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00020 #ifndef TG_MATHLIB_H
00021 #define TG_MATHLIB_H
00022
00023 #include <math.h>
00024 #include <stdlib.h>
00025
00026 #ifndef PI
00027 #define PI 3.14159265358979323846f
00028 #endif
00029
00030
00031 #define DEG2RAD (PI / 180.0f)
00032 #define RAD2DEG (180.0f / PI)
00033
00034
00035
00036 struct vec2;
00037 struct vec3;
00038 struct vec4;
00039 struct mat3;
00040 struct mat4;
00041 struct quat;
00042
00043 const float epsilon = 1e-6f;
00044
00045 inline unsigned int ilog2(unsigned int value)
00046 {
00047 unsigned int f=0, s=32;
00048 while(s) {
00049 s>>=1;
00050 if( value > static_cast<unsigned int>(1<<(f+s)) ) f+=s;
00051 }
00052 return (f+1);
00053 }
00054
00055
00056
00057
00058
00059
00060
00061 struct vec2 {
00062
00063 inline vec2() : x(0), y(0) { }
00064 inline vec2(float x,float y) : x(x), y(y) { }
00065 inline vec2(const float *v) : x(v[0]), y(v[1]) { }
00066 inline vec2(const vec2 &v) : x(v.x), y(v.y) { }
00067
00068 inline int operator==(const vec2 &v) { return (fabs(x - v.x) < epsilon && fabs(y - v.y) < epsilon); }
00069 inline int operator!=(const vec2 &v) { return !(*this == v); }
00070
00071 inline const vec2 operator*(float f) const { return vec2(x * f,y * f); }
00072 inline const vec2 operator/(float f) const { float vf = 1.0f/f; return vec2(x * vf,y * vf); }
00073 inline const vec2 operator+(const vec2 &v) const { return vec2(x + v.x,y + v.y); }
00074 inline const vec2 operator-() const { return vec2(-x,-y); }
00075 inline const vec2 operator-(const vec2 &v) const { return vec2(x - v.x,y - v.y); }
00076
00077 inline vec2 &operator*=(float f) { return *this = *this * f; }
00078 inline vec2 &operator/=(float f) { return *this = *this / f; }
00079 inline vec2 &operator+=(const vec2 &v) { return *this = *this + v; }
00080 inline vec2 &operator-=(const vec2 &v) { return *this = *this - v; }
00081
00082 inline float operator*(const vec2 &v) const { return x * v.x + y * v.y; }
00083
00084 inline operator float*() { return (float*)&x; }
00085 inline operator const float*() const { return (float*)&x; }
00086
00087 inline float &operator[](int i) { return ((float*)&x)[i]; }
00088 inline float operator[](int i) const { return v[i]; }
00089
00090 inline float length() const { return sqrt(x * x + y * y); }
00091 inline float normalize() {
00092 float inv,length = sqrt(x * x + y * y);
00093 if(length < epsilon) return 0.0;
00094 inv = 1.0f / length;
00095 x *= inv;
00096 y *= inv;
00097 return length;
00098 }
00099 inline void absolute(){
00100 x = abs(x);
00101 y = abs(y);
00102 }
00103
00104 union {
00105 struct {
00106 float x,y;
00107 };
00108 float v[2];
00109 };
00110 };
00111
00112
00113
00114
00115
00116
00117
00118 struct vec3 {
00119
00120 inline vec3() : x(0), y(0), z(0) { }
00121 inline vec3(float x,float y,float z) : x(x), y(y), z(z) { }
00122 inline vec3(const float *v) : x(v[0]), y(v[1]), z(v[2]) { }
00123 inline vec3(const vec3 &v) : x(v.x), y(v.y), z(v.z) { }
00124 inline vec3(const vec4 &v);
00125
00126 inline void random(){ x = float(rand())/float(RAND_MAX);
00127 y = float(rand())/float(RAND_MAX);
00128 z = float(rand())/float(RAND_MAX); }
00129
00130 inline int operator==(const vec3 &v) { return (fabs(x - v.x) < epsilon && fabs(y - v.y) < epsilon && fabs(z - v.z) < epsilon); }
00131 inline int operator!=(const vec3 &v) { return !(*this == v); }
00132
00133 inline const vec3 operator*(float f) const { return vec3(x * f,y * f,z * f); }
00134 inline const vec3 operator/(float f) const { float vf = 1.0f/f; return vec3(x * vf,y * vf,z * vf); }
00135 inline const vec3 operator+(const vec3 &v) const { return vec3(x + v.x,y + v.y,z + v.z); }
00136 inline const vec3 operator-() const { return vec3(-x,-y,-z); }
00137 inline const vec3 operator-(const vec3 &v) const { return vec3(x - v.x,y - v.y,z - v.z); }
00138 inline const vec3 operator^(const vec3 &v) const { return vec3(y * v.z - z * v.y,
00139 z * v.x - x * v.z, x * v.y - y * v.x); }
00140
00141 inline vec3 &operator*=(float f) { return *this = *this * f; }
00142 inline vec3 &operator/=(float f) { return *this = *this / f; }
00143 inline vec3 &operator+=(const vec3 &v) { return *this = *this + v; }
00144 inline vec3 &operator-=(const vec3 &v) { return *this = *this - v; }
00145
00146 inline float operator*(const vec3 &v) const { return x * v.x + y * v.y + z * v.z; }
00147 inline float operator*(const vec4 &v) const;
00148
00149 inline operator float*() { return &x; }
00150 inline operator const float*() const { return &x; }
00151
00152 inline float &operator[](int i) { return v[i]; }
00153 inline float operator[](int i) const { return v[i]; }
00154
00155 inline float length() const { return sqrt(x * x + y * y + z * z); }
00156 inline float normalize() {
00157 float length = sqrt(x * x + y * y + z * z);
00158 if(length < epsilon) return 0.0;
00159 float inv = 1.0f / length;
00160 x *= inv;
00161 y *= inv;
00162 z *= inv;
00163 return length;
00164 }
00165
00166 inline void cross(const vec3 &v1,const vec3 &v2) {
00167 x = v1.y * v2.z - v1.z * v2.y;
00168 y = v1.z * v2.x - v1.x * v2.z;
00169 z = v1.x * v2.y - v1.y * v2.x;
00170 }
00171 inline void absolute(){
00172 x = abs(x);
00173 y = abs(y);
00174 z = abs(z);
00175 }
00176
00177 union {
00178 struct {
00179 float x,y,z;
00180 };
00181 float v[3];
00182 };
00183 };
00184
00185 inline vec3 normalize(const vec3 &v) {
00186 float length = v.length();
00187 if(length < epsilon) return vec3(0,0,0);
00188 return v / length;
00189 }
00190
00191 inline vec3 cross(const vec3 &v1,const vec3 &v2) {
00192 vec3 ret;
00193 ret.x = v1.y * v2.z - v1.z * v2.y;
00194 ret.y = v1.z * v2.x - v1.x * v2.z;
00195 ret.z = v1.x * v2.y - v1.y * v2.x;
00196 return ret;
00197 }
00198
00199 inline vec3 absolute(const vec3 &v1) {
00200 vec3 ret;
00201 ret.x = abs(v1.x);
00202 ret.y = abs(v1.y);
00203 ret.z = abs(v1.z);
00204 return ret;
00205 }
00206
00207 inline vec3 saturate(const vec3 &v) {
00208 vec3 ret = v;
00209 if(ret.x < 0.0) ret.x = 0.0;
00210 else if(ret.x > 1.0f) ret.x = 1.0f;
00211 if(ret.y < 0.0) ret.y = 0.0;
00212 else if(ret.y > 1.0f) ret.y = 1.0f;
00213 if(ret.z < 0.0) ret.z = 0.0;
00214 else if(ret.z > 1.0f) ret.z = 1.0f;
00215 return ret;
00216 }
00217
00218
00219
00220
00221
00222
00223
00224 struct vec4 {
00225
00226 inline vec4() : x(0), y(0), z(0), w(1) { }
00227 inline vec4(float x,float y,float z,float w) : x(x), y(y), z(z), w(w) { }
00228 inline vec4(const float *v) : x(v[0]), y(v[1]), z(v[2]), w(v[3]) { }
00229 inline vec4(const vec3 &v) : x(v.x), y(v.y), z(v.z), w(1) { }
00230 inline vec4(const vec3 &v,float w) : x(v.x), y(v.y), z(v.z), w(w) { }
00231 inline vec4(const vec4 &v) : x(v.x), y(v.y), z(v.z), w(v.w) { }
00232
00233 inline void random(){ x = float(rand())/float(RAND_MAX);
00234 y = float(rand())/float(RAND_MAX);
00235 z = float(rand())/float(RAND_MAX);
00236 w = float(rand())/float(RAND_MAX); }
00237
00238 inline int operator==(const vec4 &v) { return (fabs(x - v.x) < epsilon && fabs(y - v.y) < epsilon && fabs(z - v.z) < epsilon && fabs(w - v.w) < epsilon); }
00239 inline int operator!=(const vec4 &v) { return !(*this == v); }
00240
00241 inline const vec4 operator*(float f) const { return vec4(x * f,y * f,z * f,w * f); }
00242 inline const vec4 operator/(float f) const { float vf = 1.0f/f; return vec4(x * vf,y * vf,z * vf,w * vf); }
00243 inline const vec4 operator+(const vec4 &v) const { return vec4(x + v.x,y + v.y,z + v.z,w + v.w); }
00244 inline const vec4 operator-() const { return vec4(-x,-y,-z,-w); }
00245 inline const vec4 operator-(const vec4 &v) const { return vec4(x - v.x,y - v.y,z - v.z,z - v.w); }
00246
00247 inline vec4 &operator*=(float f) { return *this = *this * f; }
00248 inline vec4 &operator/=(float f) { return *this = *this / f; }
00249 inline vec4 &operator+=(const vec4 &v) { return *this = *this + v; }
00250 inline vec4 &operator-=(const vec4 &v) { return *this = *this - v; }
00251
00252 inline float operator*(const vec3 &v) const { return x * v.x + y * v.y + z * v.z + w; }
00253 inline float operator*(const vec4 &v) const { return x * v.x + y * v.y + z * v.z + w * v.w; }
00254
00255 inline operator float*() { return (float*)&x; }
00256 inline operator const float*() const { return (float*)&x; }
00257
00258 inline float &operator[](int i) { return v[i]; }
00259 inline float operator[](int i) const { return v[i]; }
00260
00261 inline float length() const { return sqrt(x * x + y * y + z * z + w * w); }
00262 inline float normalize() {
00263 float length = sqrt(x * x + y * y + z * z + w * w);
00264 if(length < epsilon) return 0.0;
00265 float inv = 1.0f / length;
00266 x *= inv;
00267 y *= inv;
00268 z *= inv;
00269 w *= inv;
00270 return length;
00271 }
00272
00273 union {
00274 struct {
00275 float x,y,z,w;
00276 };
00277 float v[4];
00278 };
00279 };
00280
00281 inline vec3::vec3(const vec4 &v) {
00282 x = v.x;
00283 y = v.y;
00284 z = v.z;
00285 }
00286
00287 inline float vec3::operator*(const vec4 &v) const {
00288 return x * v.x + y * v.y + z * v.z + v.w;
00289 }
00290
00291 inline vec4 normalize(const vec4 &v) {
00292 float length = v.length();
00293 if(length < epsilon) return vec4(0,0,0,0);
00294 return v / length;
00295 }
00296
00297 inline vec4 saturate(const vec4 &v) {
00298 vec4 ret = v;
00299 if(ret.x < 0.0) ret.x = 0.0;
00300 else if(ret.x > 1.0f) ret.x = 1.0f;
00301 if(ret.y < 0.0) ret.y = 0.0;
00302 else if(ret.y > 1.0f) ret.y = 1.0f;
00303 if(ret.z < 0.0) ret.z = 0.0;
00304 else if(ret.z > 1.0f) ret.z = 1.0f;
00305 if(ret.w < 0.0) ret.w = 0.0;
00306 else if(ret.w > 1.0f) ret.w = 1.0f;
00307 return ret;
00308 }
00309
00310
00311
00312
00313
00314
00315
00316 struct mat3 {
00317
00318 mat3() {
00319 mat[0] = 1.0; mat[3] = 0.0; mat[6] = 0.0;
00320 mat[1] = 0.0; mat[4] = 1.0; mat[7] = 0.0;
00321 mat[2] = 0.0; mat[5] = 0.0; mat[8] = 1.0;
00322 }
00323 mat3(const float *m) {
00324 mat[0] = m[0]; mat[3] = m[3]; mat[6] = m[6];
00325 mat[1] = m[1]; mat[4] = m[4]; mat[7] = m[7];
00326 mat[2] = m[2]; mat[5] = m[5]; mat[8] = m[8];
00327 }
00328 mat3(const mat3 &m) {
00329 mat[0] = m[0]; mat[3] = m[3]; mat[6] = m[6];
00330 mat[1] = m[1]; mat[4] = m[4]; mat[7] = m[7];
00331 mat[2] = m[2]; mat[5] = m[5]; mat[8] = m[8];
00332 }
00333 mat3(const mat4 &m);
00334
00335 vec3 operator*(const vec3 &v) const {
00336 vec3 ret;
00337 ret[0] = mat[0] * v[0] + mat[3] * v[1] + mat[6] * v[2];
00338 ret[1] = mat[1] * v[0] + mat[4] * v[1] + mat[7] * v[2];
00339 ret[2] = mat[2] * v[0] + mat[5] * v[1] + mat[8] * v[2];
00340 return ret;
00341 }
00342 vec4 operator*(const vec4 &v) const {
00343 vec4 ret;
00344 ret[0] = mat[0] * v[0] + mat[3] * v[1] + mat[6] * v[2];
00345 ret[1] = mat[1] * v[0] + mat[4] * v[1] + mat[7] * v[2];
00346 ret[2] = mat[2] * v[0] + mat[5] * v[1] + mat[8] * v[2];
00347 ret[3] = v[3];
00348 return ret;
00349 }
00350 mat3 operator*(float f) const {
00351 mat3 ret;
00352 ret[0] = mat[0] * f; ret[3] = mat[3] * f; ret[6] = mat[6] * f;
00353 ret[1] = mat[1] * f; ret[4] = mat[4] * f; ret[7] = mat[7] * f;
00354 ret[2] = mat[2] * f; ret[5] = mat[5] * f; ret[8] = mat[8] * f;
00355 return ret;
00356 }
00357 mat3 operator*(const mat3 &m) const {
00358 mat3 ret;
00359 ret[0] = mat[0] * m[0] + mat[3] * m[1] + mat[6] * m[2];
00360 ret[1] = mat[1] * m[0] + mat[4] * m[1] + mat[7] * m[2];
00361 ret[2] = mat[2] * m[0] + mat[5] * m[1] + mat[8] * m[2];
00362 ret[3] = mat[0] * m[3] + mat[3] * m[4] + mat[6] * m[5];
00363 ret[4] = mat[1] * m[3] + mat[4] * m[4] + mat[7] * m[5];
00364 ret[5] = mat[2] * m[3] + mat[5] * m[4] + mat[8] * m[5];
00365 ret[6] = mat[0] * m[6] + mat[3] * m[7] + mat[6] * m[8];
00366 ret[7] = mat[1] * m[6] + mat[4] * m[7] + mat[7] * m[8];
00367 ret[8] = mat[2] * m[6] + mat[5] * m[7] + mat[8] * m[8];
00368 return ret;
00369 }
00370 mat3 operator+(const mat3 &m) const {
00371 mat3 ret;
00372 ret[0] = mat[0] + m[0]; ret[3] = mat[3] + m[3]; ret[6] = mat[6] + m[6];
00373 ret[1] = mat[1] + m[1]; ret[4] = mat[4] + m[4]; ret[7] = mat[7] + m[7];
00374 ret[2] = mat[2] + m[2]; ret[5] = mat[5] + m[5]; ret[8] = mat[8] + m[8];
00375 return ret;
00376 }
00377 mat3 operator-(const mat3 &m) const {
00378 mat3 ret;
00379 ret[0] = mat[0] - m[0]; ret[3] = mat[3] - m[3]; ret[6] = mat[6] - m[6];
00380 ret[1] = mat[1] - m[1]; ret[4] = mat[4] - m[4]; ret[7] = mat[7] - m[7];
00381 ret[2] = mat[2] - m[2]; ret[5] = mat[5] - m[5]; ret[8] = mat[8] - m[8];
00382 return ret;
00383 }
00384
00385 mat3 &operator*=(float f) { return *this = *this * f; }
00386 mat3 &operator*=(const mat3 &m) { return *this = *this * m; }
00387 mat3 &operator+=(const mat3 &m) { return *this = *this + m; }
00388 mat3 &operator-=(const mat3 &m) { return *this = *this - m; }
00389
00390 operator float*() { return mat; }
00391 operator const float*() const { return mat; }
00392
00393 float &operator[](int i) { return mat[i]; }
00394 float operator[](int i) const { return mat[i]; }
00395
00396 mat3 transpose() const {
00397 mat3 ret;
00398 ret[0] = mat[0]; ret[3] = mat[1]; ret[6] = mat[2];
00399 ret[1] = mat[3]; ret[4] = mat[4]; ret[7] = mat[5];
00400 ret[2] = mat[6]; ret[5] = mat[7]; ret[8] = mat[8];
00401 return ret;
00402 }
00403 float det() const {
00404 float det;
00405 det = mat[0] * mat[4] * mat[8];
00406 det += mat[3] * mat[7] * mat[2];
00407 det += mat[6] * mat[1] * mat[5];
00408 det -= mat[6] * mat[4] * mat[2];
00409 det -= mat[3] * mat[1] * mat[8];
00410 det -= mat[0] * mat[7] * mat[5];
00411 return det;
00412 }
00413 mat3 inverse() const {
00414 mat3 ret;
00415 float idet = 1.0f / det();
00416 ret[0] = (mat[4] * mat[8] - mat[7] * mat[5]) * idet;
00417 ret[1] = -(mat[1] * mat[8] - mat[7] * mat[2]) * idet;
00418 ret[2] = (mat[1] * mat[5] - mat[4] * mat[2]) * idet;
00419 ret[3] = -(mat[3] * mat[8] - mat[6] * mat[5]) * idet;
00420 ret[4] = (mat[0] * mat[8] - mat[6] * mat[2]) * idet;
00421 ret[5] = -(mat[0] * mat[5] - mat[3] * mat[2]) * idet;
00422 ret[6] = (mat[3] * mat[7] - mat[6] * mat[4]) * idet;
00423 ret[7] = -(mat[0] * mat[7] - mat[6] * mat[1]) * idet;
00424 ret[8] = (mat[0] * mat[4] - mat[3] * mat[1]) * idet;
00425 return ret;
00426 }
00427
00428 void zero() {
00429 mat[0] = 0.0; mat[3] = 0.0; mat[6] = 0.0;
00430 mat[1] = 0.0; mat[4] = 0.0; mat[7] = 0.0;
00431 mat[2] = 0.0; mat[5] = 0.0; mat[8] = 0.0;
00432 }
00433 void identity() {
00434 mat[0] = 1.0; mat[3] = 0.0; mat[6] = 0.0;
00435 mat[1] = 0.0; mat[4] = 1.0; mat[7] = 0.0;
00436 mat[2] = 0.0; mat[5] = 0.0; mat[8] = 1.0;
00437 }
00438 void rotate(const vec3 &axis,float angle) {
00439 float rad = angle * DEG2RAD;
00440 float c = cos(rad);
00441 float s = sin(rad);
00442 vec3 v = axis;
00443 v.normalize();
00444 float xx = v.x * v.x;
00445 float yy = v.y * v.y;
00446 float zz = v.z * v.z;
00447 float xy = v.x * v.y;
00448 float yz = v.y * v.z;
00449 float zx = v.z * v.x;
00450 float xs = v.x * s;
00451 float ys = v.y * s;
00452 float zs = v.z * s;
00453 mat[0] = (1.0f - c) * xx + c; mat[3] = (1.0f - c) * xy - zs; mat[6] = (1.0f - c) * zx + ys;
00454 mat[1] = (1.0f - c) * xy + zs; mat[4] = (1.0f - c) * yy + c; mat[7] = (1.0f - c) * yz - xs;
00455 mat[2] = (1.0f - c) * zx - ys; mat[5] = (1.0f - c) * yz + xs; mat[8] = (1.0f - c) * zz + c;
00456 }
00457 void rotate(float x,float y,float z,float angle) {
00458 rotate(vec3(x,y,z),angle);
00459 }
00460 void rotate_x(float angle) {
00461 float rad = angle * DEG2RAD;
00462 float c = cos(rad);
00463 float s = sin(rad);
00464 mat[0] = 1.0; mat[3] = 0.0; mat[6] = 0.0;
00465 mat[1] = 0.0; mat[4] = c; mat[7] = -s;
00466 mat[2] = 0.0; mat[5] = s; mat[8] = c;
00467 }
00468 void rotate_y(float angle) {
00469 float rad = angle * DEG2RAD;
00470 float c = cos(rad);
00471 float s = sin(rad);
00472 mat[0] = c; mat[3] = 0.0; mat[6] = s;
00473 mat[1] = 0.0; mat[4] = 1.0; mat[7] = 0.0;
00474 mat[2] = -s; mat[5] = 0.0; mat[8] = c;
00475 }
00476 void rotate_z(float angle) {
00477 float rad = angle * DEG2RAD;
00478 float c = cos(rad);
00479 float s = sin(rad);
00480 mat[0] = c; mat[3] = -s; mat[6] = 0.0;
00481 mat[1] = s; mat[4] = c; mat[7] = 0.0;
00482 mat[2] = 0.0; mat[5] = 0.0; mat[8] = 1.0;
00483 }
00484 void scale(const vec3 &v) {
00485 mat[0] = v.x; mat[3] = 0.0; mat[6] = 0.0;
00486 mat[1] = 0.0; mat[4] = v.y; mat[7] = 0.0;
00487 mat[2] = 0.0; mat[5] = 0.0; mat[8] = v.z;
00488 }
00489 void scale(float x,float y,float z) {
00490 scale(vec3(x,y,z));
00491 }
00492 void orthonormalize() {
00493 vec3 x(mat[0],mat[1],mat[2]);
00494 vec3 y(mat[3],mat[4],mat[5]);
00495 vec3 z;
00496 x.normalize();
00497 z.cross(x,y);
00498 z.normalize();
00499 y.cross(z,x);
00500 y.normalize();
00501 mat[0] = x.x; mat[3] = y.x; mat[6] = z.x;
00502 mat[1] = x.y; mat[4] = y.y; mat[7] = z.y;
00503 mat[2] = x.z; mat[5] = y.z; mat[8] = z.z;
00504 }
00505
00506
00507 void fromAngleAxis(float angle, const vec3& axis)
00508 {
00509 float s = sin(angle), c = cos(angle);
00510 float v = (float)1.0 - c, x = axis.x*v, y = axis.y*v, z = axis.z*v;
00511
00512 mat[0] = axis.x*x + c;
00513 mat[1] = axis.x*y - axis.z*s;
00514 mat[2] = axis.x*z + axis.y*s;
00515
00516 mat[3] = axis.y*x + axis.z*s;
00517 mat[4] = axis.y*y + c;
00518 mat[5] = axis.y*z - axis.x*s;
00519
00520 mat[6] = axis.z*x - axis.y*s;
00521 mat[7] = axis.z*y + axis.x*s;
00522 mat[8] = axis.z*z + c;
00523 }
00524
00525
00526 void fromRotVector(const vec3& r)
00527 {
00528 vec3 axis(r);
00529 float angle = axis.normalize();
00530 fromAngleAxis(angle, axis);
00531 }
00532
00533 void getAxisAngle(vec3 &axis, float &angle)
00534 {
00535 angle = acos(( mat[0] + mat[4] + mat[8] - 1.0f)/2.0f);
00536 axis.x = (mat[5] - mat[7])/sqrt(pow(mat[5] - mat[7],2)+pow(mat[6] - mat[2],2)+pow(mat[1] - mat[3],2));
00537 axis.y = (mat[6] - mat[2])/sqrt(pow(mat[5] - mat[7],2)+pow(mat[6] - mat[2],2)+pow(mat[1] - mat[3],2));
00538 axis.z = (mat[1] - mat[3])/sqrt(pow(mat[5] - mat[7],2)+pow(mat[6] - mat[2],2)+pow(mat[1] - mat[3],2));
00539 }
00540
00541 float mat[9];
00542 };
00543
00544
00545
00546
00547
00548
00549
00550 struct mat4 {
00551
00552 mat4() {
00553 mat[0] = 1.0; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00554 mat[1] = 0.0; mat[5] = 1.0; mat[9] = 0.0; mat[13] = 0.0;
00555 mat[2] = 0.0; mat[6] = 0.0; mat[10] = 1.0; mat[14] = 0.0;
00556 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00557 }
00558 mat4(const vec3 &v) {
00559 translate(v);
00560 }
00561 mat4(float x,float y,float z) {
00562 translate(x,y,z);
00563 }
00564 mat4(const vec3 &axis,float angle) {
00565 rotate(axis,angle);
00566 }
00567 mat4(float x,float y,float z,float angle) {
00568 rotate(x,y,z,angle);
00569 }
00570 mat4(const mat3 &m) {
00571 mat[0] = m[0]; mat[4] = m[3]; mat[8] = m[6]; mat[12] = 0.0;
00572 mat[1] = m[1]; mat[5] = m[4]; mat[9] = m[7]; mat[13] = 0.0;
00573 mat[2] = m[2]; mat[6] = m[5]; mat[10] = m[8]; mat[14] = 0.0;
00574 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00575 }
00576 mat4(const float *m) {
00577 mat[0] = m[0]; mat[4] = m[4]; mat[8] = m[8]; mat[12] = m[12];
00578 mat[1] = m[1]; mat[5] = m[5]; mat[9] = m[9]; mat[13] = m[13];
00579 mat[2] = m[2]; mat[6] = m[6]; mat[10] = m[10]; mat[14] = m[14];
00580 mat[3] = m[3]; mat[7] = m[7]; mat[11] = m[11]; mat[15] = m[15];
00581 }
00582 mat4(const mat4 &m) {
00583 mat[0] = m[0]; mat[4] = m[4]; mat[8] = m[8]; mat[12] = m[12];
00584 mat[1] = m[1]; mat[5] = m[5]; mat[9] = m[9]; mat[13] = m[13];
00585 mat[2] = m[2]; mat[6] = m[6]; mat[10] = m[10]; mat[14] = m[14];
00586 mat[3] = m[3]; mat[7] = m[7]; mat[11] = m[11]; mat[15] = m[15];
00587 }
00588
00589 vec3 operator*(const vec3 &v) const {
00590 vec3 ret;
00591 ret[0] = mat[0] * v[0] + mat[4] * v[1] + mat[8] * v[2] + mat[12];
00592 ret[1] = mat[1] * v[0] + mat[5] * v[1] + mat[9] * v[2] + mat[13];
00593 ret[2] = mat[2] * v[0] + mat[6] * v[1] + mat[10] * v[2] + mat[14];
00594 return ret;
00595 }
00596 vec4 operator*(const vec4 &v) const {
00597 vec4 ret;
00598 ret[0] = mat[0] * v[0] + mat[4] * v[1] + mat[8] * v[2] + mat[12] * v[3];
00599 ret[1] = mat[1] * v[0] + mat[5] * v[1] + mat[9] * v[2] + mat[13] * v[3];
00600 ret[2] = mat[2] * v[0] + mat[6] * v[1] + mat[10] * v[2] + mat[14] * v[3];
00601 ret[3] = mat[3] * v[0] + mat[7] * v[1] + mat[11] * v[2] + mat[15] * v[3];
00602 return ret;
00603 }
00604 mat4 operator*(float f) const {
00605 mat4 ret;
00606 ret[0] = mat[0] * f; ret[4] = mat[4] * f; ret[8] = mat[8] * f; ret[12] = mat[12] * f;
00607 ret[1] = mat[1] * f; ret[5] = mat[5] * f; ret[9] = mat[9] * f; ret[13] = mat[13] * f;
00608 ret[2] = mat[2] * f; ret[6] = mat[6] * f; ret[10] = mat[10] * f; ret[14] = mat[14] * f;
00609 ret[3] = mat[3] * f; ret[7] = mat[7] * f; ret[11] = mat[11] * f; ret[15] = mat[15] * f;
00610 return ret;
00611 }
00612 mat4 operator*(const mat4 &m) const {
00613 mat4 ret;
00614 ret[0] = mat[0] * m[0] + mat[4] * m[1] + mat[8] * m[2] + mat[12] * m[3];
00615 ret[1] = mat[1] * m[0] + mat[5] * m[1] + mat[9] * m[2] + mat[13] * m[3];
00616 ret[2] = mat[2] * m[0] + mat[6] * m[1] + mat[10] * m[2] + mat[14] * m[3];
00617 ret[3] = mat[3] * m[0] + mat[7] * m[1] + mat[11] * m[2] + mat[15] * m[3];
00618 ret[4] = mat[0] * m[4] + mat[4] * m[5] + mat[8] * m[6] + mat[12] * m[7];
00619 ret[5] = mat[1] * m[4] + mat[5] * m[5] + mat[9] * m[6] + mat[13] * m[7];
00620 ret[6] = mat[2] * m[4] + mat[6] * m[5] + mat[10] * m[6] + mat[14] * m[7];
00621 ret[7] = mat[3] * m[4] + mat[7] * m[5] + mat[11] * m[6] + mat[15] * m[7];
00622 ret[8] = mat[0] * m[8] + mat[4] * m[9] + mat[8] * m[10] + mat[12] * m[11];
00623 ret[9] = mat[1] * m[8] + mat[5] * m[9] + mat[9] * m[10] + mat[13] * m[11];
00624 ret[10] = mat[2] * m[8] + mat[6] * m[9] + mat[10] * m[10] + mat[14] * m[11];
00625 ret[11] = mat[3] * m[8] + mat[7] * m[9] + mat[11] * m[10] + mat[15] * m[11];
00626 ret[12] = mat[0] * m[12] + mat[4] * m[13] + mat[8] * m[14] + mat[12] * m[15];
00627 ret[13] = mat[1] * m[12] + mat[5] * m[13] + mat[9] * m[14] + mat[13] * m[15];
00628 ret[14] = mat[2] * m[12] + mat[6] * m[13] + mat[10] * m[14] + mat[14] * m[15];
00629 ret[15] = mat[3] * m[12] + mat[7] * m[13] + mat[11] * m[14] + mat[15] * m[15];
00630 return ret;
00631 }
00632 mat4 operator+(const mat4 &m) const {
00633 mat4 ret;
00634 ret[0] = mat[0] + m[0]; ret[4] = mat[4] + m[4]; ret[8] = mat[8] + m[8]; ret[12] = mat[12] + m[12];
00635 ret[1] = mat[1] + m[1]; ret[5] = mat[5] + m[5]; ret[9] = mat[9] + m[9]; ret[13] = mat[13] + m[13];
00636 ret[2] = mat[2] + m[2]; ret[6] = mat[6] + m[6]; ret[10] = mat[10] + m[10]; ret[14] = mat[14] + m[14];
00637 ret[3] = mat[3] + m[3]; ret[7] = mat[7] + m[7]; ret[11] = mat[11] + m[11]; ret[15] = mat[15] + m[15];
00638 return ret;
00639 }
00640 mat4 operator-(const mat4 &m) const {
00641 mat4 ret;
00642 ret[0] = mat[0] - m[0]; ret[4] = mat[4] - m[4]; ret[8] = mat[8] - m[8]; ret[12] = mat[12] - m[12];
00643 ret[1] = mat[1] - m[1]; ret[5] = mat[5] - m[5]; ret[9] = mat[9] - m[9]; ret[13] = mat[13] - m[13];
00644 ret[2] = mat[2] - m[2]; ret[6] = mat[6] - m[6]; ret[10] = mat[10] - m[10]; ret[14] = mat[14] - m[14];
00645 ret[3] = mat[3] - m[3]; ret[7] = mat[7] - m[7]; ret[11] = mat[11] - m[11]; ret[15] = mat[15] - m[15];
00646 return ret;
00647 }
00648
00649 mat4 &operator*=(float f) { return *this = *this * f; }
00650 mat4 &operator*=(const mat4 &m) { return *this = *this * m; }
00651 mat4 &operator+=(const mat4 &m) { return *this = *this + m; }
00652 mat4 &operator-=(const mat4 &m) { return *this = *this - m; }
00653
00654 operator float*() { return mat; }
00655 operator const float*() const { return mat; }
00656
00657 float &operator[](int i) { return mat[i]; }
00658 float operator[](int i) const { return mat[i]; }
00659
00660 mat4 rotation() const {
00661 mat4 ret;
00662 ret[0] = mat[0]; ret[4] = mat[4]; ret[8] = mat[8]; ret[12] = 0;
00663 ret[1] = mat[1]; ret[5] = mat[5]; ret[9] = mat[9]; ret[13] = 0;
00664 ret[2] = mat[2]; ret[6] = mat[6]; ret[10] = mat[10]; ret[14] = 0;
00665 ret[3] = 0; ret[7] = 0; ret[11] = 0; ret[15] = 1;
00666 return ret;
00667 }
00668 mat4 transpose() const {
00669 mat4 ret;
00670 ret[0] = mat[0]; ret[4] = mat[1]; ret[8] = mat[2]; ret[12] = mat[3];
00671 ret[1] = mat[4]; ret[5] = mat[5]; ret[9] = mat[6]; ret[13] = mat[7];
00672 ret[2] = mat[8]; ret[6] = mat[9]; ret[10] = mat[10]; ret[14] = mat[11];
00673 ret[3] = mat[12]; ret[7] = mat[13]; ret[11] = mat[14]; ret[15] = mat[15];
00674 return ret;
00675 }
00676 mat4 transpose_rotation() const {
00677 mat4 ret;
00678 ret[0] = mat[0]; ret[4] = mat[1]; ret[8] = mat[2]; ret[12] = mat[12];
00679 ret[1] = mat[4]; ret[5] = mat[5]; ret[9] = mat[6]; ret[13] = mat[13];
00680 ret[2] = mat[8]; ret[6] = mat[9]; ret[10] = mat[10]; ret[14] = mat[14];
00681 ret[3] = mat[3]; ret[7] = mat[7]; ret[14] = mat[14]; ret[15] = mat[15];
00682 return ret;
00683 }
00684
00685 float det() const {
00686 float det;
00687 det = mat[0] * mat[5] * mat[10];
00688 det += mat[4] * mat[9] * mat[2];
00689 det += mat[8] * mat[1] * mat[6];
00690 det -= mat[8] * mat[5] * mat[2];
00691 det -= mat[4] * mat[1] * mat[10];
00692 det -= mat[0] * mat[9] * mat[6];
00693 return det;
00694 }
00695
00696 mat4 inverse() const {
00697 mat4 ret;
00698 float idet = 1.0f / det();
00699 ret[0] = (mat[5] * mat[10] - mat[9] * mat[6]) * idet;
00700 ret[1] = -(mat[1] * mat[10] - mat[9] * mat[2]) * idet;
00701 ret[2] = (mat[1] * mat[6] - mat[5] * mat[2]) * idet;
00702 ret[3] = 0.0;
00703 ret[4] = -(mat[4] * mat[10] - mat[8] * mat[6]) * idet;
00704 ret[5] = (mat[0] * mat[10] - mat[8] * mat[2]) * idet;
00705 ret[6] = -(mat[0] * mat[6] - mat[4] * mat[2]) * idet;
00706 ret[7] = 0.0;
00707 ret[8] = (mat[4] * mat[9] - mat[8] * mat[5]) * idet;
00708 ret[9] = -(mat[0] * mat[9] - mat[8] * mat[1]) * idet;
00709 ret[10] = (mat[0] * mat[5] - mat[4] * mat[1]) * idet;
00710 ret[11] = 0.0;
00711 ret[12] = -(mat[12] * ret[0] + mat[13] * ret[4] + mat[14] * ret[8]);
00712 ret[13] = -(mat[12] * ret[1] + mat[13] * ret[5] + mat[14] * ret[9]);
00713 ret[14] = -(mat[12] * ret[2] + mat[13] * ret[6] + mat[14] * ret[10]);
00714 ret[15] = 1.0;
00715 return ret;
00716 }
00717
00718 void zero() {
00719 mat[0] = 0.0; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00720 mat[1] = 0.0; mat[5] = 0.0; mat[9] = 0.0; mat[13] = 0.0;
00721 mat[2] = 0.0; mat[6] = 0.0; mat[10] = 0.0; mat[14] = 0.0;
00722 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 0.0;
00723 }
00724 void identity() {
00725 mat[0] = 1.0; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00726 mat[1] = 0.0; mat[5] = 1.0; mat[9] = 0.0; mat[13] = 0.0;
00727 mat[2] = 0.0; mat[6] = 0.0; mat[10] = 1.0; mat[14] = 0.0;
00728 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00729 }
00730 void rotate(const vec3 &axis,float angle) {
00731 float rad = angle * DEG2RAD;
00732 float c = cos(rad);
00733 float s = sin(rad);
00734 vec3 v = axis;
00735 v.normalize();
00736 float xx = v.x * v.x;
00737 float yy = v.y * v.y;
00738 float zz = v.z * v.z;
00739 float xy = v.x * v.y;
00740 float yz = v.y * v.z;
00741 float zx = v.z * v.x;
00742 float xs = v.x * s;
00743 float ys = v.y * s;
00744 float zs = v.z * s;
00745 mat[0] = (1.0f - c) * xx + c; mat[4] = (1.0f - c) * xy - zs; mat[8] = (1.0f - c) * zx + ys; mat[12] = 0.0;
00746 mat[1] = (1.0f - c) * xy + zs; mat[5] = (1.0f - c) * yy + c; mat[9] = (1.0f - c) * yz - xs; mat[13] = 0.0;
00747 mat[2] = (1.0f - c) * zx - ys; mat[6] = (1.0f - c) * yz + xs; mat[10] = (1.0f - c) * zz + c; mat[14] = 0.0;
00748 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00749 }
00750 void rotate(float x,float y,float z,float angle) {
00751 rotate(vec3(x,y,z),angle);
00752 }
00753 void rotate_x(float angle) {
00754 float rad = angle * DEG2RAD;
00755 float c = cos(rad);
00756 float s = sin(rad);
00757 mat[0] = 1.0; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00758 mat[1] = 0.0; mat[5] = c; mat[9] = -s; mat[13] = 0.0;
00759 mat[2] = 0.0; mat[6] = s; mat[10] = c; mat[14] = 0.0;
00760 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00761 }
00762 void rotate_y(float angle) {
00763 float rad = angle * DEG2RAD;
00764 float c = cos(rad);
00765 float s = sin(rad);
00766 mat[0] = c; mat[4] = 0.0; mat[8] = s; mat[12] = 0.0;
00767 mat[1] = 0.0; mat[5] = 1.0; mat[9] = 0.0; mat[13] = 0.0;
00768 mat[2] = -s; mat[6] = 0.0; mat[10] = c; mat[14] = 0.0;
00769 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00770 }
00771 void rotate_z(float angle) {
00772 float rad = angle * DEG2RAD;
00773 float c = cos(rad);
00774 float s = sin(rad);
00775 mat[0] = c; mat[4] = -s; mat[8] = 0.0; mat[12] = 0.0;
00776 mat[1] = s; mat[5] = c; mat[9] = 0.0; mat[13] = 0.0;
00777 mat[2] = 0.0; mat[6] = 0.0; mat[10] = 1.0; mat[14] = 0.0;
00778 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00779 }
00780 void scale(const vec3 &v) {
00781 mat[0] = v.x; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00782 mat[1] = 0.0; mat[5] = v.y; mat[9] = 0.0; mat[13] = 0.0;
00783 mat[2] = 0.0; mat[6] = 0.0; mat[10] = v.z; mat[14] = 0.0;
00784 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00785 }
00786 void scale(float x,float y,float z) {
00787 scale(vec3(x,y,z));
00788 }
00789 void translate(const vec3 &v) {
00790 mat[0] = 1.0; mat[4] = 0.0; mat[8] = 0.0; mat[12] = v.x;
00791 mat[1] = 0.0; mat[5] = 1.0; mat[9] = 0.0; mat[13] = v.y;
00792 mat[2] = 0.0; mat[6] = 0.0; mat[10] = 1.0; mat[14] = v.z;
00793 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00794 }
00795 void translate(float x,float y,float z) {
00796 translate(vec3(x,y,z));
00797 }
00798 void reflect(const vec4 &plane) {
00799 float x = plane.x;
00800 float y = plane.y;
00801 float z = plane.z;
00802 float x2 = x * 2.0f;
00803 float y2 = y * 2.0f;
00804 float z2 = z * 2.0f;
00805 mat[0] = 1.0f - x * x2; mat[4] = -y * x2; mat[8] = -z * x2; mat[12] = -plane.w * x2;
00806 mat[1] = -x * y2; mat[5] = 1.0f - y * y2; mat[9] = -z * y2; mat[13] = -plane.w * y2;
00807 mat[2] = -x * z2; mat[6] = -y * z2; mat[10] = 1.0f - z * z2; mat[14] = -plane.w * z2;
00808 mat[3] = 0.0; mat[7] = 0.0; mat[11] = 0.0; mat[15] = 1.0;
00809 }
00810 void reflect(float x,float y,float z,float w) {
00811 reflect(vec4(x,y,z,w));
00812 }
00813
00814 void perspective(float fov,float aspect,float znear,float zfar) {
00815 if(fabs(fov - 90.0f) < epsilon) fov = 89.9f;
00816 float y = tan(fov * PI / 360.0f);
00817 float x = y;
00818 if(aspect > 1)
00819 x *= aspect;
00820 else
00821 y /= aspect;
00822 mat[0] = 1.0f / x; mat[4] = 0.0; mat[8] = 0.0; mat[12] = 0.0;
00823 mat[1] = 0.0; mat[5] = 1.0f / y; mat[9] = 0.0; mat[13] = 0.0;
00824 mat[2] = 0.0; mat[6] = 0.0; mat[10] = -(zfar + znear) / (zfar - znear); mat[14] = -(2.0f * zfar * znear) / (zfar - znear);
00825 mat[3] = 0.0; mat[7] = 0.0; mat[11] = -1.0; mat[15] = 0.0;
00826 }
00827 void look_at(const vec3 &eye,const vec3 &dir,const vec3 &up) {
00828 vec3 x,y,z;
00829 mat4 m0,m1;
00830 z = eye - dir;
00831 z.normalize();
00832 x.cross(up,z);
00833 x.normalize();
00834 y.cross(z,x);
00835 y.normalize();
00836 m0[0] = x.x; m0[4] = x.y; m0[8] = x.z; m0[12] = 0.0;
00837 m0[1] = y.x; m0[5] = y.y; m0[9] = y.z; m0[13] = 0.0;
00838 m0[2] = z.x; m0[6] = z.y; m0[10] = z.z; m0[14] = 0.0;
00839 m0[3] = 0.0; m0[7] = 0.0; m0[11] = 0.0; m0[15] = 1.0;
00840 m1.translate(-eye);
00841 *this = m0 * m1;
00842 }
00843 void look_at(const float *eye,const float *dir,const float *up) {
00844 look_at(vec3(eye),vec3(dir),vec3(up));
00845 }
00846
00847 float mat[16];
00848 };
00849
00850 inline mat3::mat3(const mat4 &m) {
00851 mat[0] = m[0]; mat[3] = m[4]; mat[6] = m[8];
00852 mat[1] = m[1]; mat[4] = m[5]; mat[7] = m[9];
00853 mat[2] = m[2]; mat[5] = m[6]; mat[8] = m[10];
00854 }
00855
00856
00857
00858
00859
00860
00861
00862 struct quat {
00863
00864 quat() : x(0), y(0), z(0), w(1) { }
00865 quat(const vec3 &dir,float angle) {
00866 set(dir,angle);
00867 }
00868 quat(float x,float y,float z,float angle) {
00869 set(x,y,z,angle);
00870 }
00871 quat(const mat3 &m) {
00872 float trace = m[0] + m[4] + m[8];
00873 if(trace > 0.0) {
00874 float s = sqrt(trace + 1.0f);
00875 q[3] = 0.5f * s;
00876 s = 0.5f / s;
00877 q[0] = (m[5] - m[7]) * s;
00878 q[1] = (m[6] - m[2]) * s;
00879 q[2] = (m[1] - m[3]) * s;
00880 } else {
00881 static int next[3] = { 1, 2, 0 };
00882 int i = 0;
00883 if(m[4] > m[0]) i = 1;
00884 if(m[8] > m[3 * i + i]) i = 2;
00885 int j = next[i];
00886 int k = next[j];
00887 float s = sqrt(m[3 * i + i] - m[3 * j + j] - m[3 * k + k] + 1.0f);
00888 q[i] = 0.5f * s;
00889 if(s != 0) s = 0.5f / s;
00890 q[3] = (m[3 * j + k] - m[3 * k + j]) * s;
00891 q[j] = (m[3 * i + j] + m[3 * j + i]) * s;
00892 q[k] = (m[3 * i + k] + m[3 * k + i]) * s;
00893 }
00894 }
00895
00896 operator float*() { return (float*)&x; }
00897 operator const float*() const { return (float*)&x; }
00898
00899 float &operator[](int i) { return q[i]; }
00900 float operator[](int i) const { return q[i]; }
00901
00902 quat operator*(const quat &q) const {
00903 quat ret;
00904 ret.x = w * q.x + x * q.x + y * q.z - z * q.y;
00905 ret.y = w * q.y + y * q.w + z * q.x - x * q.z;
00906 ret.z = w * q.z + z * q.w + x * q.y - y * q.x;
00907 ret.w = w * q.w - x * q.x - y * q.y - z * q.z;
00908 return ret;
00909 }
00910
00911 void set(const vec3 &dir,float angle) {
00912 float length = dir.length();
00913 if(length != 0.0) {
00914 length = 1.0f / length;
00915 float sinangle = sin(angle * DEG2RAD / 2.0f);
00916 x = dir[0] * length * sinangle;
00917 y = dir[1] * length * sinangle;
00918 z = dir[2] * length * sinangle;
00919 w = cos(angle * DEG2RAD / 2.0f);
00920 } else {
00921 x = y = z = 0.0;
00922 w = 1.0;
00923 }
00924 }
00925 void set(float x,float y,float z,float angle) {
00926 set(vec3(x,y,z),angle);
00927 }
00928
00929 void slerp(const quat &q0,const quat &q1,float t) {
00930 float k0,k1,cosomega = q0.x * q1.x + q0.y * q1.y + q0.z * q1.z + q0.w * q1.w;
00931 quat q;
00932 if(cosomega < 0.0) {
00933 cosomega = -cosomega;
00934 q.x = -q1.x;
00935 q.y = -q1.y;
00936 q.z = -q1.z;
00937 q.w = -q1.w;
00938 } else {
00939 q.x = q1.x;
00940 q.y = q1.y;
00941 q.z = q1.z;
00942 q.w = q1.w;
00943 }
00944 if(1.0 - cosomega > 1e-6) {
00945 float omega = acos(cosomega);
00946 float sinomega = sin(omega);
00947 k0 = sin((1.0f - t) * omega) / sinomega;
00948 k1 = sin(t * omega) / sinomega;
00949 } else {
00950 k0 = 1.0f - t;
00951 k1 = t;
00952 }
00953 x = q0.x * k0 + q.x * k1;
00954 y = q0.y * k0 + q.y * k1;
00955 z = q0.z * k0 + q.z * k1;
00956 w = q0.w * k0 + q.w * k1;
00957 }
00958
00959 mat3 to_matrix() const {
00960 mat3 ret;
00961 float x2 = x + x;
00962 float y2 = y + y;
00963 float z2 = z + z;
00964 float xx = x * x2;
00965 float yy = y * y2;
00966 float zz = z * z2;
00967 float xy = x * y2;
00968 float yz = y * z2;
00969 float xz = z * x2;
00970 float wx = w * x2;
00971 float wy = w * y2;
00972 float wz = w * z2;
00973 ret[0] = 1.0f - (yy + zz); ret[3] = xy - wz; ret[6] = xz + wy;
00974 ret[1] = xy + wz; ret[4] = 1.0f - (xx + zz); ret[7] = yz - wx;
00975 ret[2] = xz - wy; ret[5] = yz + wx; ret[8] = 1.0f - (xx + yy);
00976 return ret;
00977 }
00978
00979 union {
00980 struct {
00981 float x,y,z,w;
00982 };
00983 float q[4];
00984 };
00985 };
00986
00987
00988
00989 #endif