1 /* 2 3 algebra3.cpp, algebra3.h - C++ Vector and Matrix Algebra routines 4 5 GLUI User Interface Toolkit (LGPL) 6 Copyright (c) 1998 Paul Rademacher 7 8 WWW: http://sourceforge.net/projects/glui/ 9 Forums: http://sourceforge.net/forum/?group_id=92496 10 11 This library is free software; you can redistribute it and/or 12 modify it under the terms of the GNU Lesser General Public 13 License as published by the Free Software Foundation; either 14 version 2.1 of the License, or (at your option) any later version. 15 16 This library is distributed in the hope that it will be useful, 17 but WITHOUT ANY WARRANTY; without even the implied warranty of 18 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 19 Lesser General Public License for more details. 20 21 You should have received a copy of the GNU Lesser General Public 22 License along with this library; if not, write to the Free Software 23 Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA 24 25 */ 26 27 /************************************************************************** 28 29 There are three vector classes and two matrix classes: vec2, vec3, 30 vec4, mat3, and mat4. 31 32 All the standard arithmetic operations are defined, with '*' 33 for dot product of two vectors and multiplication of two matrices, 34 and '^' for cross product of two vectors. 35 36 Additional functions include length(), normalize(), homogenize for 37 vectors, and print(), set(), apply() for all classes. 38 39 There is a function transpose() for matrices, but note that it 40 does not actually change the matrix, 41 42 When multiplied with a matrix, a vector is treated as a row vector 43 if it precedes the matrix (v*M), and as a column vector if it 44 follows the matrix (M*v). 45 46 Matrices are stored in row-major form. 47 48 A vector of one dimension (2d, 3d, or 4d) can be cast to a vector 49 of a higher or lower dimension. If casting to a higher dimension, 50 the new component is set by default to 1.0, unless a value is 51 specified: 52 vec3 a(1.0, 2.0, 3.0 ); 53 vec4 b( a, 4.0 ); // now b == {1.0, 2.0, 3.0, 4.0}; 54 When casting to a lower dimension, the vector is homogenized in 55 the lower dimension. E.g., if a 4d {X,Y,Z,W} is cast to 3d, the 56 resulting vector is {X/W, Y/W, Z/W}. It is up to the user to 57 insure the fourth component is not zero before casting. 58 59 There are also the following function for building matrices: 60 identity2D(), translation2D(), rotation2D(), 61 scaling2D(), identity3D(), translation3D(), 62 rotation3D(), rotation3Drad(), scaling3D(), 63 perspective3D() 64 65 NOTE: When compiling for Windows, include this file first, to avoid 66 certain name conflicts 67 68 --------------------------------------------------------------------- 69 70 Author: Jean-Francois DOUEg 71 Revised: Paul Rademacher 72 Version 3.2 - Feb 1998 73 Revised: Nigel Stewart (GLUI Code Cleaning) 74 75 **************************************************************************/ 76 77 #ifndef GLUI_ALGEBRA3_H 78 #define GLUI_ALGEBRA3_H 79 80 #include <cmath> 81 #include <cstdio> 82 #include <cstdlib> 83 84 // this line defines a new type: pointer to a function which returns a 85 // float and takes as argument a float 86 typedef float (*V_FCT_PTR)(float); 87 88 class vec2; 89 class vec3; 90 class vec4; 91 class mat3; 92 class mat4; 93 94 #ifndef M_PI 95 #define M_PI 3.141592654 96 #endif 97 98 enum {VX, VY, VZ, VW}; // axes 99 enum {PA, PB, PC, PD}; // planes 100 enum {RED, GREEN, BLUE, ALPHA}; // colors 101 enum {KA, KD, KS, ES}; // phong coefficients 102 103 /**************************************************************** 104 * * 105 * 2D Vector * 106 * * 107 ****************************************************************/ 108 109 class vec2 110 { 111 friend class vec3; 112 113 protected: 114 115 float n[2]; 116 117 public: 118 119 // Constructors 120 121 vec2(); 122 vec2(float x, float y); 123 vec2(const vec2 &v); // copy constructor 124 vec2(const vec3 &v); // cast v3 to v2 125 vec2(const vec3 &v, int dropAxis); // cast v3 to v2 126 127 // Assignment operators 128 129 vec2 &operator = (const vec2 &v); // assignment of a vec2 130 vec2 &operator += (const vec2 &v); // incrementation by a vec2 131 vec2 &operator -= (const vec2 &v); // decrementation by a vec2 132 vec2 &operator *= (float d); // multiplication by a constant 133 vec2 &operator /= (float d); // division by a constant 134 135 // special functions 136 137 float length() const; // length of a vec2 138 float length2() const; // squared length of a vec2 139 vec2 &normalize(); // normalize a vec2 140 vec2 &apply(V_FCT_PTR fct); // apply a func. to each component 141 void set(float x, float y); // set vector 142 143 float &operator [] (int i); // indexing 144 const float &operator [] (int i) const; // indexing 145 146 // friends 147 148 friend vec2 operator - (const vec2 &v); // -v1 149 friend vec2 operator + (const vec2 &a, const vec2 &b); // v1 + v2 150 friend vec2 operator - (const vec2 &a, const vec2 &b); // v1 - v2 151 friend vec2 operator * (const vec2 &a, float d); // v1 * 3.0 152 friend vec2 operator * (float d, const vec2 &a); // 3.0 * v1 153 friend vec2 operator * (const mat3 &a, const vec2 &v); // M . v 154 friend vec2 operator * (const vec2 &v, const mat3 &a); // v . M 155 friend float operator * (const vec2 &a, const vec2 &b); // dot product 156 friend vec2 operator / (const vec2 &a, float d); // v1 / 3.0 157 friend vec3 operator ^ (const vec2 &a, const vec2 &b); // cross product 158 friend int operator == (const vec2 &a, const vec2 &b); // v1 == v2 ? 159 friend int operator != (const vec2 &a, const vec2 &b); // v1 != v2 ? 160 //friend ostream& operator << (ostream& s, vec2& v); // output to stream 161 //friend istream& operator >> (istream& s, vec2& v); // input from strm. 162 friend void swap(vec2 &a, vec2 &b); // swap v1 & v2 163 friend vec2 min_vec(const vec2 &a, const vec2 &b); // min(v1, v2) 164 friend vec2 max_vec(const vec2 &a, const vec2 &b); // max(v1, v2) 165 friend vec2 prod (const vec2 &a, const vec2 &b); // term by term * 166 }; 167 168 /**************************************************************** 169 * * 170 * 3D Vector * 171 * * 172 ****************************************************************/ 173 174 class vec3 175 { 176 friend class vec2; 177 friend class vec4; 178 friend class mat3; 179 180 protected: 181 182 float n[3]; 183 184 public: 185 186 // Constructors 187 188 vec3(); 189 vec3(float x, float y, float z); 190 vec3(const vec3 &v); // copy constructor 191 vec3(const vec2 &v); // cast v2 to v3 192 vec3(const vec2 &v, float d); // cast v2 to v3 193 vec3(const vec4 &v); // cast v4 to v3 194 vec3(const vec4 &v, int dropAxis); // cast v4 to v3 195 196 // Assignment operators 197 198 vec3 &operator = (const vec3 &v); // assignment of a vec3 199 vec3 &operator += (const vec3 &v); // incrementation by a vec3 200 vec3 &operator -= (const vec3 &v); // decrementation by a vec3 201 vec3 &operator *= (float d); // multiplication by a constant 202 vec3 &operator /= (float d); // division by a constant 203 204 // special functions 205 206 float length() const; // length of a vec3 207 float length2() const; // squared length of a vec3 208 vec3& normalize(); // normalize a vec3 209 vec3& homogenize(); // homogenize (div by Z) 210 vec3& apply(V_FCT_PTR fct); // apply a func. to each component 211 void set(float x, float y, float z); // set vector 212 213 void print(FILE *file, const char *name) const; // print vector to a file 214 215 216 float &operator [] (int i); // indexing 217 const float &operator [] (int i) const; // indexing 218 219 // friends 220 221 friend vec3 operator - (const vec3 &v); // -v1 222 friend vec3 operator + (const vec3 &a, const vec3 &b); // v1 + v2 223 friend vec3 operator - (const vec3 &a, const vec3 &b); // v1 - v2 224 friend vec3 operator * (const vec3 &a, float d); // v1 * 3.0 225 friend vec3 operator * (float d, const vec3 &a); // 3.0 * v1 226 friend vec3 operator * (const mat4 &a, const vec3 &v); // M . v 227 friend vec3 operator * (const vec3 &v, const mat4 &a); // v . M 228 friend float operator * (const vec3 &a, const vec3 &b); // dot product 229 friend vec3 operator / (const vec3 &a, float d); // v1 / 3.0 230 friend vec3 operator ^ (const vec3 &a, const vec3 &b); // cross product 231 friend int operator == (const vec3 &a, const vec3 &b); // v1 == v2 ? 232 friend int operator != (const vec3 &a, const vec3 &b); // v1 != v2 ? 233 //friend ostream& operator << (ostream& s, vec3& v); // output to stream 234 //friend istream& operator >> (istream& s, vec3& v); // input from strm. 235 friend void swap(vec3 &a, vec3 &b); // swap v1 & v2 236 friend vec3 min_vec(const vec3 &a, const vec3 &b); // min(v1, v2) 237 friend vec3 max_vec(const vec3 &a, const vec3 &b); // max(v1, v2) 238 friend vec3 prod(const vec3 &a, const vec3 &b); // term by term * 239 240 // necessary friend declarations 241 242 friend vec2 operator * (const mat3 &a, const vec2 &v); // linear transform 243 friend vec3 operator * (const mat3 &a, const vec3 &v); // linear transform 244 friend mat3 operator * (const mat3 &a, const mat3 &b); // matrix 3 product 245 }; 246 247 /**************************************************************** 248 * * 249 * 4D Vector * 250 * * 251 ****************************************************************/ 252 253 class vec4 254 { 255 friend class vec3; 256 friend class mat4; 257 258 protected: 259 260 float n[4]; 261 262 public: 263 264 // Constructors 265 266 vec4(); 267 vec4(float x, float y, float z, float w); 268 vec4(const vec4 &v); // copy constructor 269 vec4(const vec3 &v); // cast vec3 to vec4 270 vec4(const vec3 &v, float d); // cast vec3 to vec4 271 272 // Assignment operators 273 274 vec4 &operator = (const vec4 &v); // assignment of a vec4 275 vec4 &operator += (const vec4 &v); // incrementation by a vec4 276 vec4 &operator -= (const vec4 &v); // decrementation by a vec4 277 vec4 &operator *= (float d); // multiplication by a constant 278 vec4 &operator /= (float d); // division by a constant 279 280 // special functions 281 282 float length() const; // length of a vec4 283 float length2() const; // squared length of a vec4 284 vec4 &normalize(); // normalize a vec4 285 vec4 &apply(V_FCT_PTR fct); // apply a func. to each component 286 vec4 &homogenize(); 287 288 void print(FILE *file, const char *name) const; // print vector to a file 289 290 void set(float x, float y, float z, float a); 291 292 float &operator [] (int i); // indexing 293 const float &operator [] (int i) const; // indexing 294 295 // friends 296 297 friend vec4 operator - (const vec4 &v); // -v1 298 friend vec4 operator + (const vec4 &a, const vec4 &b); // v1 + v2 299 friend vec4 operator - (const vec4 &a, const vec4 &b); // v1 - v2 300 friend vec4 operator * (const vec4 &a, float d); // v1 * 3.0 301 friend vec4 operator * (float d, const vec4 &a); // 3.0 * v1 302 friend vec4 operator * (const mat4 &a, const vec4 &v); // M . v 303 friend vec4 operator * (const vec4 &v, const mat4 &a); // v . M 304 friend float operator * (const vec4 &a, const vec4 &b); // dot product 305 friend vec4 operator / (const vec4 &a, float d); // v1 / 3.0 306 friend int operator == (const vec4 &a, const vec4 &b); // v1 == v2 ? 307 friend int operator != (const vec4 &a, const vec4 &b); // v1 != v2 ? 308 //friend ostream& operator << (ostream& s, vec4& v); // output to stream 309 //friend istream& operator >> (istream& s, vec4& v); // input from strm. 310 friend void swap(vec4 &a, vec4 &b); // swap v1 & v2 311 friend vec4 min_vec(const vec4 &a, const vec4 &b); // min(v1, v2) 312 friend vec4 max_vec(const vec4 &a, const vec4 &b); // max(v1, v2) 313 friend vec4 prod (const vec4 &a, const vec4 &b); // term by term * 314 315 // necessary friend declarations 316 317 friend vec3 operator * (const mat4 &a, const vec3 &v); // linear transform 318 friend mat4 operator * (const mat4 &a, const mat4 &b); // matrix 4 product 319 }; 320 321 /**************************************************************** 322 * * 323 * 3x3 Matrix * 324 * * 325 ****************************************************************/ 326 327 class mat3 328 { 329 protected: 330 331 vec3 v[3]; 332 333 public: 334 335 // Constructors 336 337 mat3(); 338 mat3(const vec3 &v0, const vec3 &v1, const vec3 &v2); 339 mat3(const mat3 &m); 340 341 // Assignment operators 342 343 mat3 &operator = (const mat3 &m); // assignment of a mat3 344 mat3 &operator += (const mat3 &m); // incrementation by a mat3 345 mat3 &operator -= (const mat3 &m); // decrementation by a mat3 346 mat3 &operator *= (float d); // multiplication by a constant 347 mat3 &operator /= (float d); // division by a constant 348 349 // special functions 350 351 mat3 transpose() const; // transpose 352 mat3 inverse() const; // inverse 353 mat3 &apply(V_FCT_PTR fct); // apply a func. to each element 354 355 void print(FILE *file, const char *name ) const; // print matrix to a file 356 357 void set(const vec3 &v0, const vec3 &v1, const vec3 &v2); 358 359 vec3 &operator [] (int i); // indexing 360 const vec3 &operator [] (int i) const; // indexing 361 362 // friends 363 364 friend mat3 operator - (const mat3 &a); // -m1 365 friend mat3 operator + (const mat3 &a, const mat3 &b); // m1 + m2 366 friend mat3 operator - (const mat3 &a, const mat3 &b); // m1 - m2 367 friend mat3 operator * (const mat3 &a, const mat3 &b); // m1 * m2 368 friend mat3 operator * (const mat3 &a, float d); // m1 * 3.0 369 friend mat3 operator * (float d, const mat3 &a); // 3.0 * m1 370 friend mat3 operator / (const mat3 &a, float d); // m1 / 3.0 371 friend int operator == (const mat3 &a, const mat3 &b); // m1 == m2 ? 372 friend int operator != (const mat3 &a, const mat3 &b); // m1 != m2 ? 373 //friend ostream& operator << (ostream& s, mat3& m); // output to stream 374 //friend istream& operator >> (istream& s, mat3& m); // input from strm. 375 friend void swap(mat3 &a, mat3 &b); // swap m1 & m2 376 377 // necessary friend declarations 378 379 friend vec3 operator * (const mat3 &a, const vec3 &v); // linear transform 380 friend vec2 operator * (const mat3 &a, const vec2 &v); // linear transform 381 }; 382 383 /**************************************************************** 384 * * 385 * 4x4 Matrix * 386 * * 387 ****************************************************************/ 388 389 class mat4 390 { 391 protected: 392 393 vec4 v[4]; 394 395 public: 396 397 // Constructors 398 399 mat4(); 400 mat4(const vec4 &v0, const vec4 &v1, const vec4 &v2, const vec4 &v3); 401 mat4(const mat4 &m); 402 mat4(float a00, float a01, float a02, float a03, 403 float a10, float a11, float a12, float a13, 404 float a20, float a21, float a22, float a23, 405 float a30, float a31, float a32, float a33 ); 406 407 408 // Assignment operators 409 410 mat4 &operator = (const mat4 &m); // assignment of a mat4 411 mat4 &operator += (const mat4 &m); // incrementation by a mat4 412 mat4 &operator -= (const mat4 &m); // decrementation by a mat4 413 mat4 &operator *= (float d); // multiplication by a constant 414 mat4 &operator /= (float d); // division by a constant 415 416 // special functions 417 418 mat4 transpose() const; // transpose 419 mat4 inverse() const; // inverse 420 mat4 &apply(V_FCT_PTR fct); // apply a func. to each element 421 422 void print(FILE *file, const char *name) const; // print matrix to a file 423 424 vec4 &operator [] (int i); // indexing 425 const vec4 &operator [] (int i) const; // indexing 426 427 void swap_rows(int i, int j); // swap rows i and j 428 void swap_cols(int i, int j); // swap cols i and j 429 430 // friends 431 432 friend mat4 operator - (const mat4 &a); // -m1 433 friend mat4 operator + (const mat4 &a, const mat4 &b); // m1 + m2 434 friend mat4 operator - (const mat4 &a, const mat4 &b); // m1 - m2 435 friend mat4 operator * (const mat4 &a, const mat4 &b); // m1 * m2 436 friend mat4 operator * (const mat4 &a, float d); // m1 * 4.0 437 friend mat4 operator * (float d, const mat4 &a); // 4.0 * m1 438 friend mat4 operator / (const mat4 &a, float d); // m1 / 3.0 439 friend int operator == (const mat4 &a, const mat4 &b); // m1 == m2 ? 440 friend int operator != (const mat4 &a, const mat4 &b); // m1 != m2 ? 441 //friend ostream& operator << (ostream& s, mat4& m); // output to stream 442 //friend istream& operator >> (istream& s, mat4& m); // input from strm. 443 friend void swap(mat4 &a, mat4 &b); // swap m1 & m2 444 445 // necessary friend declarations 446 447 friend vec4 operator * (const mat4 &a, const vec4 &v); // linear transform 448 //friend vec4 operator * (const vec4& v, const mat4& a); // linear transform 449 friend vec3 operator * (const mat4 &a, const vec3 &v); // linear transform 450 friend vec3 operator * (const vec3 &v, const mat4 &a); // linear transform 451 }; 452 453 /**************************************************************** 454 * * 455 * 2D functions and 3D functions * 456 * * 457 ****************************************************************/ 458 459 mat3 identity2D (); // identity 2D 460 mat3 translation2D(const vec2 &v); // translation 2D 461 mat3 rotation2D (const vec2 &Center, float angleDeg); // rotation 2D 462 mat3 scaling2D (const vec2 &scaleVector); // scaling 2D 463 mat4 identity3D (); // identity 3D 464 mat4 translation3D(const vec3 &v); // translation 3D 465 mat4 rotation3D (const vec3 &Axis, float angleDeg); // rotation 3D 466 mat4 rotation3Drad(const vec3 &Axis, float angleRad); // rotation 3D 467 mat4 scaling3D (const vec3 &scaleVector); // scaling 3D 468 mat4 perspective3D(float d); // perspective 3D 469 470 vec3 operator * (const vec3 &v, const mat3 &a); 471 vec2 operator * (const vec2 &v, const mat3 &a); 472 vec3 operator * (const vec3 &v, const mat4 &a); 473 vec4 operator * (const vec4 &v, const mat4 &a); 474 475 #endif 476