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00024 #ifndef _VECMATH_H_
00025 #define _VECMATH_H_
00026
00027 #include <cmath>
00028 #include <QString>
00029
00030 template<class T> class Vector2;
00031 template<class T> class Vector3;
00032 template<class T> class Vector4;
00033 template<class T> class Matrix4;
00034
00035 typedef Vector2<double> Vec2d;
00036 typedef Vector2<float> Vec2f;
00037 typedef Vector2<int> Vec2i;
00038
00041 typedef Vector3<double> Vec3d;
00042
00045 typedef Vector3<float> Vec3f;
00046
00049 typedef Vector4<double> Vec4d;
00050
00053 typedef Vector4<float> Vec4f;
00054
00057 typedef Vector4<int> Vec4i;
00058
00061 typedef Matrix4<double> Mat4d;
00062
00065 typedef Matrix4<float> Mat4f;
00066
00067
00071 template<class T> class Vector2
00072 {
00073 public:
00074 inline Vector2();
00075 inline Vector2(const Vector2<T>&);
00076 inline Vector2(T, T);
00077
00078 inline Vector2& operator=(const Vector2<T>&);
00079 inline Vector2& operator=(const T*);
00080 inline void set(T, T);
00081
00082 inline bool operator==(const Vector2<T>&) const;
00083 inline bool operator!=(const Vector2<T>&) const;
00084
00085 inline const T& operator[](int x) const;
00086 inline T& operator[](int);
00087 inline operator const T*() const;
00088 inline operator T*();
00089
00090 inline Vector2& operator+=(const Vector2<T>&);
00091 inline Vector2& operator-=(const Vector2<T>&);
00092 inline Vector2& operator*=(T);
00093 inline Vector2& operator/=(T);
00094
00095 inline Vector2 operator-(const Vector2<T>&) const;
00096 inline Vector2 operator+(const Vector2<T>&) const;
00097
00098 inline Vector2 operator-() const;
00099 inline Vector2 operator+() const;
00100
00101 inline Vector2 operator*(T) const;
00102 inline Vector2 operator/(T) const;
00103
00104
00105 inline T dot(const Vector2<T>&) const;
00106
00107 inline T length() const;
00108 inline T lengthSquared() const;
00109 inline void normalize();
00110
00111 T v[2];
00112 };
00113
00114
00118 template<class T> class Vector3
00119 {
00120 public:
00121 inline Vector3();
00122 inline Vector3(const Vector3&);
00123 template <class T2> inline Vector3(const Vector3<T2>&);
00124 inline Vector3(T, T, T);
00125 inline Vector3(T);
00126
00127 inline Vector3& operator=(const Vector3&);
00128 inline Vector3& operator=(const T*);
00129 template <class T2> inline Vector3& operator=(const Vector3<T2>&);
00130 inline void set(T, T, T);
00131
00132 inline bool operator==(const Vector3<T>&) const;
00133 inline bool operator!=(const Vector3<T>&) const;
00134
00135 inline T& operator[](int);
00136 inline const T& operator[](int) const;
00137 inline operator const T*() const;
00138 inline operator T*();
00139 inline const T* data() const {return v;}
00140 inline T* data() {return v;}
00141
00142 inline Vector3& operator+=(const Vector3<T>&);
00143 inline Vector3& operator-=(const Vector3<T>&);
00144 inline Vector3& operator*=(T);
00145 inline Vector3& operator/=(T);
00146
00147 inline Vector3 operator-(const Vector3<T>&) const;
00148 inline Vector3 operator+(const Vector3<T>&) const;
00149
00150 inline Vector3 operator-() const;
00151 inline Vector3 operator+() const;
00152
00153 inline Vector3 operator*(T) const;
00154 inline Vector3 operator/(T) const;
00155
00156
00157 inline T dot(const Vector3<T>&) const;
00158 inline Vector3 operator^(const Vector3<T>&) const;
00159
00160
00161 inline T latitude() const;
00162
00163 inline T longitude() const;
00164
00165
00166 inline T angle(const Vector3<T>&) const;
00167
00168 inline T length() const;
00169 inline T lengthSquared() const;
00170 inline void normalize();
00171
00172 inline void transfo4d(const Mat4d&);
00173 inline void transfo4d(const Mat4f&);
00174 T v[3];
00175
00176 QString toString() const {return QString("[%1, %2, %3]").arg(v[0]).arg(v[1]).arg(v[2]);}
00177 QString toStringLonLat() const {return QString("[") + QString::number(longitude()*180./M_PI, 'g', 12) + "," + QString::number(latitude()*180./M_PI, 'g', 12)+"]";}
00178 };
00179
00180
00184 template<class T> class Vector4
00185 {
00186 public:
00187 inline Vector4();
00188 inline Vector4(const Vector4<T>&);
00189 inline Vector4(const Vector3<T>&);
00190 inline Vector4(T, T, T);
00191 inline Vector4(T, T, T, T);
00192
00193 inline Vector4& operator=(const Vector4<T>&);
00194 inline Vector4& operator=(const Vector3<T>&);
00195 inline Vector4& operator=(const T*);
00196 inline void set(T, T, T, T);
00197
00198 inline bool operator==(const Vector4<T>&) const;
00199 inline bool operator!=(const Vector4<T>&) const;
00200
00201 inline T& operator[](int);
00202 inline const T& operator[](int) const;
00203 inline operator T*();
00204 inline operator const T*() const;
00205
00206 inline Vector4& operator+=(const Vector4<T>&);
00207 inline Vector4& operator-=(const Vector4<T>&);
00208 inline Vector4& operator*=(T);
00209 inline Vector4& operator/=(T);
00210
00211 inline Vector4 operator-(const Vector4<T>&) const;
00212 inline Vector4 operator+(const Vector4<T>&) const;
00213
00214 inline Vector4 operator-() const;
00215 inline Vector4 operator+() const;
00216
00217 inline Vector4 operator*(T) const;
00218 inline Vector4 operator/(T) const;
00219
00220
00221 inline T dot(const Vector4<T>&) const;
00222
00223 inline T length() const;
00224 inline T lengthSquared() const;
00225 inline void normalize();
00226
00227 inline void transfo4d(const Mat4d&);
00228
00229 T v[4];
00230 };
00231
00235 template<class T> class Matrix4
00236 {
00237 public:
00238 Matrix4();
00239 Matrix4(const Matrix4<T>& m);
00240 Matrix4(T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T);
00241 Matrix4(const T*);
00242 Matrix4(const Vector4<T>&, const Vector4<T>&,
00243 const Vector4<T>&, const Vector4<T>&);
00244
00245 inline Matrix4& operator=(const Matrix4<T>&);
00246 inline Matrix4& operator=(const T*);
00247 inline void set(T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T);
00248
00249 inline T& operator[](int);
00250 inline operator T*();
00251 inline operator const T*() const;
00252
00253 inline Matrix4 operator-(const Matrix4<T>&) const;
00254 inline Matrix4 operator+(const Matrix4<T>&) const;
00255 inline Matrix4 operator*(const Matrix4<T>&) const;
00256
00257 inline Vector3<T> operator*(const Vector3<T>&) const;
00258 inline Vector3<T> multiplyWithoutTranslation(const Vector3<T>& a) const;
00259 inline Vector4<T> operator*(const Vector4<T>&) const;
00260
00261 inline void transfo(Vector3<T>&) const;
00262
00263 static Matrix4<T> identity();
00264 static Matrix4<T> translation(const Vector3<T>&);
00265
00266
00267 static Matrix4<T> rotation(const Vector3<T>&, T);
00268 static Matrix4<T> xrotation(T);
00269 static Matrix4<T> yrotation(T);
00270 static Matrix4<T> zrotation(T);
00271 static Matrix4<T> scaling(const Vector3<T>&);
00272 static Matrix4<T> scaling(T);
00273
00274 Matrix4<T> transpose() const;
00275 Matrix4<T> inverse() const;
00276
00277 inline void print(void) const;
00278
00279 T r[16];
00280 };
00281
00283 template<class T> QDataStream& operator<<(QDataStream& out, const Vector2<T>& v) {out << v[0] << v[1]; return out;}
00284 template<class T> QDataStream& operator<<(QDataStream& out, const Vector3<T>& v) {out << v[0] << v[1] << v[2]; return out;}
00285 template<class T> QDataStream& operator<<(QDataStream& out, const Vector4<T>& v) {out << v[0] << v[1] << v[2] << v[3]; return out;}
00286 template<class T> QDataStream& operator<<(QDataStream& out, const Matrix4<T>& m) {out << m[0] << m[1] << m[2] << m[3] << m[4] << m[5] << m[6] << m[7] << m[8] << m[9] << m[10] << m[11] << m[12] << m[13] << m[14] << m[15]; return out;}
00287
00288 template<class T> QDataStream& operator>>(QDataStream& in, Vector2<T>& v) {in >> v[0] >> v[1]; return in;}
00289 template<class T> QDataStream& operator>>(QDataStream& in, Vector3<T>& v) {in >> v[0] >> v[1] >> v[2]; return in;}
00290 template<class T> QDataStream& operator>>(QDataStream& in, Vector4<T>& v) {in >> v[0] >> v[1] >> v[2] >> v[3]; return in;}
00291 template<class T> QDataStream& operator>>(QDataStream& in, Matrix4<T>& m) {in >> m[0] >> m[1] >> m[2] >> m[3] >> m[4] >> m[5] >> m[6] >> m[7] >> m[8] >> m[9] >> m[10] >> m[11] >> m[12] >> m[13] >> m[14] >> m[15]; return in;}
00292
00294
00295 template<class T> Vector2<T>::Vector2() {}
00296
00297 template<class T> Vector2<T>::Vector2(const Vector2<T>& a)
00298 {
00299 v[0]=a.v[0]; v[1]=a.v[1];
00300 }
00301
00302 template<class T> Vector2<T>::Vector2(T x, T y)
00303 {
00304 v[0]=x; v[1]=y;
00305 }
00306
00307 template<class T> Vector2<T>& Vector2<T>::operator=(const Vector2<T>& a)
00308 {
00309 v[0]=a.v[0]; v[1]=a.v[1];
00310 return *this;
00311 }
00312
00313 template<class T> Vector2<T>& Vector2<T>::operator=(const T* a)
00314 {
00315 v[0]=a[0]; v[1]=a[1];
00316 return *this;
00317 }
00318
00319 template<class T> void Vector2<T>::set(T x, T y)
00320 {
00321 v[0]=x; v[1]=y;
00322 }
00323
00324
00325 template<class T> bool Vector2<T>::operator==(const Vector2<T>& a) const
00326 {
00327 return (v[0] == a.v[0] && v[1] == a.v[1]);
00328 }
00329
00330 template<class T> bool Vector2<T>::operator!=(const Vector2<T>& a) const
00331 {
00332 return (v[0] != a.v[0] || v[1] != a.v[1]);
00333 }
00334
00335 template<class T> const T& Vector2<T>::operator[](int x) const
00336 {
00337 return v[x];
00338 }
00339
00340 template<class T> T& Vector2<T>::operator[](int x)
00341 {
00342 return v[x];
00343 }
00344
00345 template<class T> Vector2<T>::operator const T*() const
00346 {
00347 return v;
00348 }
00349
00350 template<class T> Vector2<T>::operator T*()
00351 {
00352 return v;
00353 }
00354
00355
00356 template<class T> Vector2<T>& Vector2<T>::operator+=(const Vector2<T>& a)
00357 {
00358 v[0] += a.v[0]; v[1] += a.v[1];
00359 return *this;
00360 }
00361
00362 template<class T> Vector2<T>& Vector2<T>::operator-=(const Vector2<T>& a)
00363 {
00364 v[0] -= a.v[0]; v[1] -= a.v[1];
00365 return *this;
00366 }
00367
00368 template<class T> Vector2<T>& Vector2<T>::operator*=(T s)
00369 {
00370 v[0] *= s; v[1] *= s;
00371 return *this;
00372 }
00373
00374 template<class T> Vector2<T> Vector2<T>::operator-() const
00375 {
00376 return Vector2<T>(-v[0], -v[1]);
00377 }
00378
00379 template<class T> Vector2<T> Vector2<T>::operator+() const
00380 {
00381 return *this;
00382 }
00383
00384 template<class T> Vector2<T> Vector2<T>::operator+(const Vector2<T>& b) const
00385 {
00386 return Vector2<T>(v[0] + b.v[0], v[1] + b.v[1]);
00387 }
00388
00389 template<class T> Vector2<T> Vector2<T>::operator-(const Vector2<T>& b) const
00390 {
00391 return Vector2<T>(v[0] - b.v[0], v[1] - b.v[1]);
00392 }
00393
00394 template<class T> Vector2<T> Vector2<T>::operator*(T s) const
00395 {
00396 return Vector2<T>(s * v[0], s * v[1]);
00397 }
00398
00399 template<class T> Vector2<T> Vector2<T>::operator/(T s) const
00400 {
00401 return Vector2<T>(v[0]/s, v[1]/s);
00402 }
00403
00404
00405 template<class T> T Vector2<T>::dot(const Vector2<T>& b) const
00406 {
00407 return v[0] * b.v[0] + v[1] * b.v[1];
00408 }
00409
00410
00411 template<class T> T Vector2<T>::length() const
00412 {
00413 return (T) std::sqrt(v[0] * v[0] + v[1] * v[1]);
00414 }
00415
00416 template<class T> T Vector2<T>::lengthSquared() const
00417 {
00418 return v[0] * v[0] + v[1] * v[1];
00419 }
00420
00421 template<class T> void Vector2<T>::normalize()
00422 {
00423 T s = (T) 1 / std::sqrt(v[0] * v[0] + v[1] * v[1]);
00424 v[0] *= s;
00425 v[1] *= s;
00426 }
00427
00428
00429
00430
00431
00432
00434
00435 template<class T> Vector3<T>::Vector3() {}
00436
00437 template<class T> Vector3<T>::Vector3(const Vector3& a)
00438 {
00439 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2];
00440 }
00441
00442 template<class T> template<class T2> Vector3<T>::Vector3(const Vector3<T2>& a)
00443 {
00444 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2];
00445 }
00446
00447 template<class T> Vector3<T>::Vector3(T x)
00448 {
00449 v[0]=x; v[1]=x; v[2]=x;
00450 }
00451
00452 template<class T> Vector3<T>::Vector3(T x, T y, T z)
00453 {
00454 v[0]=x; v[1]=y; v[2]=z;
00455 }
00456
00457 template<class T> Vector3<T>& Vector3<T>::operator=(const Vector3& a)
00458 {
00459 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2];
00460 return *this;
00461 }
00462
00463 template<class T> template <class T2> Vector3<T>& Vector3<T>::operator=(const Vector3<T2>& a)
00464 {
00465 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2];
00466 return *this;
00467 }
00468
00469 template<class T> Vector3<T>& Vector3<T>::operator=(const T* a)
00470 {
00471 v[0]=a[0]; v[1]=a[1]; v[2]=a[2];
00472 return *this;
00473 }
00474
00475 template<class T> void Vector3<T>::set(T x, T y, T z)
00476 {
00477 v[0]=x; v[1]=y; v[2]=z;
00478 }
00479
00480
00481 template<class T> bool Vector3<T>::operator==(const Vector3<T>& a) const
00482 {
00483 return (v[0] == a.v[0] && v[1] == a.v[1] && v[2] == a.v[2]);
00484 }
00485
00486 template<class T> bool Vector3<T>::operator!=(const Vector3<T>& a) const
00487 {
00488 return (v[0] != a.v[0] || v[1] != a.v[1] || v[2] != a.v[2]);
00489 }
00490
00491
00492 template<class T> T& Vector3<T>::operator[](int x)
00493 {
00494 return v[x];
00495 }
00496
00497 template<class T> const T& Vector3<T>::operator[](int x) const
00498 {
00499 return v[x];
00500 }
00501
00502 template<class T> Vector3<T>::operator const T*() const
00503 {
00504 return v;
00505 }
00506
00507 template<class T> Vector3<T>::operator T*()
00508 {
00509 return v;
00510 }
00511
00512 template<class T> Vector3<T>& Vector3<T>::operator+=(const Vector3<T>& a)
00513 {
00514 v[0] += a.v[0]; v[1] += a.v[1]; v[2] += a.v[2];
00515 return *this;
00516 }
00517
00518 template<class T> Vector3<T>& Vector3<T>::operator-=(const Vector3<T>& a)
00519 {
00520 v[0] -= a.v[0]; v[1] -= a.v[1]; v[2] -= a.v[2];
00521 return *this;
00522 }
00523
00524 template<class T> Vector3<T>& Vector3<T>::operator*=(T s)
00525 {
00526 v[0] *= s; v[1] *= s; v[2] *= s;
00527 return *this;
00528 }
00529
00530 template<class T> Vector3<T>& Vector3<T>::operator/=(T s)
00531 {
00532 v[0] /= s; v[1] /= s; v[2] /= s;
00533 return *this;
00534 }
00535
00536 template<class T> Vector3<T> Vector3<T>::operator-() const
00537 {
00538 return Vector3<T>(-v[0], -v[1], -v[2]);
00539 }
00540
00541 template<class T> Vector3<T> Vector3<T>::operator+() const
00542 {
00543 return *this;
00544 }
00545
00546 template<class T> Vector3<T> Vector3<T>::operator+(const Vector3<T>& b) const
00547 {
00548 return Vector3<T>(v[0] + b.v[0], v[1] + b.v[1], v[2] + b.v[2]);
00549 }
00550
00551 template<class T> Vector3<T> Vector3<T>::operator-(const Vector3<T>& b) const
00552 {
00553 return Vector3<T>(v[0] - b.v[0], v[1] - b.v[1], v[2] - b.v[2]);
00554 }
00555
00556 template<class T> Vector3<T> Vector3<T>::operator*(T s) const
00557 {
00558 return Vector3<T>(s * v[0], s * v[1], s * v[2]);
00559 }
00560
00561 template<class T> Vector3<T> Vector3<T>::operator/(T s) const
00562 {
00563 return Vector3<T>(v[0]/s, v[1]/s, v[2]/s);
00564 }
00565
00566
00567 template<class T> T Vector3<T>::dot(const Vector3<T>& b) const
00568 {
00569 return v[0] * b.v[0] + v[1] * b.v[1] + v[2] * b.v[2];
00570 }
00571
00572
00573
00574 template<class T> Vector3<T> Vector3<T>::operator^(const Vector3<T>& b) const
00575 {
00576 return Vector3<T>(v[1] * b.v[2] - v[2] * b.v[1],
00577 v[2] * b.v[0] - v[0] * b.v[2],
00578 v[0] * b.v[1] - v[1] * b.v[0]);
00579 }
00580
00581
00582 template<class T> T Vector3<T>::angle(const Vector3<T>& b) const
00583 {
00584 return std::acos(dot(b)/sqrt(lengthSquared()*b.lengthSquared()));
00585 }
00586
00587 template<class T> T Vector3<T>::length() const
00588 {
00589 return (T) sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
00590 }
00591
00592 template<class T> T Vector3<T>::lengthSquared() const
00593 {
00594 return v[0] * v[0] + v[1] * v[1] + v[2] * v[2];
00595 }
00596
00597 template<class T> void Vector3<T>::normalize()
00598 {
00599 T s = (T) (1. / std::sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]));
00600 v[0] *= s;
00601 v[1] *= s;
00602 v[2] *= s;
00603 }
00604
00605 template<class T> void Vector3<T>::transfo4d(const Mat4d& m)
00606 {
00607 const T v0 = v[0];
00608 const T v1 = v[1];
00609 v[0]=m.r[0]*v0 + m.r[4]*v1 + m.r[8]*v[2] + m.r[12];
00610 v[1]=m.r[1]*v0 + m.r[5]*v1 + m.r[9]*v[2] + m.r[13];
00611 v[2]=m.r[2]*v0 + m.r[6]*v1 + m.r[10]*v[2] + m.r[14];
00612 }
00613
00614 template<class T> void Vector3<T>::transfo4d(const Mat4f& m)
00615 {
00616 const T v0 = v[0];
00617 const T v1 = v[1];
00618 v[0]=m.r[0]*v0 + m.r[4]*v1 + m.r[8]*v[2] + m.r[12];
00619 v[1]=m.r[1]*v0 + m.r[5]*v1 + m.r[9]*v[2] + m.r[13];
00620 v[2]=m.r[2]*v0 + m.r[6]*v1 + m.r[10]*v[2] + m.r[14];
00621 }
00622
00623
00624 template<class T> T Vector3<T>::latitude() const
00625 {
00626 return std::asin(v[2]/length());
00627 }
00628
00629
00630 template<class T> T Vector3<T>::longitude() const
00631 {
00632 return std::atan2(v[1],v[0]);
00633 }
00634
00635
00637
00638 template<class T> Vector4<T>::Vector4() {}
00639
00640 template<class T> Vector4<T>::Vector4(const Vector4<T>& a)
00641 {
00642 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=a.v[3];
00643 }
00644
00645 template<class T> Vector4<T>::Vector4(const Vector3<T>& a)
00646 {
00647 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=1;
00648 }
00649
00650 template<class T> Vector4<T>::Vector4(T x, T y, T z)
00651 {
00652 v[0]=x; v[1]=y; v[2]=z; v[3]=1;
00653 }
00654
00655 template<class T> Vector4<T>::Vector4(T x, T y, T z, T a)
00656 {
00657 v[0]=x; v[1]=y; v[2]=z; v[3]=a;
00658 }
00659
00660 template<class T> Vector4<T>& Vector4<T>::operator=(const Vector4<T>& a)
00661 {
00662 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=a.v[3];
00663 return *this;
00664 }
00665
00666 template<class T> Vector4<T>& Vector4<T>::operator=(const Vector3<T>& a)
00667 {
00668 v[0]=a.v[0]; v[1]=a.v[1]; v[2]=a.v[2]; v[3]=1;
00669 return *this;
00670 }
00671
00672 template<class T> Vector4<T>& Vector4<T>::operator=(const T* a)
00673 {
00674 v[0]=a[0]; v[1]=a[1]; v[2]=a[2]; v[3]=a[3];
00675 return *this;
00676 }
00677
00678 template<class T> void Vector4<T>::set(T x, T y, T z, T a)
00679 {
00680 v[0]=x; v[1]=y; v[2]=z; v[3]=a;
00681 }
00682
00683 template<class T> bool Vector4<T>::operator==(const Vector4<T>& a) const
00684 {
00685 return (v[0] == a.v[0] && v[1] == a.v[1] && v[2] == a.v[2] && v[3] == a.v[3]);
00686 }
00687
00688 template<class T> bool Vector4<T>::operator!=(const Vector4<T>& a) const
00689 {
00690 return (v[0] != a.v[0] || v[1] != a.v[1] || v[2] != a.v[2] || v[3] != a.v[3]);
00691 }
00692
00693 template<class T> T& Vector4<T>::operator[](int x)
00694 {
00695 return v[x];
00696 }
00697
00698 template<class T> const T& Vector4<T>::operator[](int x) const
00699 {
00700 return v[x];
00701 }
00702
00703 template<class T> Vector4<T>::operator T*()
00704 {
00705 return v;
00706 }
00707
00708 template<class T> Vector4<T>::operator const T*() const
00709 {
00710 return v;
00711 }
00712
00713 template<class T> Vector4<T>& Vector4<T>::operator+=(const Vector4<T>& a)
00714 {
00715 v[0] += a.v[0]; v[1] += a.v[1]; v[2] += a.v[2]; v[3] += a.v[3];
00716 return *this;
00717 }
00718
00719 template<class T> Vector4<T>& Vector4<T>::operator-=(const Vector4<T>& a)
00720 {
00721 v[0] -= a.v[0]; v[1] -= a.v[1]; v[2] -= a.v[2]; v[3] -= a/v[3];
00722 return *this;
00723 }
00724
00725 template<class T> Vector4<T>& Vector4<T>::operator*=(T s)
00726 {
00727 v[0] *= s; v[1] *= s; v[2] *= s; v[3] *= s;
00728 return *this;
00729 }
00730
00731 template<class T> Vector4<T> Vector4<T>::operator-() const
00732 {
00733 return Vector4<T>(-v[0], -v[1], -v[2], -v[3]);
00734 }
00735
00736 template<class T> Vector4<T> Vector4<T>::operator+() const
00737 {
00738 return *this;
00739 }
00740
00741 template<class T> Vector4<T> Vector4<T>::operator+(const Vector4<T>& b) const
00742 {
00743 return Vector4<T>(v[0] + b.v[0], v[1] + b.v[1], v[2] + b.v[2], v[3] + b.v[3]);
00744 }
00745
00746 template<class T> Vector4<T> Vector4<T>::operator-(const Vector4<T>& b) const
00747 {
00748 return Vector4<T>(v[0] - b.v[0], v[1] - b.v[1], v[2] - b.v[2], v[3] - b.v[3]);
00749 }
00750
00751 template<class T> Vector4<T> Vector4<T>::operator*(T s) const
00752 {
00753 return Vector4<T>(s * v[0], s * v[1], s * v[2], s * v[3]);
00754 }
00755
00756 template<class T> Vector4<T> Vector4<T>::operator/(T s) const
00757 {
00758 return Vector4<T>(v[0]/s, v[1]/s, v[2]/s, v[3]/s);
00759 }
00760
00761 template<class T> T Vector4<T>::dot(const Vector4<T>& b) const
00762 {
00763 return v[0] * b.v[0] + v[1] * b.v[1] + v[2] * b.v[2] + v[3] * b.v[3];
00764 }
00765
00766 template<class T> T Vector4<T>::length() const
00767 {
00768 return (T) sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3]);
00769 }
00770
00771 template<class T> T Vector4<T>::lengthSquared() const
00772 {
00773 return v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3];
00774 }
00775
00776 template<class T> void Vector4<T>::normalize()
00777 {
00778 T s = (T) (1. / sqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + v[3] * v[3]));
00779 v[0] *= s;
00780 v[1] *= s;
00781 v[2] *= s;
00782 v[3] *= s;
00783 }
00784
00785 template<class T> void Vector4<T>::transfo4d(const Mat4d& m)
00786 {
00787 (*this)=m*(*this);
00788 }
00789
00790
00791
00792
00793
00794
00795
00797
00798 template<class T> Matrix4<T>::Matrix4() {}
00799
00800 template<class T> Matrix4<T>::Matrix4(const Matrix4<T>& m)
00801 {
00802 memcpy(r,m.r,sizeof(T)*16);
00803 }
00804
00805 template<class T> Matrix4<T>::Matrix4(const T* m)
00806 {
00807 memcpy(r,m,sizeof(T)*16);
00808 }
00809
00810 template<class T> Matrix4<T>& Matrix4<T>::operator=(const Matrix4<T>& m)
00811 {
00812 memcpy(r,m.r,sizeof(T)*16);
00813 return (*this);
00814 }
00815
00816 template<class T> Matrix4<T>::Matrix4(const Vector4<T>& v0,
00817 const Vector4<T>& v1,
00818 const Vector4<T>& v2,
00819 const Vector4<T>& v3)
00820 {
00821 r[0] = v0.v[0];
00822 r[1] = v0.v[1];
00823 r[2] = v0.v[2];
00824 r[3] = v0.v[3];
00825 r[4] = v1.v[0];
00826 r[5] = v1.v[1];
00827 r[6] = v1.v[2];
00828 r[7] = v1.v[3];
00829 r[8] = v2.v[0];
00830 r[9] = v2.v[1];
00831 r[10] = v2.v[2];
00832 r[11] = v2.v[3];
00833 r[12] = v3.v[0];
00834 r[13] = v3.v[1];
00835 r[14] = v3.v[2];
00836 r[15] = v3.v[3];
00837 }
00838
00839
00840 template<class T> Matrix4<T>::Matrix4(T a, T b, T c, T d, T e, T f, T g, T h, T i, T j, T k, T l, T m, T n, T o, T p)
00841 {
00842 r[0]=a; r[1]=b; r[2]=c; r[3]=d; r[4]=e; r[5]=f; r[6]=g; r[7]=h;
00843 r[8]=i; r[9]=j; r[10]=k; r[11]=l; r[12]=m; r[13]=n; r[14]=o; r[15]=p;
00844 }
00845
00846 template<class T> void Matrix4<T>::set(T a, T b, T c, T d, T e, T f, T g, T h, T i, T j, T k, T l, T m, T n, T o, T p)
00847 {
00848 r[0]=a; r[1]=b; r[2]=c; r[3]=d; r[4]=e; r[5]=f; r[6]=g; r[7]=h;
00849 r[8]=i; r[9]=j; r[10]=k; r[11]=l; r[12]=m; r[13]=n; r[14]=o; r[15]=p;
00850 }
00851
00852 template<class T> T& Matrix4<T>::operator[](int n)
00853 {
00854 return r[n];
00855 }
00856
00857 template<class T> Matrix4<T>::operator T*()
00858 {
00859 return r;
00860 }
00861
00862 template<class T> Matrix4<T>::operator const T*() const
00863 {
00864 return r;
00865 }
00866
00867 template<class T> Matrix4<T> Matrix4<T>::identity()
00868 {
00869 return Matrix4<T>( 1, 0, 0, 0,
00870 0, 1, 0, 0,
00871 0, 0, 1, 0,
00872 0, 0, 0, 1 );
00873 }
00874
00875
00876 template<class T> Matrix4<T> Matrix4<T>::translation(const Vector3<T>& a)
00877 {
00878 return Matrix4<T>( 1, 0, 0, 0,
00879 0, 1, 0, 0,
00880 0, 0, 1, 0,
00881 a.v[0], a.v[1], a.v[2], 1);
00882 }
00883
00884
00885 template<class T> Matrix4<T> Matrix4<T>::rotation(const Vector3<T>& axis, T angle)
00886 {
00887 Vec3d a(axis);
00888 a.normalize();
00889 const T c = (T) cos(angle);
00890 const T s = (T) sin(angle);
00891 const T d = 1-c;
00892 return Matrix4<T>( a[0]*a[0]*d+c , a[1]*a[0]*d+a[2]*s, a[0]*a[2]*d-a[1]*s, 0,
00893 a[0]*a[1]*d-a[2]*s, a[1]*a[1]*d+c , a[1]*a[2]*d+a[0]*s, 0,
00894 a[0]*a[2]*d+a[1]*s, a[1]*a[2]*d-a[0]*s, a[2]*a[2]*d+c , 0,
00895 0,0,0,1 );
00896 }
00897
00898 template<class T> Matrix4<T> Matrix4<T>::xrotation(T angle)
00899 {
00900 T c = (T) cos(angle);
00901 T s = (T) sin(angle);
00902
00903 return Matrix4<T>(1, 0, 0, 0,
00904 0, c, s, 0,
00905 0,-s, c, 0,
00906 0, 0, 0, 1 );
00907 }
00908
00909
00910 template<class T> Matrix4<T> Matrix4<T>::yrotation(T angle)
00911 {
00912 T c = (T) cos(angle);
00913 T s = (T) sin(angle);
00914
00915 return Matrix4<T>( c, 0,-s, 0,
00916 0, 1, 0, 0,
00917 s, 0, c, 0,
00918 0, 0, 0, 1 );
00919 }
00920
00921
00922 template<class T> Matrix4<T> Matrix4<T>::zrotation(T angle)
00923 {
00924 T c = (T) cos(angle);
00925 T s = (T) sin(angle);
00926
00927 return Matrix4<T>(c, s, 0, 0,
00928 -s, c, 0, 0,
00929 0, 0, 1, 0,
00930 0, 0, 0, 1 );
00931 }
00932
00933
00934 template<class T> Matrix4<T> Matrix4<T>::scaling(const Vector3<T>& s)
00935 {
00936 return Matrix4<T>(s[0], 0 , 0 , 0,
00937 0 ,s[1], 0 , 0,
00938 0 , 0 ,s[2], 0,
00939 0 , 0 , 0 , 1);
00940 }
00941
00942
00943 template<class T> Matrix4<T> Matrix4<T>::scaling(T scale)
00944 {
00945 return scaling(Vector3<T>(scale, scale, scale));
00946 }
00947
00948
00949 template<class T> Vector3<T> Matrix4<T>::operator*(const Vector3<T>& a) const
00950 {
00951 return Vector3<T>( r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12],
00952 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13],
00953 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14] );
00954 }
00955
00956 template<class T> Vector3<T> Matrix4<T>::multiplyWithoutTranslation(const Vector3<T>& a) const
00957 {
00958 return Vector3<T>( r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2],
00959 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2],
00960 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] );
00961 }
00962
00963
00964 template<class T> Vector4<T> Matrix4<T>::operator*(const Vector4<T>& a) const
00965 {
00966 return Vector4<T>( r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12]*a.v[3],
00967 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13]*a.v[3],
00968 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14]*a.v[3] );
00969 }
00970
00971 template<class T> void Matrix4<T>::transfo(Vector3<T>& a) const
00972 {
00973 a.set( r[0]*a.v[0] + r[4]*a.v[1] + r[8]*a.v[2] + r[12],
00974 r[1]*a.v[0] + r[5]*a.v[1] + r[9]*a.v[2] + r[13],
00975 r[2]*a.v[0] + r[6]*a.v[1] + r[10]*a.v[2] + r[14]);
00976 }
00977
00978 template<class T> Matrix4<T> Matrix4<T>::transpose() const
00979 {
00980 return Matrix4<T>( r[0], r[4], r[8], r[12],
00981 r[1], r[5], r[9], r[13],
00982 r[2], r[6], r[10], r[14],
00983 r[3], r[7], r[11], r[15]);
00984 }
00985
00986 template<class T> Matrix4<T> Matrix4<T>::operator*(const Matrix4<T>& a) const
00987 {
00988 #define MATMUL(R, C) (r[R] * a.r[C] + r[R+4] * a.r[C+1] + r[R+8] * a.r[C+2] + r[R+12] * a.r[C+3])
00989 return Matrix4<T>( MATMUL(0,0), MATMUL(1,0), MATMUL(2,0), MATMUL(3,0),
00990 MATMUL(0,4), MATMUL(1,4), MATMUL(2,4), MATMUL(3,4),
00991 MATMUL(0,8), MATMUL(1,8), MATMUL(2,8), MATMUL(3,8),
00992 MATMUL(0,12), MATMUL(1,12), MATMUL(2,12), MATMUL(3,12) );
00993 #undef MATMUL
00994 }
00995
00996
00997 template<class T> Matrix4<T> Matrix4<T>::operator+(const Matrix4<T>& a) const
00998 {
00999 return Matrix4<T>( r[0]+a.r[0], r[1]+a.r[1], r[2]+a.r[2], r[3]+a.r[3],
01000 r[4]+a.r[4], r[5]+a.r[5], r[6]+a.r[6], r[7]+a.r[7],
01001 r[8]+a.r[8], r[9]+a.r[9], r[10]+a.r[10], r[11]+a.r[11],
01002 r[12]+a.r[12], r[13]+a.r[13], r[14]+a.r[14], r[15]+a.r[15] );
01003 }
01004
01005 template<class T> Matrix4<T> Matrix4<T>::operator-(const Matrix4<T>& a) const
01006 {
01007 return Matrix4<T>( r[0]-a.r[0], r[1]-a.r[1], r[2]-a.r[2], r[3]-a.r[3],
01008 r[4]-a.r[4], r[5]-a.r[5], r[6]-a.r[6], r[7]-a.r[7],
01009 r[8]-a.r[8], r[9]-a.r[9], r[10]-a.r[10], r[11]-a.r[11],
01010 r[12]-a.r[12], r[13]-a.r[13], r[14]-a.r[14], r[15]-a.r[15] );
01011 }
01012
01013
01014
01015
01016
01017
01018
01019 template<class T> Matrix4<T> Matrix4<T>::inverse() const
01020 {
01021 const T * m = r;
01022 T out[16];
01023
01024
01025 #define SWAP_ROWS(a, b) { T *_tmp = a; (a)=(b); (b)=_tmp; }
01026 #define MAT(m,r,c) (m)[(c)*4+(r)]
01027
01028 T wtmp[4][8];
01029 T m0, m1, m2, m3, s;
01030 T *r0, *r1, *r2, *r3;
01031
01032 r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3];
01033
01034 r0[0] = MAT(m, 0, 0), r0[1] = MAT(m, 0, 1),
01035 r0[2] = MAT(m, 0, 2), r0[3] = MAT(m, 0, 3),
01036 r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0,
01037 r1[0] = MAT(m, 1, 0), r1[1] = MAT(m, 1, 1),
01038 r1[2] = MAT(m, 1, 2), r1[3] = MAT(m, 1, 3),
01039 r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0,
01040 r2[0] = MAT(m, 2, 0), r2[1] = MAT(m, 2, 1),
01041 r2[2] = MAT(m, 2, 2), r2[3] = MAT(m, 2, 3),
01042 r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0,
01043 r3[0] = MAT(m, 3, 0), r3[1] = MAT(m, 3, 1),
01044 r3[2] = MAT(m, 3, 2), r3[3] = MAT(m, 3, 3),
01045 r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0;
01046
01047
01048 if (fabs(r3[0]) > fabs(r2[0]))
01049 SWAP_ROWS(r3, r2);
01050 if (fabs(r2[0]) > fabs(r1[0]))
01051 SWAP_ROWS(r2, r1);
01052 if (fabs(r1[0]) > fabs(r0[0]))
01053 SWAP_ROWS(r1, r0);
01054 if (0.0 == r0[0])
01055 return Matrix4<T>();
01056
01057
01058 m1 = r1[0] / r0[0];
01059 m2 = r2[0] / r0[0];
01060 m3 = r3[0] / r0[0];
01061 s = r0[1];
01062 r1[1] -= m1 * s;
01063 r2[1] -= m2 * s;
01064 r3[1] -= m3 * s;
01065 s = r0[2];
01066 r1[2] -= m1 * s;
01067 r2[2] -= m2 * s;
01068 r3[2] -= m3 * s;
01069 s = r0[3];
01070 r1[3] -= m1 * s;
01071 r2[3] -= m2 * s;
01072 r3[3] -= m3 * s;
01073 s = r0[4];
01074 if (s != 0.0) {
01075 r1[4] -= m1 * s;
01076 r2[4] -= m2 * s;
01077 r3[4] -= m3 * s;
01078 }
01079 s = r0[5];
01080 if (s != 0.0) {
01081 r1[5] -= m1 * s;
01082 r2[5] -= m2 * s;
01083 r3[5] -= m3 * s;
01084 }
01085 s = r0[6];
01086 if (s != 0.0) {
01087 r1[6] -= m1 * s;
01088 r2[6] -= m2 * s;
01089 r3[6] -= m3 * s;
01090 }
01091 s = r0[7];
01092 if (s != 0.0) {
01093 r1[7] -= m1 * s;
01094 r2[7] -= m2 * s;
01095 r3[7] -= m3 * s;
01096 }
01097
01098
01099 if (fabs(r3[1]) > fabs(r2[1]))
01100 SWAP_ROWS(r3, r2);
01101 if (fabs(r2[1]) > fabs(r1[1]))
01102 SWAP_ROWS(r2, r1);
01103 if (0.0 == r1[1])
01104 return Matrix4<T>();
01105
01106
01107 m2 = r2[1] / r1[1];
01108 m3 = r3[1] / r1[1];
01109 r2[2] -= m2 * r1[2];
01110 r3[2] -= m3 * r1[2];
01111 r2[3] -= m2 * r1[3];
01112 r3[3] -= m3 * r1[3];
01113 s = r1[4];
01114 if (0.0 != s) {
01115 r2[4] -= m2 * s;
01116 r3[4] -= m3 * s;
01117 }
01118 s = r1[5];
01119 if (0.0 != s) {
01120 r2[5] -= m2 * s;
01121 r3[5] -= m3 * s;
01122 }
01123 s = r1[6];
01124 if (0.0 != s) {
01125 r2[6] -= m2 * s;
01126 r3[6] -= m3 * s;
01127 }
01128 s = r1[7];
01129 if (0.0 != s) {
01130 r2[7] -= m2 * s;
01131 r3[7] -= m3 * s;
01132 }
01133
01134
01135 if (fabs(r3[2]) > fabs(r2[2]))
01136 SWAP_ROWS(r3, r2);
01137 if (0.0 == r2[2])
01138 return Matrix4<T>();
01139
01140
01141 m3 = r3[2] / r2[2];
01142 r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4],
01143 r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7];
01144
01145
01146 if (0.0 == r3[3])
01147 return Matrix4<T>();
01148
01149 s = 1.0 / r3[3];
01150 r3[4] *= s;
01151 r3[5] *= s;
01152 r3[6] *= s;
01153 r3[7] *= s;
01154
01155 m2 = r2[3];
01156 s = 1.0 / r2[2];
01157 r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2),
01158 r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2);
01159 m1 = r1[3];
01160 r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1,
01161 r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1;
01162 m0 = r0[3];
01163 r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0,
01164 r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0;
01165
01166 m1 = r1[2];
01167 s = 1.0 / r1[1];
01168 r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1),
01169 r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1);
01170 m0 = r0[2];
01171 r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0,
01172 r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0;
01173
01174 m0 = r0[1];
01175 s = 1.0 / r0[0];
01176 r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0),
01177 r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0);
01178
01179 MAT(out, 0, 0) = r0[4];
01180 MAT(out, 0, 1) = r0[5], MAT(out, 0, 2) = r0[6];
01181 MAT(out, 0, 3) = r0[7], MAT(out, 1, 0) = r1[4];
01182 MAT(out, 1, 1) = r1[5], MAT(out, 1, 2) = r1[6];
01183 MAT(out, 1, 3) = r1[7], MAT(out, 2, 0) = r2[4];
01184 MAT(out, 2, 1) = r2[5], MAT(out, 2, 2) = r2[6];
01185 MAT(out, 2, 3) = r2[7], MAT(out, 3, 0) = r3[4];
01186 MAT(out, 3, 1) = r3[5], MAT(out, 3, 2) = r3[6];
01187 MAT(out, 3, 3) = r3[7];
01188
01189 return Matrix4<T>(out);
01190
01191 #undef MAT
01192 #undef SWAP_ROWS
01193 }
01194
01195
01196 template<class T> void Matrix4<T>::print(void) const
01197 {
01198 printf("[%5.2lf %5.2lf %5.2lf %17.12le]\n"
01199 "[%5.2lf %5.2lf %5.2lf %17.12le]\n"
01200 "[%5.2lf %5.2lf %5.2lf %17.12le]\n"
01201 "[%5.2lf %5.2lf %5.2lf %17.12le]\n\n",
01202 r[0],r[4],r[8],r[12],
01203 r[1],r[5],r[9],r[13],
01204 r[2],r[6],r[10],r[14],
01205 r[3],r[7],r[11],r[15]);
01206 }
01207
01208
01209 template<class T> inline
01210 T operator*(const Vector2<T>&a,const Vector2<T>&b) {
01211 return a.v[0] * b.v[0] + a.v[1] * b.v[1];
01212 }
01213
01214 template<class T> inline
01215 T operator*(const Vector3<T>&a,const Vector3<T>&b) {
01216 return a.v[0] * b.v[0] + a.v[1] * b.v[1] + a.v[2] * b.v[2];
01217 }
01218
01219 template<class T> inline
01220 T operator*(const Vector4<T>&a,const Vector4<T>&b) {
01221 return a.v[0]*b.v[0] + a.v[1]*b.v[1] + a.v[2]*b.v[2] + a.v[3]*b.v[3];
01222 }
01223
01224 template<class T> inline
01225 Vector2<T> operator*(T s,const Vector2<T>&v) {
01226 return Vector2<T>(s*v[0],s*v[1]);
01227 }
01228
01229 template<class T> inline
01230 Vector3<T> operator*(T s,const Vector3<T>&v) {
01231 return Vector3<T>(s*v[0],s*v[1],s*v[2]);
01232 }
01233
01234 template<class T> inline
01235 Vector4<T> operator*(T s,const Vector4<T>&v) {
01236 return Vector4<T>(s*v[0],s*v[1],s*v[2],s*v[3]);
01237 }
01238
01239
01240 #endif // _VECMATH_H_