy, double sz) { x = sx; y = sy; z = sz; }
00195 
00197   double Norm () const;
00198 
00200   double SquaredNorm () const;
00201 
00207   csDVector3 Unit () const { return (*this)/(this->Norm()); }
00208 
00210   inline static double Norm (const csDVector3& v) { return v.Norm(); }
00211 
00213   inline static csDVector3 Unit (const csDVector3& v) { return v.Unit(); }
00214 
00216   void Normalize();
00217 };
00218 
00219 
00223 class CS_CRYSTALSPACE_EXPORT csDMatrix3
00224 {
00225 public:
00226   double m11, m12, m13;
00227   double m21, m22, m23;
00228   double m31, m32, m33;
00229 
00230 public:
00232   csDMatrix3 ();
00233 
00235   csDMatrix3 (double m11, double m12, double m13,
00236             double m21, double m22, double m23,
00237             double m31, double m32, double m33);
00238 
00240   inline csDVector3 Row1() const { return csDVector3 (m11,m12,m13); }
00241 
00243   inline csDVector3 Row2() const { return csDVector3 (m21,m22,m23); }
00244 
00246   inline csDVector3 Row3() const { return csDVector3 (m31,m32,m33); }
00247 
00249   inline csDVector3 Col1() const { return csDVector3 (m11,m21,m31); }
00250 
00252   inline csDVector3 Col2() const { return csDVector3 (m12,m22,m32); }
00253 
00255   inline csDVector3 Col3() const { return csDVector3 (m13,m23,m33); }
00256 
00258   inline void Set (double m11, double m12, double m13,
00259                    double m21, double m22, double m23,
00260                    double m31, double m32, double m33)
00261   {
00262     csDMatrix3::m11 = m11; csDMatrix3::m12 = m12; csDMatrix3::m13 = m13;
00263     csDMatrix3::m21 = m21; csDMatrix3::m22 = m22; csDMatrix3::m23 = m23;
00264     csDMatrix3::m31 = m31; csDMatrix3::m32 = m32; csDMatrix3::m33 = m33;
00265   }
00266 
00268   csDMatrix3& operator+= (const csDMatrix3& m);
00269 
00271   csDMatrix3& operator-= (const csDMatrix3& m);
00272 
00274   csDMatrix3& operator*= (const csDMatrix3& m);
00275 
00277   csDMatrix3& operator*= (double s);
00278 
00280   csDMatrix3& operator/= (double s);
00281 
00283   inline csDMatrix3 operator+ () const { return *this; }
00285   inline csDMatrix3 operator- () const
00286   {
00287    return csDMatrix3(-m11,-m12,-m13,
00288                     -m21,-m22,-m23,
00289                     -m31,-m32,-m33);
00290   }
00291 
00293   void Transpose ();
00294 
00296   csDMatrix3 GetTranspose () const;
00297 
00299   inline csDMatrix3 GetInverse () const
00300   {
00301     csDMatrix3 C(
00302              (m22*m33 - m23*m32), -(m12*m33 - m13*m32),  (m12*m23 - m13*m22),
00303             -(m21*m33 - m23*m31),  (m11*m33 - m13*m31), -(m11*m23 - m13*m21),
00304              (m21*m32 - m22*m31), -(m11*m32 - m12*m31),  (m11*m22 - m12*m21) );
00305     double s = (double)1./(m11*C.m11 + m12*C.m21 + m13*C.m31);
00306 
00307     C *= s;
00308 
00309     return C;
00310   }
00311 
00313   void Invert() { *this = GetInverse (); }
00314 
00316   double Determinant () const;
00317 
00319   void Identity ();
00320 
00322   friend csDMatrix3 operator+ (const csDMatrix3& m1, const csDMatrix3& m2);
00324   friend csDMatrix3 operator- (const csDMatrix3& m1, const csDMatrix3& m2);
00326   friend csDMatrix3 operator* (const csDMatrix3& m1, const csDMatrix3& m2);
00327 
00329   inline friend csDVector3 operator* (const csDMatrix3& m, const csDVector3& v)
00330   {
00331    return csDVector3 (m.m11*v.x + m.m12*v.y + m.m13*v.z,
00332                      m.m21*v.x + m.m22*v.y + m.m23*v.z,
00333                      m.m31*v.x + m.m32*v.y + m.m33*v.z);
00334   }
00335 
00337   friend csDMatrix3 operator* (const csDMatrix3& m, double f);
00339   friend csDMatrix3 operator* (double f, const csDMatrix3& m);
00341   friend csDMatrix3 operator/ (const csDMatrix3& m, double f);
00343   friend bool operator== (const csDMatrix3& m1, const csDMatrix3& m2);
00345   friend bool operator!= (const csDMatrix3& m1, const csDMatrix3& m2);
00347   friend bool operator< (const csDMatrix3& m, double f);
00349   friend bool operator> (double f, const csDMatrix3& m);
00350 };
00351 
00352 
00358 class CS_CRYSTALSPACE_EXPORT csDPlane
00359 {
00360 public:
00362   csDVector3 norm;
00363 
00365   double DD;
00366 
00368   csDPlane () : norm(0,0,1), DD(0) {}
00369 
00371   csDPlane (const csDVector3& plane_norm, double d=0) :
00372   norm(plane_norm), DD(d) {}
00373 
00375   csDPlane (double a, double b, double c, double d=0) : norm(a,b,c), DD(d) {}
00376 
00378   inline csDVector3& Normal () { return norm; }
00380   inline const csDVector3& Normal () const { return norm; }
00381 
00383   inline double A () const { return norm.x; }
00385   inline double B () const { return norm.y; }
00387   inline double C () const { return norm.z; }
00389   inline double D () const { return DD; }
00390 
00392   inline double& A () { return norm.x; }
00394   inline double& B () { return norm.y; }
00396   inline double& C () { return norm.z; }
00398   inline double& D () { return DD; }
00399 
00401   inline void Set (double a, double b, double c, double d)
00402    { norm.x = a; norm.y = b; norm.z = c; DD = d; }
00403 
00405   inline double Classify (const csDVector3& pt) const { return norm*pt+DD; }
00406 
00408   static double Classify (double A, double B, double C, double D,
00409                          const csDVector3& pt)
00410   { return A*pt.x + B*pt.y + C*pt.z + D; }
00411 
00417   inline double Distance (const csDVector3& pt) const
00418   { return ABS (Classify (pt)); }
00419 
00421   void Invert () { norm = -norm;  DD = -DD; }
00422 
00424   void Normalize ()
00425   {
00426     double f = norm.Norm ();
00427     if (f) { norm /= f;  DD /= f; }
00428   }
00429 
00430 };
00431 
00436 class CS_CRYSTALSPACE_EXPORT csDMath3
00437 {
00438 public:
00446   static int WhichSide3D (const csDVector3& p,
00447                           const csDVector3& v1, const csDVector3& v2)
00448   {
00449     // double s = p * (v1%v2); (original expression: expanded to the below:)
00450     double s = p.x*(v1.y*v2.z-v1.z*v2.y) + p.y*(v1.z*v2.x-v1.x*v2.z) +
00451               p.z*(v1.x*v2.y-v1.y*v2.x);
00452     if (s < 0) return 1;
00453     else if (s > 0) return -1;
00454     else return 0;
00455   }
00456 
00462   static bool Visible (const csDVector3& p, const csDVector3& t1,
00463                        const csDVector3& t2, const csDVector3& t3);
00464 
00470   static bool Visible (const csDVector3& p, const csDPlane& pl)
00471   { return pl.Classify (p) <= 0; }
00472 
00482   static void Between (const csDVector3& v1, const csDVector3& v2,
00483                        csDVector3& v, double pct, double wid);
00484 
00491   static void SetMinMax (const csDVector3& v,
00492                          csDVector3& min, csDVector3& max)
00493   {
00494     if (v.x > max.x) max.x = v.x; else if (v.x < min.x ) min.x = v.x;
00495     if (v.y > max.y) max.y = v.y; else if (v.y < min.y ) min.y = v.y;
00496     if (v.z > max.z) max.z = v.z; else if (v.z < min.z ) min.z = v.z;
00497   }
00498 
00504   inline static double DoubleArea3 (const csDVector3 &a, const csDVector3 &b,
00505                              const csDVector3 &c)
00506   {
00507     csDVector3 v1 = b - a;
00508     csDVector3 v2 = c - a;
00509     return (v1 % v2).Norm ();
00510   }
00511 
00517   inline static void CalcNormal (csDVector3& norm,     const csDVector3& v1,
00518                                  const csDVector3& v2, const csDVector3& v3)
00519   {
00520     norm = (v1-v2)%(v1-v3);
00521   }
00522 
00528   static void CalcNormal (csDVector3& norm,
00529                           const csDVector3& v, const csDVector3& u)
00530   { norm = u%v; /* NOT v%u - vertexes are defined clockwise */ }
00531 
00538   static void CalcPlane (const csDVector3& v1, const csDVector3& v2,
00539          const csDVector3& v3, csDVector3& normal, double& D)
00540   {
00541     normal = (v1-v2)%(v1-v3);
00542     D = - (normal * v1);
00543   }
00544 
00551   static bool PlanesEqual (const csDPlane& p1, const csDPlane& p2)
00552   {
00553     return ( ( p1.norm - p2.norm) < (double).001 ) &&
00554              (  ABS (p1.DD-p2.DD) < (double).001 );
00555   }
00556 
00562   static bool PlanesClose (const csDPlane& p1, const csDPlane& p2);
00563 };
00564 
00569 class CS_CRYSTALSPACE_EXPORT csDSquaredDist
00570 {
00571 public:
00573   static double PointPoint (const csDVector3& p1, const csDVector3& p2)
00574   { return dSqr (p1.x - p2.x) + dSqr (p1.y - p2.y) + dSqr (p1.z - p2.z); }
00575 
00577   static double PointLine (const csDVector3& p,
00578                           const csDVector3& l1, const csDVector3& l2);
00579 
00581   static double PointPlane (const csDVector3& p, const csDPlane& plane)
00582   { double r = plane.Classify (p);  return r * r; }
00583 
00590   static double PointPoly (const csDVector3& p, csDVector3 *V, int n,
00591                           const csDPlane& plane, double sqdist = -1);
00592 };
00593 
00599 class CS_CRYSTALSPACE_EXPORT csDIntersect3
00600 {
00601 public:
00606   static void Plane (
00607     const csDVector3& u, const csDVector3& v, // segment
00608     const csDVector3& normal, const csDVector3& a, // plane
00609     csDVector3& isect);                    // intersection point
00610 
00619   static bool Plane (
00620     const csDVector3& u, const csDVector3& v, // segment
00621     double A, double B, double C, double D, // plane Ax+By+Cz+D=0
00622     csDVector3& isect,                     // intersection point
00623     double& dist);                       // distance from u to isect
00624 
00633   static bool Plane (
00634     const csDVector3& u, const csDVector3& v, // segment
00635     const csDPlane& p,                     // plane Ax+By+Cz+D=0
00636     csDVector3& isect,                     // intersection point
00637     double& dist);                       // distance from u to isect
00638 
00644   static bool Planes(const csDPlane& p1, const csDPlane& p2,
00645                      const csDPlane& p3, csDVector3& isect);
00646 
00653   static double Z0Plane (
00654     const csDVector3& u, const csDVector3& v, // segment
00655     csDVector3& isect);                    // intersection point
00656 
00663   static double ZPlane (double zval,      // plane z = zval
00664     const csDVector3& u, const csDVector3& v, // segment
00665     csDVector3& isect);                    // intersection point
00666 
00671   static double XFrustum (
00672     double A, const csDVector3& u, const csDVector3& v, csDVector3& isect);
00673 
00678   static double YFrustum (
00679     double B, const csDVector3& u, const csDVector3& v, csDVector3& isect);
00680 };
00681 
00684 #endif // __CS_MATH3D_D_H__

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