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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
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; }
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,
00606 const csDVector3& normal, const csDVector3& a,
00607 csDVector3& isect);
00608
00617 static bool Plane (
00618 const csDVector3& u, const csDVector3& v,
00619 double A, double B, double C, double D,
00620 csDVector3& isect,
00621 double& dist);
00622
00631 static bool Plane (
00632 const csDVector3& u, const csDVector3& v,
00633 const csDPlane& p,
00634 csDVector3& isect,
00635 double& dist);
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,
00653 csDVector3& isect);
00654
00661 static double ZPlane (double zval,
00662 const csDVector3& u, const csDVector3& v,
00663 csDVector3& isect);
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__