raymath.h (82281B)
1 /********************************************************************************************** 2 * 3 * raymath v2.0 - Math functions to work with Vector2, Vector3, Matrix and Quaternions 4 * 5 * CONVENTIONS: 6 * - Matrix structure is defined as row-major (memory layout) but parameters naming AND all 7 * math operations performed by the library consider the structure as it was column-major 8 * It is like transposed versions of the matrices are used for all the maths 9 * It benefits some functions making them cache-friendly and also avoids matrix 10 * transpositions sometimes required by OpenGL 11 * Example: In memory order, row0 is [m0 m4 m8 m12] but in semantic math row0 is [m0 m1 m2 m3] 12 * - Functions are always self-contained, no function use another raymath function inside, 13 * required code is directly re-implemented inside 14 * - Functions input parameters are always received by value (2 unavoidable exceptions) 15 * - Functions use always a "result" variable for return (except C++ operators) 16 * - Functions are always defined inline 17 * - Angles are always in radians (DEG2RAD/RAD2DEG macros provided for convenience) 18 * - No compound literals used to make sure libray is compatible with C++ 19 * 20 * CONFIGURATION: 21 * #define RAYMATH_IMPLEMENTATION 22 * Generates the implementation of the library into the included file. 23 * If not defined, the library is in header only mode and can be included in other headers 24 * or source files without problems. But only ONE file should hold the implementation. 25 * 26 * #define RAYMATH_STATIC_INLINE 27 * Define static inline functions code, so #include header suffices for use. 28 * This may use up lots of memory. 29 * 30 * #define RAYMATH_DISABLE_CPP_OPERATORS 31 * Disables C++ operator overloads for raymath types. 32 * 33 * LICENSE: zlib/libpng 34 * 35 * Copyright (c) 2015-2024 Ramon Santamaria (@raysan5) 36 * 37 * This software is provided "as-is", without any express or implied warranty. In no event 38 * will the authors be held liable for any damages arising from the use of this software. 39 * 40 * Permission is granted to anyone to use this software for any purpose, including commercial 41 * applications, and to alter it and redistribute it freely, subject to the following restrictions: 42 * 43 * 1. The origin of this software must not be misrepresented; you must not claim that you 44 * wrote the original software. If you use this software in a product, an acknowledgment 45 * in the product documentation would be appreciated but is not required. 46 * 47 * 2. Altered source versions must be plainly marked as such, and must not be misrepresented 48 * as being the original software. 49 * 50 * 3. This notice may not be removed or altered from any source distribution. 51 * 52 **********************************************************************************************/ 53 54 #ifndef RAYMATH_H 55 #define RAYMATH_H 56 57 #if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_STATIC_INLINE) 58 #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_STATIC_INLINE is contradictory" 59 #endif 60 61 // Function specifiers definition 62 #if defined(RAYMATH_IMPLEMENTATION) 63 #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) 64 #define RMAPI __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll) 65 #elif defined(BUILD_LIBTYPE_SHARED) 66 #define RMAPI __attribute__((visibility("default"))) // We are building raylib as a Unix shared library (.so/.dylib) 67 #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) 68 #define RMAPI __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) 69 #else 70 #define RMAPI extern inline // Provide external definition 71 #endif 72 #elif defined(RAYMATH_STATIC_INLINE) 73 #define RMAPI static inline // Functions may be inlined, no external out-of-line definition 74 #else 75 #if defined(__TINYC__) 76 #define RMAPI static inline // plain inline not supported by tinycc (See issue #435) 77 #else 78 #define RMAPI inline // Functions may be inlined or external definition used 79 #endif 80 #endif 81 82 83 //---------------------------------------------------------------------------------- 84 // Defines and Macros 85 //---------------------------------------------------------------------------------- 86 #ifndef PI 87 #define PI 3.14159265358979323846f 88 #endif 89 90 #ifndef EPSILON 91 #define EPSILON 0.000001f 92 #endif 93 94 #ifndef DEG2RAD 95 #define DEG2RAD (PI/180.0f) 96 #endif 97 98 #ifndef RAD2DEG 99 #define RAD2DEG (180.0f/PI) 100 #endif 101 102 // Get float vector for Matrix 103 #ifndef MatrixToFloat 104 #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) 105 #endif 106 107 // Get float vector for Vector3 108 #ifndef Vector3ToFloat 109 #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) 110 #endif 111 112 //---------------------------------------------------------------------------------- 113 // Types and Structures Definition 114 //---------------------------------------------------------------------------------- 115 #if !defined(RL_VECTOR2_TYPE) 116 // Vector2 type 117 typedef struct Vector2 { 118 float x; 119 float y; 120 } Vector2; 121 #define RL_VECTOR2_TYPE 122 #endif 123 124 #if !defined(RL_VECTOR3_TYPE) 125 // Vector3 type 126 typedef struct Vector3 { 127 float x; 128 float y; 129 float z; 130 } Vector3; 131 #define RL_VECTOR3_TYPE 132 #endif 133 134 #if !defined(RL_VECTOR4_TYPE) 135 // Vector4 type 136 typedef struct Vector4 { 137 float x; 138 float y; 139 float z; 140 float w; 141 } Vector4; 142 #define RL_VECTOR4_TYPE 143 #endif 144 145 #if !defined(RL_QUATERNION_TYPE) 146 // Quaternion type 147 typedef Vector4 Quaternion; 148 #define RL_QUATERNION_TYPE 149 #endif 150 151 #if !defined(RL_MATRIX_TYPE) 152 // Matrix type (OpenGL style 4x4 - right handed, column major) 153 typedef struct Matrix { 154 float m0, m4, m8, m12; // Matrix first row (4 components) 155 float m1, m5, m9, m13; // Matrix second row (4 components) 156 float m2, m6, m10, m14; // Matrix third row (4 components) 157 float m3, m7, m11, m15; // Matrix fourth row (4 components) 158 } Matrix; 159 #define RL_MATRIX_TYPE 160 #endif 161 162 // NOTE: Helper types to be used instead of array return types for *ToFloat functions 163 typedef struct float3 { 164 float v[3]; 165 } float3; 166 167 typedef struct float16 { 168 float v[16]; 169 } float16; 170 171 #include <math.h> // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), fminf(), fmaxf(), fabsf() 172 173 //---------------------------------------------------------------------------------- 174 // Module Functions Definition - Utils math 175 //---------------------------------------------------------------------------------- 176 177 // Clamp float value 178 RMAPI float Clamp(float value, float min, float max) 179 { 180 float result = (value < min)? min : value; 181 182 if (result > max) result = max; 183 184 return result; 185 } 186 187 // Calculate linear interpolation between two floats 188 RMAPI float Lerp(float start, float end, float amount) 189 { 190 float result = start + amount*(end - start); 191 192 return result; 193 } 194 195 // Normalize input value within input range 196 RMAPI float Normalize(float value, float start, float end) 197 { 198 float result = (value - start)/(end - start); 199 200 return result; 201 } 202 203 // Remap input value within input range to output range 204 RMAPI float Remap(float value, float inputStart, float inputEnd, float outputStart, float outputEnd) 205 { 206 float result = (value - inputStart)/(inputEnd - inputStart)*(outputEnd - outputStart) + outputStart; 207 208 return result; 209 } 210 211 // Wrap input value from min to max 212 RMAPI float Wrap(float value, float min, float max) 213 { 214 float result = value - (max - min)*floorf((value - min)/(max - min)); 215 216 return result; 217 } 218 219 // Check whether two given floats are almost equal 220 RMAPI int FloatEquals(float x, float y) 221 { 222 #if !defined(EPSILON) 223 #define EPSILON 0.000001f 224 #endif 225 226 int result = (fabsf(x - y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(x), fabsf(y)))); 227 228 return result; 229 } 230 231 //---------------------------------------------------------------------------------- 232 // Module Functions Definition - Vector2 math 233 //---------------------------------------------------------------------------------- 234 235 // Vector with components value 0.0f 236 RMAPI Vector2 Vector2Zero(void) 237 { 238 Vector2 result = { 0.0f, 0.0f }; 239 240 return result; 241 } 242 243 // Vector with components value 1.0f 244 RMAPI Vector2 Vector2One(void) 245 { 246 Vector2 result = { 1.0f, 1.0f }; 247 248 return result; 249 } 250 251 // Add two vectors (v1 + v2) 252 RMAPI Vector2 Vector2Add(Vector2 v1, Vector2 v2) 253 { 254 Vector2 result = { v1.x + v2.x, v1.y + v2.y }; 255 256 return result; 257 } 258 259 // Add vector and float value 260 RMAPI Vector2 Vector2AddValue(Vector2 v, float add) 261 { 262 Vector2 result = { v.x + add, v.y + add }; 263 264 return result; 265 } 266 267 // Subtract two vectors (v1 - v2) 268 RMAPI Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) 269 { 270 Vector2 result = { v1.x - v2.x, v1.y - v2.y }; 271 272 return result; 273 } 274 275 // Subtract vector by float value 276 RMAPI Vector2 Vector2SubtractValue(Vector2 v, float sub) 277 { 278 Vector2 result = { v.x - sub, v.y - sub }; 279 280 return result; 281 } 282 283 // Calculate vector length 284 RMAPI float Vector2Length(Vector2 v) 285 { 286 float result = sqrtf((v.x*v.x) + (v.y*v.y)); 287 288 return result; 289 } 290 291 // Calculate vector square length 292 RMAPI float Vector2LengthSqr(Vector2 v) 293 { 294 float result = (v.x*v.x) + (v.y*v.y); 295 296 return result; 297 } 298 299 // Calculate two vectors dot product 300 RMAPI float Vector2DotProduct(Vector2 v1, Vector2 v2) 301 { 302 float result = (v1.x*v2.x + v1.y*v2.y); 303 304 return result; 305 } 306 307 // Calculate distance between two vectors 308 RMAPI float Vector2Distance(Vector2 v1, Vector2 v2) 309 { 310 float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); 311 312 return result; 313 } 314 315 // Calculate square distance between two vectors 316 RMAPI float Vector2DistanceSqr(Vector2 v1, Vector2 v2) 317 { 318 float result = ((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); 319 320 return result; 321 } 322 323 // Calculate angle between two vectors 324 // NOTE: Angle is calculated from origin point (0, 0) 325 RMAPI float Vector2Angle(Vector2 v1, Vector2 v2) 326 { 327 float result = 0.0f; 328 329 float dot = v1.x*v2.x + v1.y*v2.y; 330 float det = v1.x*v2.y - v1.y*v2.x; 331 332 result = atan2f(det, dot); 333 334 return result; 335 } 336 337 // Calculate angle defined by a two vectors line 338 // NOTE: Parameters need to be normalized 339 // Current implementation should be aligned with glm::angle 340 RMAPI float Vector2LineAngle(Vector2 start, Vector2 end) 341 { 342 float result = 0.0f; 343 344 // TODO(10/9/2023): Currently angles move clockwise, determine if this is wanted behavior 345 result = -atan2f(end.y - start.y, end.x - start.x); 346 347 return result; 348 } 349 350 // Scale vector (multiply by value) 351 RMAPI Vector2 Vector2Scale(Vector2 v, float scale) 352 { 353 Vector2 result = { v.x*scale, v.y*scale }; 354 355 return result; 356 } 357 358 // Multiply vector by vector 359 RMAPI Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) 360 { 361 Vector2 result = { v1.x*v2.x, v1.y*v2.y }; 362 363 return result; 364 } 365 366 // Negate vector 367 RMAPI Vector2 Vector2Negate(Vector2 v) 368 { 369 Vector2 result = { -v.x, -v.y }; 370 371 return result; 372 } 373 374 // Divide vector by vector 375 RMAPI Vector2 Vector2Divide(Vector2 v1, Vector2 v2) 376 { 377 Vector2 result = { v1.x/v2.x, v1.y/v2.y }; 378 379 return result; 380 } 381 382 // Normalize provided vector 383 RMAPI Vector2 Vector2Normalize(Vector2 v) 384 { 385 Vector2 result = { 0 }; 386 float length = sqrtf((v.x*v.x) + (v.y*v.y)); 387 388 if (length > 0) 389 { 390 float ilength = 1.0f/length; 391 result.x = v.x*ilength; 392 result.y = v.y*ilength; 393 } 394 395 return result; 396 } 397 398 // Transforms a Vector2 by a given Matrix 399 RMAPI Vector2 Vector2Transform(Vector2 v, Matrix mat) 400 { 401 Vector2 result = { 0 }; 402 403 float x = v.x; 404 float y = v.y; 405 float z = 0; 406 407 result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; 408 result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; 409 410 return result; 411 } 412 413 // Calculate linear interpolation between two vectors 414 RMAPI Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount) 415 { 416 Vector2 result = { 0 }; 417 418 result.x = v1.x + amount*(v2.x - v1.x); 419 result.y = v1.y + amount*(v2.y - v1.y); 420 421 return result; 422 } 423 424 // Calculate reflected vector to normal 425 RMAPI Vector2 Vector2Reflect(Vector2 v, Vector2 normal) 426 { 427 Vector2 result = { 0 }; 428 429 float dotProduct = (v.x*normal.x + v.y*normal.y); // Dot product 430 431 result.x = v.x - (2.0f*normal.x)*dotProduct; 432 result.y = v.y - (2.0f*normal.y)*dotProduct; 433 434 return result; 435 } 436 437 // Get min value for each pair of components 438 RMAPI Vector2 Vector2Min(Vector2 v1, Vector2 v2) 439 { 440 Vector2 result = { 0 }; 441 442 result.x = fminf(v1.x, v2.x); 443 result.y = fminf(v1.y, v2.y); 444 445 return result; 446 } 447 448 // Get max value for each pair of components 449 RMAPI Vector2 Vector2Max(Vector2 v1, Vector2 v2) 450 { 451 Vector2 result = { 0 }; 452 453 result.x = fmaxf(v1.x, v2.x); 454 result.y = fmaxf(v1.y, v2.y); 455 456 return result; 457 } 458 459 // Rotate vector by angle 460 RMAPI Vector2 Vector2Rotate(Vector2 v, float angle) 461 { 462 Vector2 result = { 0 }; 463 464 float cosres = cosf(angle); 465 float sinres = sinf(angle); 466 467 result.x = v.x*cosres - v.y*sinres; 468 result.y = v.x*sinres + v.y*cosres; 469 470 return result; 471 } 472 473 // Move Vector towards target 474 RMAPI Vector2 Vector2MoveTowards(Vector2 v, Vector2 target, float maxDistance) 475 { 476 Vector2 result = { 0 }; 477 478 float dx = target.x - v.x; 479 float dy = target.y - v.y; 480 float value = (dx*dx) + (dy*dy); 481 482 if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target; 483 484 float dist = sqrtf(value); 485 486 result.x = v.x + dx/dist*maxDistance; 487 result.y = v.y + dy/dist*maxDistance; 488 489 return result; 490 } 491 492 // Invert the given vector 493 RMAPI Vector2 Vector2Invert(Vector2 v) 494 { 495 Vector2 result = { 1.0f/v.x, 1.0f/v.y }; 496 497 return result; 498 } 499 500 // Clamp the components of the vector between 501 // min and max values specified by the given vectors 502 RMAPI Vector2 Vector2Clamp(Vector2 v, Vector2 min, Vector2 max) 503 { 504 Vector2 result = { 0 }; 505 506 result.x = fminf(max.x, fmaxf(min.x, v.x)); 507 result.y = fminf(max.y, fmaxf(min.y, v.y)); 508 509 return result; 510 } 511 512 // Clamp the magnitude of the vector between two min and max values 513 RMAPI Vector2 Vector2ClampValue(Vector2 v, float min, float max) 514 { 515 Vector2 result = v; 516 517 float length = (v.x*v.x) + (v.y*v.y); 518 if (length > 0.0f) 519 { 520 length = sqrtf(length); 521 522 float scale = 1; // By default, 1 as the neutral element. 523 if (length < min) 524 { 525 scale = min/length; 526 } 527 else if (length > max) 528 { 529 scale = max/length; 530 } 531 532 result.x = v.x*scale; 533 result.y = v.y*scale; 534 } 535 536 return result; 537 } 538 539 // Check whether two given vectors are almost equal 540 RMAPI int Vector2Equals(Vector2 p, Vector2 q) 541 { 542 #if !defined(EPSILON) 543 #define EPSILON 0.000001f 544 #endif 545 546 int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && 547 ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))); 548 549 return result; 550 } 551 552 // Compute the direction of a refracted ray 553 // v: normalized direction of the incoming ray 554 // n: normalized normal vector of the interface of two optical media 555 // r: ratio of the refractive index of the medium from where the ray comes 556 // to the refractive index of the medium on the other side of the surface 557 RMAPI Vector2 Vector2Refract(Vector2 v, Vector2 n, float r) 558 { 559 Vector2 result = { 0 }; 560 561 float dot = v.x*n.x + v.y*n.y; 562 float d = 1.0f - r*r*(1.0f - dot*dot); 563 564 if (d >= 0.0f) 565 { 566 d = sqrtf(d); 567 v.x = r*v.x - (r*dot + d)*n.x; 568 v.y = r*v.y - (r*dot + d)*n.y; 569 570 result = v; 571 } 572 573 return result; 574 } 575 576 577 //---------------------------------------------------------------------------------- 578 // Module Functions Definition - Vector3 math 579 //---------------------------------------------------------------------------------- 580 581 // Vector with components value 0.0f 582 RMAPI Vector3 Vector3Zero(void) 583 { 584 Vector3 result = { 0.0f, 0.0f, 0.0f }; 585 586 return result; 587 } 588 589 // Vector with components value 1.0f 590 RMAPI Vector3 Vector3One(void) 591 { 592 Vector3 result = { 1.0f, 1.0f, 1.0f }; 593 594 return result; 595 } 596 597 // Add two vectors 598 RMAPI Vector3 Vector3Add(Vector3 v1, Vector3 v2) 599 { 600 Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z }; 601 602 return result; 603 } 604 605 // Add vector and float value 606 RMAPI Vector3 Vector3AddValue(Vector3 v, float add) 607 { 608 Vector3 result = { v.x + add, v.y + add, v.z + add }; 609 610 return result; 611 } 612 613 // Subtract two vectors 614 RMAPI Vector3 Vector3Subtract(Vector3 v1, Vector3 v2) 615 { 616 Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z }; 617 618 return result; 619 } 620 621 // Subtract vector by float value 622 RMAPI Vector3 Vector3SubtractValue(Vector3 v, float sub) 623 { 624 Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; 625 626 return result; 627 } 628 629 // Multiply vector by scalar 630 RMAPI Vector3 Vector3Scale(Vector3 v, float scalar) 631 { 632 Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; 633 634 return result; 635 } 636 637 // Multiply vector by vector 638 RMAPI Vector3 Vector3Multiply(Vector3 v1, Vector3 v2) 639 { 640 Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z }; 641 642 return result; 643 } 644 645 // Calculate two vectors cross product 646 RMAPI Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2) 647 { 648 Vector3 result = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x }; 649 650 return result; 651 } 652 653 // Calculate one vector perpendicular vector 654 RMAPI Vector3 Vector3Perpendicular(Vector3 v) 655 { 656 Vector3 result = { 0 }; 657 658 float min = fabsf(v.x); 659 Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; 660 661 if (fabsf(v.y) < min) 662 { 663 min = fabsf(v.y); 664 Vector3 tmp = {0.0f, 1.0f, 0.0f}; 665 cardinalAxis = tmp; 666 } 667 668 if (fabsf(v.z) < min) 669 { 670 Vector3 tmp = {0.0f, 0.0f, 1.0f}; 671 cardinalAxis = tmp; 672 } 673 674 // Cross product between vectors 675 result.x = v.y*cardinalAxis.z - v.z*cardinalAxis.y; 676 result.y = v.z*cardinalAxis.x - v.x*cardinalAxis.z; 677 result.z = v.x*cardinalAxis.y - v.y*cardinalAxis.x; 678 679 return result; 680 } 681 682 // Calculate vector length 683 RMAPI float Vector3Length(const Vector3 v) 684 { 685 float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 686 687 return result; 688 } 689 690 // Calculate vector square length 691 RMAPI float Vector3LengthSqr(const Vector3 v) 692 { 693 float result = v.x*v.x + v.y*v.y + v.z*v.z; 694 695 return result; 696 } 697 698 // Calculate two vectors dot product 699 RMAPI float Vector3DotProduct(Vector3 v1, Vector3 v2) 700 { 701 float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); 702 703 return result; 704 } 705 706 // Calculate distance between two vectors 707 RMAPI float Vector3Distance(Vector3 v1, Vector3 v2) 708 { 709 float result = 0.0f; 710 711 float dx = v2.x - v1.x; 712 float dy = v2.y - v1.y; 713 float dz = v2.z - v1.z; 714 result = sqrtf(dx*dx + dy*dy + dz*dz); 715 716 return result; 717 } 718 719 // Calculate square distance between two vectors 720 RMAPI float Vector3DistanceSqr(Vector3 v1, Vector3 v2) 721 { 722 float result = 0.0f; 723 724 float dx = v2.x - v1.x; 725 float dy = v2.y - v1.y; 726 float dz = v2.z - v1.z; 727 result = dx*dx + dy*dy + dz*dz; 728 729 return result; 730 } 731 732 // Calculate angle between two vectors 733 RMAPI float Vector3Angle(Vector3 v1, Vector3 v2) 734 { 735 float result = 0.0f; 736 737 Vector3 cross = { v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x }; 738 float len = sqrtf(cross.x*cross.x + cross.y*cross.y + cross.z*cross.z); 739 float dot = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); 740 result = atan2f(len, dot); 741 742 return result; 743 } 744 745 // Negate provided vector (invert direction) 746 RMAPI Vector3 Vector3Negate(Vector3 v) 747 { 748 Vector3 result = { -v.x, -v.y, -v.z }; 749 750 return result; 751 } 752 753 // Divide vector by vector 754 RMAPI Vector3 Vector3Divide(Vector3 v1, Vector3 v2) 755 { 756 Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z }; 757 758 return result; 759 } 760 761 // Normalize provided vector 762 RMAPI Vector3 Vector3Normalize(Vector3 v) 763 { 764 Vector3 result = v; 765 766 float length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 767 if (length != 0.0f) 768 { 769 float ilength = 1.0f/length; 770 771 result.x *= ilength; 772 result.y *= ilength; 773 result.z *= ilength; 774 } 775 776 return result; 777 } 778 779 //Calculate the projection of the vector v1 on to v2 780 RMAPI Vector3 Vector3Project(Vector3 v1, Vector3 v2) 781 { 782 Vector3 result = { 0 }; 783 784 float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); 785 float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z); 786 787 float mag = v1dv2/v2dv2; 788 789 result.x = v2.x*mag; 790 result.y = v2.y*mag; 791 result.z = v2.z*mag; 792 793 return result; 794 } 795 796 //Calculate the rejection of the vector v1 on to v2 797 RMAPI Vector3 Vector3Reject(Vector3 v1, Vector3 v2) 798 { 799 Vector3 result = { 0 }; 800 801 float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); 802 float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z); 803 804 float mag = v1dv2/v2dv2; 805 806 result.x = v1.x - (v2.x*mag); 807 result.y = v1.y - (v2.y*mag); 808 result.z = v1.z - (v2.z*mag); 809 810 return result; 811 } 812 813 // Orthonormalize provided vectors 814 // Makes vectors normalized and orthogonal to each other 815 // Gram-Schmidt function implementation 816 RMAPI void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) 817 { 818 float length = 0.0f; 819 float ilength = 0.0f; 820 821 // Vector3Normalize(*v1); 822 Vector3 v = *v1; 823 length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 824 if (length == 0.0f) length = 1.0f; 825 ilength = 1.0f/length; 826 v1->x *= ilength; 827 v1->y *= ilength; 828 v1->z *= ilength; 829 830 // Vector3CrossProduct(*v1, *v2) 831 Vector3 vn1 = { v1->y*v2->z - v1->z*v2->y, v1->z*v2->x - v1->x*v2->z, v1->x*v2->y - v1->y*v2->x }; 832 833 // Vector3Normalize(vn1); 834 v = vn1; 835 length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 836 if (length == 0.0f) length = 1.0f; 837 ilength = 1.0f/length; 838 vn1.x *= ilength; 839 vn1.y *= ilength; 840 vn1.z *= ilength; 841 842 // Vector3CrossProduct(vn1, *v1) 843 Vector3 vn2 = { vn1.y*v1->z - vn1.z*v1->y, vn1.z*v1->x - vn1.x*v1->z, vn1.x*v1->y - vn1.y*v1->x }; 844 845 *v2 = vn2; 846 } 847 848 // Transforms a Vector3 by a given Matrix 849 RMAPI Vector3 Vector3Transform(Vector3 v, Matrix mat) 850 { 851 Vector3 result = { 0 }; 852 853 float x = v.x; 854 float y = v.y; 855 float z = v.z; 856 857 result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; 858 result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; 859 result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; 860 861 return result; 862 } 863 864 // Transform a vector by quaternion rotation 865 RMAPI Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q) 866 { 867 Vector3 result = { 0 }; 868 869 result.x = v.x*(q.x*q.x + q.w*q.w - q.y*q.y - q.z*q.z) + v.y*(2*q.x*q.y - 2*q.w*q.z) + v.z*(2*q.x*q.z + 2*q.w*q.y); 870 result.y = v.x*(2*q.w*q.z + 2*q.x*q.y) + v.y*(q.w*q.w - q.x*q.x + q.y*q.y - q.z*q.z) + v.z*(-2*q.w*q.x + 2*q.y*q.z); 871 result.z = v.x*(-2*q.w*q.y + 2*q.x*q.z) + v.y*(2*q.w*q.x + 2*q.y*q.z)+ v.z*(q.w*q.w - q.x*q.x - q.y*q.y + q.z*q.z); 872 873 return result; 874 } 875 876 // Rotates a vector around an axis 877 RMAPI Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle) 878 { 879 // Using Euler-Rodrigues Formula 880 // Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula 881 882 Vector3 result = v; 883 884 // Vector3Normalize(axis); 885 float length = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z); 886 if (length == 0.0f) length = 1.0f; 887 float ilength = 1.0f/length; 888 axis.x *= ilength; 889 axis.y *= ilength; 890 axis.z *= ilength; 891 892 angle /= 2.0f; 893 float a = sinf(angle); 894 float b = axis.x*a; 895 float c = axis.y*a; 896 float d = axis.z*a; 897 a = cosf(angle); 898 Vector3 w = { b, c, d }; 899 900 // Vector3CrossProduct(w, v) 901 Vector3 wv = { w.y*v.z - w.z*v.y, w.z*v.x - w.x*v.z, w.x*v.y - w.y*v.x }; 902 903 // Vector3CrossProduct(w, wv) 904 Vector3 wwv = { w.y*wv.z - w.z*wv.y, w.z*wv.x - w.x*wv.z, w.x*wv.y - w.y*wv.x }; 905 906 // Vector3Scale(wv, 2*a) 907 a *= 2; 908 wv.x *= a; 909 wv.y *= a; 910 wv.z *= a; 911 912 // Vector3Scale(wwv, 2) 913 wwv.x *= 2; 914 wwv.y *= 2; 915 wwv.z *= 2; 916 917 result.x += wv.x; 918 result.y += wv.y; 919 result.z += wv.z; 920 921 result.x += wwv.x; 922 result.y += wwv.y; 923 result.z += wwv.z; 924 925 return result; 926 } 927 928 // Move Vector towards target 929 RMAPI Vector3 Vector3MoveTowards(Vector3 v, Vector3 target, float maxDistance) 930 { 931 Vector3 result = { 0 }; 932 933 float dx = target.x - v.x; 934 float dy = target.y - v.y; 935 float dz = target.z - v.z; 936 float value = (dx*dx) + (dy*dy) + (dz*dz); 937 938 if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target; 939 940 float dist = sqrtf(value); 941 942 result.x = v.x + dx/dist*maxDistance; 943 result.y = v.y + dy/dist*maxDistance; 944 result.z = v.z + dz/dist*maxDistance; 945 946 return result; 947 } 948 949 // Calculate linear interpolation between two vectors 950 RMAPI Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount) 951 { 952 Vector3 result = { 0 }; 953 954 result.x = v1.x + amount*(v2.x - v1.x); 955 result.y = v1.y + amount*(v2.y - v1.y); 956 result.z = v1.z + amount*(v2.z - v1.z); 957 958 return result; 959 } 960 961 // Calculate cubic hermite interpolation between two vectors and their tangents 962 // as described in the GLTF 2.0 specification: https://registry.khronos.org/glTF/specs/2.0/glTF-2.0.html#interpolation-cubic 963 RMAPI Vector3 Vector3CubicHermite(Vector3 v1, Vector3 tangent1, Vector3 v2, Vector3 tangent2, float amount) 964 { 965 Vector3 result = { 0 }; 966 967 float amountPow2 = amount*amount; 968 float amountPow3 = amount*amount*amount; 969 970 result.x = (2*amountPow3 - 3*amountPow2 + 1)*v1.x + (amountPow3 - 2*amountPow2 + amount)*tangent1.x + (-2*amountPow3 + 3*amountPow2)*v2.x + (amountPow3 - amountPow2)*tangent2.x; 971 result.y = (2*amountPow3 - 3*amountPow2 + 1)*v1.y + (amountPow3 - 2*amountPow2 + amount)*tangent1.y + (-2*amountPow3 + 3*amountPow2)*v2.y + (amountPow3 - amountPow2)*tangent2.y; 972 result.z = (2*amountPow3 - 3*amountPow2 + 1)*v1.z + (amountPow3 - 2*amountPow2 + amount)*tangent1.z + (-2*amountPow3 + 3*amountPow2)*v2.z + (amountPow3 - amountPow2)*tangent2.z; 973 974 return result; 975 } 976 977 // Calculate reflected vector to normal 978 RMAPI Vector3 Vector3Reflect(Vector3 v, Vector3 normal) 979 { 980 Vector3 result = { 0 }; 981 982 // I is the original vector 983 // N is the normal of the incident plane 984 // R = I - (2*N*(DotProduct[I, N])) 985 986 float dotProduct = (v.x*normal.x + v.y*normal.y + v.z*normal.z); 987 988 result.x = v.x - (2.0f*normal.x)*dotProduct; 989 result.y = v.y - (2.0f*normal.y)*dotProduct; 990 result.z = v.z - (2.0f*normal.z)*dotProduct; 991 992 return result; 993 } 994 995 // Get min value for each pair of components 996 RMAPI Vector3 Vector3Min(Vector3 v1, Vector3 v2) 997 { 998 Vector3 result = { 0 }; 999 1000 result.x = fminf(v1.x, v2.x); 1001 result.y = fminf(v1.y, v2.y); 1002 result.z = fminf(v1.z, v2.z); 1003 1004 return result; 1005 } 1006 1007 // Get max value for each pair of components 1008 RMAPI Vector3 Vector3Max(Vector3 v1, Vector3 v2) 1009 { 1010 Vector3 result = { 0 }; 1011 1012 result.x = fmaxf(v1.x, v2.x); 1013 result.y = fmaxf(v1.y, v2.y); 1014 result.z = fmaxf(v1.z, v2.z); 1015 1016 return result; 1017 } 1018 1019 // Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) 1020 // NOTE: Assumes P is on the plane of the triangle 1021 RMAPI Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) 1022 { 1023 Vector3 result = { 0 }; 1024 1025 Vector3 v0 = { b.x - a.x, b.y - a.y, b.z - a.z }; // Vector3Subtract(b, a) 1026 Vector3 v1 = { c.x - a.x, c.y - a.y, c.z - a.z }; // Vector3Subtract(c, a) 1027 Vector3 v2 = { p.x - a.x, p.y - a.y, p.z - a.z }; // Vector3Subtract(p, a) 1028 float d00 = (v0.x*v0.x + v0.y*v0.y + v0.z*v0.z); // Vector3DotProduct(v0, v0) 1029 float d01 = (v0.x*v1.x + v0.y*v1.y + v0.z*v1.z); // Vector3DotProduct(v0, v1) 1030 float d11 = (v1.x*v1.x + v1.y*v1.y + v1.z*v1.z); // Vector3DotProduct(v1, v1) 1031 float d20 = (v2.x*v0.x + v2.y*v0.y + v2.z*v0.z); // Vector3DotProduct(v2, v0) 1032 float d21 = (v2.x*v1.x + v2.y*v1.y + v2.z*v1.z); // Vector3DotProduct(v2, v1) 1033 1034 float denom = d00*d11 - d01*d01; 1035 1036 result.y = (d11*d20 - d01*d21)/denom; 1037 result.z = (d00*d21 - d01*d20)/denom; 1038 result.x = 1.0f - (result.z + result.y); 1039 1040 return result; 1041 } 1042 1043 // Projects a Vector3 from screen space into object space 1044 // NOTE: We are avoiding calling other raymath functions despite available 1045 RMAPI Vector3 Vector3Unproject(Vector3 source, Matrix projection, Matrix view) 1046 { 1047 Vector3 result = { 0 }; 1048 1049 // Calculate unprojected matrix (multiply view matrix by projection matrix) and invert it 1050 Matrix matViewProj = { // MatrixMultiply(view, projection); 1051 view.m0*projection.m0 + view.m1*projection.m4 + view.m2*projection.m8 + view.m3*projection.m12, 1052 view.m0*projection.m1 + view.m1*projection.m5 + view.m2*projection.m9 + view.m3*projection.m13, 1053 view.m0*projection.m2 + view.m1*projection.m6 + view.m2*projection.m10 + view.m3*projection.m14, 1054 view.m0*projection.m3 + view.m1*projection.m7 + view.m2*projection.m11 + view.m3*projection.m15, 1055 view.m4*projection.m0 + view.m5*projection.m4 + view.m6*projection.m8 + view.m7*projection.m12, 1056 view.m4*projection.m1 + view.m5*projection.m5 + view.m6*projection.m9 + view.m7*projection.m13, 1057 view.m4*projection.m2 + view.m5*projection.m6 + view.m6*projection.m10 + view.m7*projection.m14, 1058 view.m4*projection.m3 + view.m5*projection.m7 + view.m6*projection.m11 + view.m7*projection.m15, 1059 view.m8*projection.m0 + view.m9*projection.m4 + view.m10*projection.m8 + view.m11*projection.m12, 1060 view.m8*projection.m1 + view.m9*projection.m5 + view.m10*projection.m9 + view.m11*projection.m13, 1061 view.m8*projection.m2 + view.m9*projection.m6 + view.m10*projection.m10 + view.m11*projection.m14, 1062 view.m8*projection.m3 + view.m9*projection.m7 + view.m10*projection.m11 + view.m11*projection.m15, 1063 view.m12*projection.m0 + view.m13*projection.m4 + view.m14*projection.m8 + view.m15*projection.m12, 1064 view.m12*projection.m1 + view.m13*projection.m5 + view.m14*projection.m9 + view.m15*projection.m13, 1065 view.m12*projection.m2 + view.m13*projection.m6 + view.m14*projection.m10 + view.m15*projection.m14, 1066 view.m12*projection.m3 + view.m13*projection.m7 + view.m14*projection.m11 + view.m15*projection.m15 }; 1067 1068 // Calculate inverted matrix -> MatrixInvert(matViewProj); 1069 // Cache the matrix values (speed optimization) 1070 float a00 = matViewProj.m0, a01 = matViewProj.m1, a02 = matViewProj.m2, a03 = matViewProj.m3; 1071 float a10 = matViewProj.m4, a11 = matViewProj.m5, a12 = matViewProj.m6, a13 = matViewProj.m7; 1072 float a20 = matViewProj.m8, a21 = matViewProj.m9, a22 = matViewProj.m10, a23 = matViewProj.m11; 1073 float a30 = matViewProj.m12, a31 = matViewProj.m13, a32 = matViewProj.m14, a33 = matViewProj.m15; 1074 1075 float b00 = a00*a11 - a01*a10; 1076 float b01 = a00*a12 - a02*a10; 1077 float b02 = a00*a13 - a03*a10; 1078 float b03 = a01*a12 - a02*a11; 1079 float b04 = a01*a13 - a03*a11; 1080 float b05 = a02*a13 - a03*a12; 1081 float b06 = a20*a31 - a21*a30; 1082 float b07 = a20*a32 - a22*a30; 1083 float b08 = a20*a33 - a23*a30; 1084 float b09 = a21*a32 - a22*a31; 1085 float b10 = a21*a33 - a23*a31; 1086 float b11 = a22*a33 - a23*a32; 1087 1088 // Calculate the invert determinant (inlined to avoid double-caching) 1089 float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); 1090 1091 Matrix matViewProjInv = { 1092 (a11*b11 - a12*b10 + a13*b09)*invDet, 1093 (-a01*b11 + a02*b10 - a03*b09)*invDet, 1094 (a31*b05 - a32*b04 + a33*b03)*invDet, 1095 (-a21*b05 + a22*b04 - a23*b03)*invDet, 1096 (-a10*b11 + a12*b08 - a13*b07)*invDet, 1097 (a00*b11 - a02*b08 + a03*b07)*invDet, 1098 (-a30*b05 + a32*b02 - a33*b01)*invDet, 1099 (a20*b05 - a22*b02 + a23*b01)*invDet, 1100 (a10*b10 - a11*b08 + a13*b06)*invDet, 1101 (-a00*b10 + a01*b08 - a03*b06)*invDet, 1102 (a30*b04 - a31*b02 + a33*b00)*invDet, 1103 (-a20*b04 + a21*b02 - a23*b00)*invDet, 1104 (-a10*b09 + a11*b07 - a12*b06)*invDet, 1105 (a00*b09 - a01*b07 + a02*b06)*invDet, 1106 (-a30*b03 + a31*b01 - a32*b00)*invDet, 1107 (a20*b03 - a21*b01 + a22*b00)*invDet }; 1108 1109 // Create quaternion from source point 1110 Quaternion quat = { source.x, source.y, source.z, 1.0f }; 1111 1112 // Multiply quat point by unprojecte matrix 1113 Quaternion qtransformed = { // QuaternionTransform(quat, matViewProjInv) 1114 matViewProjInv.m0*quat.x + matViewProjInv.m4*quat.y + matViewProjInv.m8*quat.z + matViewProjInv.m12*quat.w, 1115 matViewProjInv.m1*quat.x + matViewProjInv.m5*quat.y + matViewProjInv.m9*quat.z + matViewProjInv.m13*quat.w, 1116 matViewProjInv.m2*quat.x + matViewProjInv.m6*quat.y + matViewProjInv.m10*quat.z + matViewProjInv.m14*quat.w, 1117 matViewProjInv.m3*quat.x + matViewProjInv.m7*quat.y + matViewProjInv.m11*quat.z + matViewProjInv.m15*quat.w }; 1118 1119 // Normalized world points in vectors 1120 result.x = qtransformed.x/qtransformed.w; 1121 result.y = qtransformed.y/qtransformed.w; 1122 result.z = qtransformed.z/qtransformed.w; 1123 1124 return result; 1125 } 1126 1127 // Get Vector3 as float array 1128 RMAPI float3 Vector3ToFloatV(Vector3 v) 1129 { 1130 float3 buffer = { 0 }; 1131 1132 buffer.v[0] = v.x; 1133 buffer.v[1] = v.y; 1134 buffer.v[2] = v.z; 1135 1136 return buffer; 1137 } 1138 1139 // Invert the given vector 1140 RMAPI Vector3 Vector3Invert(Vector3 v) 1141 { 1142 Vector3 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z }; 1143 1144 return result; 1145 } 1146 1147 // Clamp the components of the vector between 1148 // min and max values specified by the given vectors 1149 RMAPI Vector3 Vector3Clamp(Vector3 v, Vector3 min, Vector3 max) 1150 { 1151 Vector3 result = { 0 }; 1152 1153 result.x = fminf(max.x, fmaxf(min.x, v.x)); 1154 result.y = fminf(max.y, fmaxf(min.y, v.y)); 1155 result.z = fminf(max.z, fmaxf(min.z, v.z)); 1156 1157 return result; 1158 } 1159 1160 // Clamp the magnitude of the vector between two values 1161 RMAPI Vector3 Vector3ClampValue(Vector3 v, float min, float max) 1162 { 1163 Vector3 result = v; 1164 1165 float length = (v.x*v.x) + (v.y*v.y) + (v.z*v.z); 1166 if (length > 0.0f) 1167 { 1168 length = sqrtf(length); 1169 1170 float scale = 1; // By default, 1 as the neutral element. 1171 if (length < min) 1172 { 1173 scale = min/length; 1174 } 1175 else if (length > max) 1176 { 1177 scale = max/length; 1178 } 1179 1180 result.x = v.x*scale; 1181 result.y = v.y*scale; 1182 result.z = v.z*scale; 1183 } 1184 1185 return result; 1186 } 1187 1188 // Check whether two given vectors are almost equal 1189 RMAPI int Vector3Equals(Vector3 p, Vector3 q) 1190 { 1191 #if !defined(EPSILON) 1192 #define EPSILON 0.000001f 1193 #endif 1194 1195 int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && 1196 ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && 1197 ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))); 1198 1199 return result; 1200 } 1201 1202 // Compute the direction of a refracted ray 1203 // v: normalized direction of the incoming ray 1204 // n: normalized normal vector of the interface of two optical media 1205 // r: ratio of the refractive index of the medium from where the ray comes 1206 // to the refractive index of the medium on the other side of the surface 1207 RMAPI Vector3 Vector3Refract(Vector3 v, Vector3 n, float r) 1208 { 1209 Vector3 result = { 0 }; 1210 1211 float dot = v.x*n.x + v.y*n.y + v.z*n.z; 1212 float d = 1.0f - r*r*(1.0f - dot*dot); 1213 1214 if (d >= 0.0f) 1215 { 1216 d = sqrtf(d); 1217 v.x = r*v.x - (r*dot + d)*n.x; 1218 v.y = r*v.y - (r*dot + d)*n.y; 1219 v.z = r*v.z - (r*dot + d)*n.z; 1220 1221 result = v; 1222 } 1223 1224 return result; 1225 } 1226 1227 1228 //---------------------------------------------------------------------------------- 1229 // Module Functions Definition - Vector4 math 1230 //---------------------------------------------------------------------------------- 1231 1232 RMAPI Vector4 Vector4Zero(void) 1233 { 1234 Vector4 result = { 0.0f, 0.0f, 0.0f, 0.0f }; 1235 return result; 1236 } 1237 1238 RMAPI Vector4 Vector4One(void) 1239 { 1240 Vector4 result = { 1.0f, 1.0f, 1.0f, 1.0f }; 1241 return result; 1242 } 1243 1244 RMAPI Vector4 Vector4Add(Vector4 v1, Vector4 v2) 1245 { 1246 Vector4 result = { 1247 v1.x + v2.x, 1248 v1.y + v2.y, 1249 v1.z + v2.z, 1250 v1.w + v2.w 1251 }; 1252 return result; 1253 } 1254 1255 RMAPI Vector4 Vector4AddValue(Vector4 v, float add) 1256 { 1257 Vector4 result = { 1258 v.x + add, 1259 v.y + add, 1260 v.z + add, 1261 v.w + add 1262 }; 1263 return result; 1264 } 1265 1266 RMAPI Vector4 Vector4Subtract(Vector4 v1, Vector4 v2) 1267 { 1268 Vector4 result = { 1269 v1.x - v2.x, 1270 v1.y - v2.y, 1271 v1.z - v2.z, 1272 v1.w - v2.w 1273 }; 1274 return result; 1275 } 1276 1277 RMAPI Vector4 Vector4SubtractValue(Vector4 v, float add) 1278 { 1279 Vector4 result = { 1280 v.x - add, 1281 v.y - add, 1282 v.z - add, 1283 v.w - add 1284 }; 1285 return result; 1286 } 1287 1288 RMAPI float Vector4Length(Vector4 v) 1289 { 1290 float result = sqrtf((v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w)); 1291 return result; 1292 } 1293 1294 RMAPI float Vector4LengthSqr(Vector4 v) 1295 { 1296 float result = (v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w); 1297 return result; 1298 } 1299 1300 RMAPI float Vector4DotProduct(Vector4 v1, Vector4 v2) 1301 { 1302 float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z + v1.w*v2.w); 1303 return result; 1304 } 1305 1306 // Calculate distance between two vectors 1307 RMAPI float Vector4Distance(Vector4 v1, Vector4 v2) 1308 { 1309 float result = sqrtf( 1310 (v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y) + 1311 (v1.z - v2.z)*(v1.z - v2.z) + (v1.w - v2.w)*(v1.w - v2.w)); 1312 return result; 1313 } 1314 1315 // Calculate square distance between two vectors 1316 RMAPI float Vector4DistanceSqr(Vector4 v1, Vector4 v2) 1317 { 1318 float result = 1319 (v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y) + 1320 (v1.z - v2.z)*(v1.z - v2.z) + (v1.w - v2.w)*(v1.w - v2.w); 1321 1322 return result; 1323 } 1324 1325 RMAPI Vector4 Vector4Scale(Vector4 v, float scale) 1326 { 1327 Vector4 result = { v.x*scale, v.y*scale, v.z*scale, v.w*scale }; 1328 return result; 1329 } 1330 1331 // Multiply vector by vector 1332 RMAPI Vector4 Vector4Multiply(Vector4 v1, Vector4 v2) 1333 { 1334 Vector4 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z, v1.w*v2.w }; 1335 return result; 1336 } 1337 1338 // Negate vector 1339 RMAPI Vector4 Vector4Negate(Vector4 v) 1340 { 1341 Vector4 result = { -v.x, -v.y, -v.z, -v.w }; 1342 return result; 1343 } 1344 1345 // Divide vector by vector 1346 RMAPI Vector4 Vector4Divide(Vector4 v1, Vector4 v2) 1347 { 1348 Vector4 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z, v1.w/v2.w }; 1349 return result; 1350 } 1351 1352 // Normalize provided vector 1353 RMAPI Vector4 Vector4Normalize(Vector4 v) 1354 { 1355 Vector4 result = { 0 }; 1356 float length = sqrtf((v.x*v.x) + (v.y*v.y) + (v.z*v.z) + (v.w*v.w)); 1357 1358 if (length > 0) 1359 { 1360 float ilength = 1.0f/length; 1361 result.x = v.x*ilength; 1362 result.y = v.y*ilength; 1363 result.z = v.z*ilength; 1364 result.w = v.w*ilength; 1365 } 1366 1367 return result; 1368 } 1369 1370 // Get min value for each pair of components 1371 RMAPI Vector4 Vector4Min(Vector4 v1, Vector4 v2) 1372 { 1373 Vector4 result = { 0 }; 1374 1375 result.x = fminf(v1.x, v2.x); 1376 result.y = fminf(v1.y, v2.y); 1377 result.z = fminf(v1.z, v2.z); 1378 result.w = fminf(v1.w, v2.w); 1379 1380 return result; 1381 } 1382 1383 // Get max value for each pair of components 1384 RMAPI Vector4 Vector4Max(Vector4 v1, Vector4 v2) 1385 { 1386 Vector4 result = { 0 }; 1387 1388 result.x = fmaxf(v1.x, v2.x); 1389 result.y = fmaxf(v1.y, v2.y); 1390 result.z = fmaxf(v1.z, v2.z); 1391 result.w = fmaxf(v1.w, v2.w); 1392 1393 return result; 1394 } 1395 1396 // Calculate linear interpolation between two vectors 1397 RMAPI Vector4 Vector4Lerp(Vector4 v1, Vector4 v2, float amount) 1398 { 1399 Vector4 result = { 0 }; 1400 1401 result.x = v1.x + amount*(v2.x - v1.x); 1402 result.y = v1.y + amount*(v2.y - v1.y); 1403 result.z = v1.z + amount*(v2.z - v1.z); 1404 result.w = v1.w + amount*(v2.w - v1.w); 1405 1406 return result; 1407 } 1408 1409 // Move Vector towards target 1410 RMAPI Vector4 Vector4MoveTowards(Vector4 v, Vector4 target, float maxDistance) 1411 { 1412 Vector4 result = { 0 }; 1413 1414 float dx = target.x - v.x; 1415 float dy = target.y - v.y; 1416 float dz = target.z - v.z; 1417 float dw = target.w - v.w; 1418 float value = (dx*dx) + (dy*dy) + (dz*dz) + (dw*dw); 1419 1420 if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target; 1421 1422 float dist = sqrtf(value); 1423 1424 result.x = v.x + dx/dist*maxDistance; 1425 result.y = v.y + dy/dist*maxDistance; 1426 result.z = v.z + dz/dist*maxDistance; 1427 result.w = v.w + dw/dist*maxDistance; 1428 1429 return result; 1430 } 1431 1432 // Invert the given vector 1433 RMAPI Vector4 Vector4Invert(Vector4 v) 1434 { 1435 Vector4 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z, 1.0f/v.w }; 1436 return result; 1437 } 1438 1439 // Check whether two given vectors are almost equal 1440 RMAPI int Vector4Equals(Vector4 p, Vector4 q) 1441 { 1442 #if !defined(EPSILON) 1443 #define EPSILON 0.000001f 1444 #endif 1445 1446 int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && 1447 ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && 1448 ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) && 1449 ((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w))))); 1450 return result; 1451 } 1452 1453 1454 //---------------------------------------------------------------------------------- 1455 // Module Functions Definition - Matrix math 1456 //---------------------------------------------------------------------------------- 1457 1458 // Compute matrix determinant 1459 RMAPI float MatrixDeterminant(Matrix mat) 1460 { 1461 float result = 0.0f; 1462 1463 // Cache the matrix values (speed optimization) 1464 float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3; 1465 float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7; 1466 float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11; 1467 float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15; 1468 1469 result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 + 1470 a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 + 1471 a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 + 1472 a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 + 1473 a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 + 1474 a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33; 1475 1476 return result; 1477 } 1478 1479 // Get the trace of the matrix (sum of the values along the diagonal) 1480 RMAPI float MatrixTrace(Matrix mat) 1481 { 1482 float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); 1483 1484 return result; 1485 } 1486 1487 // Transposes provided matrix 1488 RMAPI Matrix MatrixTranspose(Matrix mat) 1489 { 1490 Matrix result = { 0 }; 1491 1492 result.m0 = mat.m0; 1493 result.m1 = mat.m4; 1494 result.m2 = mat.m8; 1495 result.m3 = mat.m12; 1496 result.m4 = mat.m1; 1497 result.m5 = mat.m5; 1498 result.m6 = mat.m9; 1499 result.m7 = mat.m13; 1500 result.m8 = mat.m2; 1501 result.m9 = mat.m6; 1502 result.m10 = mat.m10; 1503 result.m11 = mat.m14; 1504 result.m12 = mat.m3; 1505 result.m13 = mat.m7; 1506 result.m14 = mat.m11; 1507 result.m15 = mat.m15; 1508 1509 return result; 1510 } 1511 1512 // Invert provided matrix 1513 RMAPI Matrix MatrixInvert(Matrix mat) 1514 { 1515 Matrix result = { 0 }; 1516 1517 // Cache the matrix values (speed optimization) 1518 float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3; 1519 float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7; 1520 float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11; 1521 float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15; 1522 1523 float b00 = a00*a11 - a01*a10; 1524 float b01 = a00*a12 - a02*a10; 1525 float b02 = a00*a13 - a03*a10; 1526 float b03 = a01*a12 - a02*a11; 1527 float b04 = a01*a13 - a03*a11; 1528 float b05 = a02*a13 - a03*a12; 1529 float b06 = a20*a31 - a21*a30; 1530 float b07 = a20*a32 - a22*a30; 1531 float b08 = a20*a33 - a23*a30; 1532 float b09 = a21*a32 - a22*a31; 1533 float b10 = a21*a33 - a23*a31; 1534 float b11 = a22*a33 - a23*a32; 1535 1536 // Calculate the invert determinant (inlined to avoid double-caching) 1537 float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); 1538 1539 result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; 1540 result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; 1541 result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; 1542 result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; 1543 result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; 1544 result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; 1545 result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; 1546 result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; 1547 result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; 1548 result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; 1549 result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; 1550 result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; 1551 result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; 1552 result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; 1553 result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; 1554 result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; 1555 1556 return result; 1557 } 1558 1559 // Get identity matrix 1560 RMAPI Matrix MatrixIdentity(void) 1561 { 1562 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 1563 0.0f, 1.0f, 0.0f, 0.0f, 1564 0.0f, 0.0f, 1.0f, 0.0f, 1565 0.0f, 0.0f, 0.0f, 1.0f }; 1566 1567 return result; 1568 } 1569 1570 // Add two matrices 1571 RMAPI Matrix MatrixAdd(Matrix left, Matrix right) 1572 { 1573 Matrix result = { 0 }; 1574 1575 result.m0 = left.m0 + right.m0; 1576 result.m1 = left.m1 + right.m1; 1577 result.m2 = left.m2 + right.m2; 1578 result.m3 = left.m3 + right.m3; 1579 result.m4 = left.m4 + right.m4; 1580 result.m5 = left.m5 + right.m5; 1581 result.m6 = left.m6 + right.m6; 1582 result.m7 = left.m7 + right.m7; 1583 result.m8 = left.m8 + right.m8; 1584 result.m9 = left.m9 + right.m9; 1585 result.m10 = left.m10 + right.m10; 1586 result.m11 = left.m11 + right.m11; 1587 result.m12 = left.m12 + right.m12; 1588 result.m13 = left.m13 + right.m13; 1589 result.m14 = left.m14 + right.m14; 1590 result.m15 = left.m15 + right.m15; 1591 1592 return result; 1593 } 1594 1595 // Subtract two matrices (left - right) 1596 RMAPI Matrix MatrixSubtract(Matrix left, Matrix right) 1597 { 1598 Matrix result = { 0 }; 1599 1600 result.m0 = left.m0 - right.m0; 1601 result.m1 = left.m1 - right.m1; 1602 result.m2 = left.m2 - right.m2; 1603 result.m3 = left.m3 - right.m3; 1604 result.m4 = left.m4 - right.m4; 1605 result.m5 = left.m5 - right.m5; 1606 result.m6 = left.m6 - right.m6; 1607 result.m7 = left.m7 - right.m7; 1608 result.m8 = left.m8 - right.m8; 1609 result.m9 = left.m9 - right.m9; 1610 result.m10 = left.m10 - right.m10; 1611 result.m11 = left.m11 - right.m11; 1612 result.m12 = left.m12 - right.m12; 1613 result.m13 = left.m13 - right.m13; 1614 result.m14 = left.m14 - right.m14; 1615 result.m15 = left.m15 - right.m15; 1616 1617 return result; 1618 } 1619 1620 // Get two matrix multiplication 1621 // NOTE: When multiplying matrices... the order matters! 1622 RMAPI Matrix MatrixMultiply(Matrix left, Matrix right) 1623 { 1624 Matrix result = { 0 }; 1625 1626 result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12; 1627 result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13; 1628 result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14; 1629 result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15; 1630 result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12; 1631 result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13; 1632 result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14; 1633 result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15; 1634 result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12; 1635 result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13; 1636 result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14; 1637 result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15; 1638 result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12; 1639 result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13; 1640 result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14; 1641 result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15; 1642 1643 return result; 1644 } 1645 1646 // Get translation matrix 1647 RMAPI Matrix MatrixTranslate(float x, float y, float z) 1648 { 1649 Matrix result = { 1.0f, 0.0f, 0.0f, x, 1650 0.0f, 1.0f, 0.0f, y, 1651 0.0f, 0.0f, 1.0f, z, 1652 0.0f, 0.0f, 0.0f, 1.0f }; 1653 1654 return result; 1655 } 1656 1657 // Create rotation matrix from axis and angle 1658 // NOTE: Angle should be provided in radians 1659 RMAPI Matrix MatrixRotate(Vector3 axis, float angle) 1660 { 1661 Matrix result = { 0 }; 1662 1663 float x = axis.x, y = axis.y, z = axis.z; 1664 1665 float lengthSquared = x*x + y*y + z*z; 1666 1667 if ((lengthSquared != 1.0f) && (lengthSquared != 0.0f)) 1668 { 1669 float ilength = 1.0f/sqrtf(lengthSquared); 1670 x *= ilength; 1671 y *= ilength; 1672 z *= ilength; 1673 } 1674 1675 float sinres = sinf(angle); 1676 float cosres = cosf(angle); 1677 float t = 1.0f - cosres; 1678 1679 result.m0 = x*x*t + cosres; 1680 result.m1 = y*x*t + z*sinres; 1681 result.m2 = z*x*t - y*sinres; 1682 result.m3 = 0.0f; 1683 1684 result.m4 = x*y*t - z*sinres; 1685 result.m5 = y*y*t + cosres; 1686 result.m6 = z*y*t + x*sinres; 1687 result.m7 = 0.0f; 1688 1689 result.m8 = x*z*t + y*sinres; 1690 result.m9 = y*z*t - x*sinres; 1691 result.m10 = z*z*t + cosres; 1692 result.m11 = 0.0f; 1693 1694 result.m12 = 0.0f; 1695 result.m13 = 0.0f; 1696 result.m14 = 0.0f; 1697 result.m15 = 1.0f; 1698 1699 return result; 1700 } 1701 1702 // Get x-rotation matrix 1703 // NOTE: Angle must be provided in radians 1704 RMAPI Matrix MatrixRotateX(float angle) 1705 { 1706 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 1707 0.0f, 1.0f, 0.0f, 0.0f, 1708 0.0f, 0.0f, 1.0f, 0.0f, 1709 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() 1710 1711 float cosres = cosf(angle); 1712 float sinres = sinf(angle); 1713 1714 result.m5 = cosres; 1715 result.m6 = sinres; 1716 result.m9 = -sinres; 1717 result.m10 = cosres; 1718 1719 return result; 1720 } 1721 1722 // Get y-rotation matrix 1723 // NOTE: Angle must be provided in radians 1724 RMAPI Matrix MatrixRotateY(float angle) 1725 { 1726 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 1727 0.0f, 1.0f, 0.0f, 0.0f, 1728 0.0f, 0.0f, 1.0f, 0.0f, 1729 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() 1730 1731 float cosres = cosf(angle); 1732 float sinres = sinf(angle); 1733 1734 result.m0 = cosres; 1735 result.m2 = -sinres; 1736 result.m8 = sinres; 1737 result.m10 = cosres; 1738 1739 return result; 1740 } 1741 1742 // Get z-rotation matrix 1743 // NOTE: Angle must be provided in radians 1744 RMAPI Matrix MatrixRotateZ(float angle) 1745 { 1746 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 1747 0.0f, 1.0f, 0.0f, 0.0f, 1748 0.0f, 0.0f, 1.0f, 0.0f, 1749 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() 1750 1751 float cosres = cosf(angle); 1752 float sinres = sinf(angle); 1753 1754 result.m0 = cosres; 1755 result.m1 = sinres; 1756 result.m4 = -sinres; 1757 result.m5 = cosres; 1758 1759 return result; 1760 } 1761 1762 1763 // Get xyz-rotation matrix 1764 // NOTE: Angle must be provided in radians 1765 RMAPI Matrix MatrixRotateXYZ(Vector3 angle) 1766 { 1767 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 1768 0.0f, 1.0f, 0.0f, 0.0f, 1769 0.0f, 0.0f, 1.0f, 0.0f, 1770 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() 1771 1772 float cosz = cosf(-angle.z); 1773 float sinz = sinf(-angle.z); 1774 float cosy = cosf(-angle.y); 1775 float siny = sinf(-angle.y); 1776 float cosx = cosf(-angle.x); 1777 float sinx = sinf(-angle.x); 1778 1779 result.m0 = cosz*cosy; 1780 result.m1 = (cosz*siny*sinx) - (sinz*cosx); 1781 result.m2 = (cosz*siny*cosx) + (sinz*sinx); 1782 1783 result.m4 = sinz*cosy; 1784 result.m5 = (sinz*siny*sinx) + (cosz*cosx); 1785 result.m6 = (sinz*siny*cosx) - (cosz*sinx); 1786 1787 result.m8 = -siny; 1788 result.m9 = cosy*sinx; 1789 result.m10= cosy*cosx; 1790 1791 return result; 1792 } 1793 1794 // Get zyx-rotation matrix 1795 // NOTE: Angle must be provided in radians 1796 RMAPI Matrix MatrixRotateZYX(Vector3 angle) 1797 { 1798 Matrix result = { 0 }; 1799 1800 float cz = cosf(angle.z); 1801 float sz = sinf(angle.z); 1802 float cy = cosf(angle.y); 1803 float sy = sinf(angle.y); 1804 float cx = cosf(angle.x); 1805 float sx = sinf(angle.x); 1806 1807 result.m0 = cz*cy; 1808 result.m4 = cz*sy*sx - cx*sz; 1809 result.m8 = sz*sx + cz*cx*sy; 1810 result.m12 = 0; 1811 1812 result.m1 = cy*sz; 1813 result.m5 = cz*cx + sz*sy*sx; 1814 result.m9 = cx*sz*sy - cz*sx; 1815 result.m13 = 0; 1816 1817 result.m2 = -sy; 1818 result.m6 = cy*sx; 1819 result.m10 = cy*cx; 1820 result.m14 = 0; 1821 1822 result.m3 = 0; 1823 result.m7 = 0; 1824 result.m11 = 0; 1825 result.m15 = 1; 1826 1827 return result; 1828 } 1829 1830 // Get scaling matrix 1831 RMAPI Matrix MatrixScale(float x, float y, float z) 1832 { 1833 Matrix result = { x, 0.0f, 0.0f, 0.0f, 1834 0.0f, y, 0.0f, 0.0f, 1835 0.0f, 0.0f, z, 0.0f, 1836 0.0f, 0.0f, 0.0f, 1.0f }; 1837 1838 return result; 1839 } 1840 1841 // Get perspective projection matrix 1842 RMAPI Matrix MatrixFrustum(double left, double right, double bottom, double top, double nearPlane, double farPlane) 1843 { 1844 Matrix result = { 0 }; 1845 1846 float rl = (float)(right - left); 1847 float tb = (float)(top - bottom); 1848 float fn = (float)(farPlane - nearPlane); 1849 1850 result.m0 = ((float)nearPlane*2.0f)/rl; 1851 result.m1 = 0.0f; 1852 result.m2 = 0.0f; 1853 result.m3 = 0.0f; 1854 1855 result.m4 = 0.0f; 1856 result.m5 = ((float)nearPlane*2.0f)/tb; 1857 result.m6 = 0.0f; 1858 result.m7 = 0.0f; 1859 1860 result.m8 = ((float)right + (float)left)/rl; 1861 result.m9 = ((float)top + (float)bottom)/tb; 1862 result.m10 = -((float)farPlane + (float)nearPlane)/fn; 1863 result.m11 = -1.0f; 1864 1865 result.m12 = 0.0f; 1866 result.m13 = 0.0f; 1867 result.m14 = -((float)farPlane*(float)nearPlane*2.0f)/fn; 1868 result.m15 = 0.0f; 1869 1870 return result; 1871 } 1872 1873 // Get perspective projection matrix 1874 // NOTE: Fovy angle must be provided in radians 1875 RMAPI Matrix MatrixPerspective(double fovY, double aspect, double nearPlane, double farPlane) 1876 { 1877 Matrix result = { 0 }; 1878 1879 double top = nearPlane*tan(fovY*0.5); 1880 double bottom = -top; 1881 double right = top*aspect; 1882 double left = -right; 1883 1884 // MatrixFrustum(-right, right, -top, top, near, far); 1885 float rl = (float)(right - left); 1886 float tb = (float)(top - bottom); 1887 float fn = (float)(farPlane - nearPlane); 1888 1889 result.m0 = ((float)nearPlane*2.0f)/rl; 1890 result.m5 = ((float)nearPlane*2.0f)/tb; 1891 result.m8 = ((float)right + (float)left)/rl; 1892 result.m9 = ((float)top + (float)bottom)/tb; 1893 result.m10 = -((float)farPlane + (float)nearPlane)/fn; 1894 result.m11 = -1.0f; 1895 result.m14 = -((float)farPlane*(float)nearPlane*2.0f)/fn; 1896 1897 return result; 1898 } 1899 1900 // Get orthographic projection matrix 1901 RMAPI Matrix MatrixOrtho(double left, double right, double bottom, double top, double nearPlane, double farPlane) 1902 { 1903 Matrix result = { 0 }; 1904 1905 float rl = (float)(right - left); 1906 float tb = (float)(top - bottom); 1907 float fn = (float)(farPlane - nearPlane); 1908 1909 result.m0 = 2.0f/rl; 1910 result.m1 = 0.0f; 1911 result.m2 = 0.0f; 1912 result.m3 = 0.0f; 1913 result.m4 = 0.0f; 1914 result.m5 = 2.0f/tb; 1915 result.m6 = 0.0f; 1916 result.m7 = 0.0f; 1917 result.m8 = 0.0f; 1918 result.m9 = 0.0f; 1919 result.m10 = -2.0f/fn; 1920 result.m11 = 0.0f; 1921 result.m12 = -((float)left + (float)right)/rl; 1922 result.m13 = -((float)top + (float)bottom)/tb; 1923 result.m14 = -((float)farPlane + (float)nearPlane)/fn; 1924 result.m15 = 1.0f; 1925 1926 return result; 1927 } 1928 1929 // Get camera look-at matrix (view matrix) 1930 RMAPI Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) 1931 { 1932 Matrix result = { 0 }; 1933 1934 float length = 0.0f; 1935 float ilength = 0.0f; 1936 1937 // Vector3Subtract(eye, target) 1938 Vector3 vz = { eye.x - target.x, eye.y - target.y, eye.z - target.z }; 1939 1940 // Vector3Normalize(vz) 1941 Vector3 v = vz; 1942 length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 1943 if (length == 0.0f) length = 1.0f; 1944 ilength = 1.0f/length; 1945 vz.x *= ilength; 1946 vz.y *= ilength; 1947 vz.z *= ilength; 1948 1949 // Vector3CrossProduct(up, vz) 1950 Vector3 vx = { up.y*vz.z - up.z*vz.y, up.z*vz.x - up.x*vz.z, up.x*vz.y - up.y*vz.x }; 1951 1952 // Vector3Normalize(x) 1953 v = vx; 1954 length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); 1955 if (length == 0.0f) length = 1.0f; 1956 ilength = 1.0f/length; 1957 vx.x *= ilength; 1958 vx.y *= ilength; 1959 vx.z *= ilength; 1960 1961 // Vector3CrossProduct(vz, vx) 1962 Vector3 vy = { vz.y*vx.z - vz.z*vx.y, vz.z*vx.x - vz.x*vx.z, vz.x*vx.y - vz.y*vx.x }; 1963 1964 result.m0 = vx.x; 1965 result.m1 = vy.x; 1966 result.m2 = vz.x; 1967 result.m3 = 0.0f; 1968 result.m4 = vx.y; 1969 result.m5 = vy.y; 1970 result.m6 = vz.y; 1971 result.m7 = 0.0f; 1972 result.m8 = vx.z; 1973 result.m9 = vy.z; 1974 result.m10 = vz.z; 1975 result.m11 = 0.0f; 1976 result.m12 = -(vx.x*eye.x + vx.y*eye.y + vx.z*eye.z); // Vector3DotProduct(vx, eye) 1977 result.m13 = -(vy.x*eye.x + vy.y*eye.y + vy.z*eye.z); // Vector3DotProduct(vy, eye) 1978 result.m14 = -(vz.x*eye.x + vz.y*eye.y + vz.z*eye.z); // Vector3DotProduct(vz, eye) 1979 result.m15 = 1.0f; 1980 1981 return result; 1982 } 1983 1984 // Get float array of matrix data 1985 RMAPI float16 MatrixToFloatV(Matrix mat) 1986 { 1987 float16 result = { 0 }; 1988 1989 result.v[0] = mat.m0; 1990 result.v[1] = mat.m1; 1991 result.v[2] = mat.m2; 1992 result.v[3] = mat.m3; 1993 result.v[4] = mat.m4; 1994 result.v[5] = mat.m5; 1995 result.v[6] = mat.m6; 1996 result.v[7] = mat.m7; 1997 result.v[8] = mat.m8; 1998 result.v[9] = mat.m9; 1999 result.v[10] = mat.m10; 2000 result.v[11] = mat.m11; 2001 result.v[12] = mat.m12; 2002 result.v[13] = mat.m13; 2003 result.v[14] = mat.m14; 2004 result.v[15] = mat.m15; 2005 2006 return result; 2007 } 2008 2009 //---------------------------------------------------------------------------------- 2010 // Module Functions Definition - Quaternion math 2011 //---------------------------------------------------------------------------------- 2012 2013 // Add two quaternions 2014 RMAPI Quaternion QuaternionAdd(Quaternion q1, Quaternion q2) 2015 { 2016 Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w}; 2017 2018 return result; 2019 } 2020 2021 // Add quaternion and float value 2022 RMAPI Quaternion QuaternionAddValue(Quaternion q, float add) 2023 { 2024 Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add}; 2025 2026 return result; 2027 } 2028 2029 // Subtract two quaternions 2030 RMAPI Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2) 2031 { 2032 Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w}; 2033 2034 return result; 2035 } 2036 2037 // Subtract quaternion and float value 2038 RMAPI Quaternion QuaternionSubtractValue(Quaternion q, float sub) 2039 { 2040 Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; 2041 2042 return result; 2043 } 2044 2045 // Get identity quaternion 2046 RMAPI Quaternion QuaternionIdentity(void) 2047 { 2048 Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; 2049 2050 return result; 2051 } 2052 2053 // Computes the length of a quaternion 2054 RMAPI float QuaternionLength(Quaternion q) 2055 { 2056 float result = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2057 2058 return result; 2059 } 2060 2061 // Normalize provided quaternion 2062 RMAPI Quaternion QuaternionNormalize(Quaternion q) 2063 { 2064 Quaternion result = { 0 }; 2065 2066 float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2067 if (length == 0.0f) length = 1.0f; 2068 float ilength = 1.0f/length; 2069 2070 result.x = q.x*ilength; 2071 result.y = q.y*ilength; 2072 result.z = q.z*ilength; 2073 result.w = q.w*ilength; 2074 2075 return result; 2076 } 2077 2078 // Invert provided quaternion 2079 RMAPI Quaternion QuaternionInvert(Quaternion q) 2080 { 2081 Quaternion result = q; 2082 2083 float lengthSq = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w; 2084 2085 if (lengthSq != 0.0f) 2086 { 2087 float invLength = 1.0f/lengthSq; 2088 2089 result.x *= -invLength; 2090 result.y *= -invLength; 2091 result.z *= -invLength; 2092 result.w *= invLength; 2093 } 2094 2095 return result; 2096 } 2097 2098 // Calculate two quaternion multiplication 2099 RMAPI Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) 2100 { 2101 Quaternion result = { 0 }; 2102 2103 float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w; 2104 float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w; 2105 2106 result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby; 2107 result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz; 2108 result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx; 2109 result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz; 2110 2111 return result; 2112 } 2113 2114 // Scale quaternion by float value 2115 RMAPI Quaternion QuaternionScale(Quaternion q, float mul) 2116 { 2117 Quaternion result = { 0 }; 2118 2119 result.x = q.x*mul; 2120 result.y = q.y*mul; 2121 result.z = q.z*mul; 2122 result.w = q.w*mul; 2123 2124 return result; 2125 } 2126 2127 // Divide two quaternions 2128 RMAPI Quaternion QuaternionDivide(Quaternion q1, Quaternion q2) 2129 { 2130 Quaternion result = { q1.x/q2.x, q1.y/q2.y, q1.z/q2.z, q1.w/q2.w }; 2131 2132 return result; 2133 } 2134 2135 // Calculate linear interpolation between two quaternions 2136 RMAPI Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount) 2137 { 2138 Quaternion result = { 0 }; 2139 2140 result.x = q1.x + amount*(q2.x - q1.x); 2141 result.y = q1.y + amount*(q2.y - q1.y); 2142 result.z = q1.z + amount*(q2.z - q1.z); 2143 result.w = q1.w + amount*(q2.w - q1.w); 2144 2145 return result; 2146 } 2147 2148 // Calculate slerp-optimized interpolation between two quaternions 2149 RMAPI Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) 2150 { 2151 Quaternion result = { 0 }; 2152 2153 // QuaternionLerp(q1, q2, amount) 2154 result.x = q1.x + amount*(q2.x - q1.x); 2155 result.y = q1.y + amount*(q2.y - q1.y); 2156 result.z = q1.z + amount*(q2.z - q1.z); 2157 result.w = q1.w + amount*(q2.w - q1.w); 2158 2159 // QuaternionNormalize(q); 2160 Quaternion q = result; 2161 float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2162 if (length == 0.0f) length = 1.0f; 2163 float ilength = 1.0f/length; 2164 2165 result.x = q.x*ilength; 2166 result.y = q.y*ilength; 2167 result.z = q.z*ilength; 2168 result.w = q.w*ilength; 2169 2170 return result; 2171 } 2172 2173 // Calculates spherical linear interpolation between two quaternions 2174 RMAPI Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) 2175 { 2176 Quaternion result = { 0 }; 2177 2178 #if !defined(EPSILON) 2179 #define EPSILON 0.000001f 2180 #endif 2181 2182 float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w; 2183 2184 if (cosHalfTheta < 0) 2185 { 2186 q2.x = -q2.x; q2.y = -q2.y; q2.z = -q2.z; q2.w = -q2.w; 2187 cosHalfTheta = -cosHalfTheta; 2188 } 2189 2190 if (fabsf(cosHalfTheta) >= 1.0f) result = q1; 2191 else if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount); 2192 else 2193 { 2194 float halfTheta = acosf(cosHalfTheta); 2195 float sinHalfTheta = sqrtf(1.0f - cosHalfTheta*cosHalfTheta); 2196 2197 if (fabsf(sinHalfTheta) < EPSILON) 2198 { 2199 result.x = (q1.x*0.5f + q2.x*0.5f); 2200 result.y = (q1.y*0.5f + q2.y*0.5f); 2201 result.z = (q1.z*0.5f + q2.z*0.5f); 2202 result.w = (q1.w*0.5f + q2.w*0.5f); 2203 } 2204 else 2205 { 2206 float ratioA = sinf((1 - amount)*halfTheta)/sinHalfTheta; 2207 float ratioB = sinf(amount*halfTheta)/sinHalfTheta; 2208 2209 result.x = (q1.x*ratioA + q2.x*ratioB); 2210 result.y = (q1.y*ratioA + q2.y*ratioB); 2211 result.z = (q1.z*ratioA + q2.z*ratioB); 2212 result.w = (q1.w*ratioA + q2.w*ratioB); 2213 } 2214 } 2215 2216 return result; 2217 } 2218 2219 // Calculate quaternion cubic spline interpolation using Cubic Hermite Spline algorithm 2220 // as described in the GLTF 2.0 specification: https://registry.khronos.org/glTF/specs/2.0/glTF-2.0.html#interpolation-cubic 2221 RMAPI Quaternion QuaternionCubicHermiteSpline(Quaternion q1, Quaternion outTangent1, Quaternion q2, Quaternion inTangent2, float t) 2222 { 2223 float t2 = t*t; 2224 float t3 = t2*t; 2225 float h00 = 2*t3 - 3*t2 + 1; 2226 float h10 = t3 - 2*t2 + t; 2227 float h01 = -2*t3 + 3*t2; 2228 float h11 = t3 - t2; 2229 2230 Quaternion p0 = QuaternionScale(q1, h00); 2231 Quaternion m0 = QuaternionScale(outTangent1, h10); 2232 Quaternion p1 = QuaternionScale(q2, h01); 2233 Quaternion m1 = QuaternionScale(inTangent2, h11); 2234 2235 Quaternion result = { 0 }; 2236 2237 result = QuaternionAdd(p0, m0); 2238 result = QuaternionAdd(result, p1); 2239 result = QuaternionAdd(result, m1); 2240 result = QuaternionNormalize(result); 2241 2242 return result; 2243 } 2244 2245 // Calculate quaternion based on the rotation from one vector to another 2246 RMAPI Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) 2247 { 2248 Quaternion result = { 0 }; 2249 2250 float cos2Theta = (from.x*to.x + from.y*to.y + from.z*to.z); // Vector3DotProduct(from, to) 2251 Vector3 cross = { from.y*to.z - from.z*to.y, from.z*to.x - from.x*to.z, from.x*to.y - from.y*to.x }; // Vector3CrossProduct(from, to) 2252 2253 result.x = cross.x; 2254 result.y = cross.y; 2255 result.z = cross.z; 2256 result.w = 1.0f + cos2Theta; 2257 2258 // QuaternionNormalize(q); 2259 // NOTE: Normalize to essentially nlerp the original and identity to 0.5 2260 Quaternion q = result; 2261 float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2262 if (length == 0.0f) length = 1.0f; 2263 float ilength = 1.0f/length; 2264 2265 result.x = q.x*ilength; 2266 result.y = q.y*ilength; 2267 result.z = q.z*ilength; 2268 result.w = q.w*ilength; 2269 2270 return result; 2271 } 2272 2273 // Get a quaternion for a given rotation matrix 2274 RMAPI Quaternion QuaternionFromMatrix(Matrix mat) 2275 { 2276 Quaternion result = { 0 }; 2277 2278 float fourWSquaredMinus1 = mat.m0 + mat.m5 + mat.m10; 2279 float fourXSquaredMinus1 = mat.m0 - mat.m5 - mat.m10; 2280 float fourYSquaredMinus1 = mat.m5 - mat.m0 - mat.m10; 2281 float fourZSquaredMinus1 = mat.m10 - mat.m0 - mat.m5; 2282 2283 int biggestIndex = 0; 2284 float fourBiggestSquaredMinus1 = fourWSquaredMinus1; 2285 if (fourXSquaredMinus1 > fourBiggestSquaredMinus1) 2286 { 2287 fourBiggestSquaredMinus1 = fourXSquaredMinus1; 2288 biggestIndex = 1; 2289 } 2290 2291 if (fourYSquaredMinus1 > fourBiggestSquaredMinus1) 2292 { 2293 fourBiggestSquaredMinus1 = fourYSquaredMinus1; 2294 biggestIndex = 2; 2295 } 2296 2297 if (fourZSquaredMinus1 > fourBiggestSquaredMinus1) 2298 { 2299 fourBiggestSquaredMinus1 = fourZSquaredMinus1; 2300 biggestIndex = 3; 2301 } 2302 2303 float biggestVal = sqrtf(fourBiggestSquaredMinus1 + 1.0f)*0.5f; 2304 float mult = 0.25f/biggestVal; 2305 2306 switch (biggestIndex) 2307 { 2308 case 0: 2309 result.w = biggestVal; 2310 result.x = (mat.m6 - mat.m9)*mult; 2311 result.y = (mat.m8 - mat.m2)*mult; 2312 result.z = (mat.m1 - mat.m4)*mult; 2313 break; 2314 case 1: 2315 result.x = biggestVal; 2316 result.w = (mat.m6 - mat.m9)*mult; 2317 result.y = (mat.m1 + mat.m4)*mult; 2318 result.z = (mat.m8 + mat.m2)*mult; 2319 break; 2320 case 2: 2321 result.y = biggestVal; 2322 result.w = (mat.m8 - mat.m2)*mult; 2323 result.x = (mat.m1 + mat.m4)*mult; 2324 result.z = (mat.m6 + mat.m9)*mult; 2325 break; 2326 case 3: 2327 result.z = biggestVal; 2328 result.w = (mat.m1 - mat.m4)*mult; 2329 result.x = (mat.m8 + mat.m2)*mult; 2330 result.y = (mat.m6 + mat.m9)*mult; 2331 break; 2332 } 2333 2334 return result; 2335 } 2336 2337 // Get a matrix for a given quaternion 2338 RMAPI Matrix QuaternionToMatrix(Quaternion q) 2339 { 2340 Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, 2341 0.0f, 1.0f, 0.0f, 0.0f, 2342 0.0f, 0.0f, 1.0f, 0.0f, 2343 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() 2344 2345 float a2 = q.x*q.x; 2346 float b2 = q.y*q.y; 2347 float c2 = q.z*q.z; 2348 float ac = q.x*q.z; 2349 float ab = q.x*q.y; 2350 float bc = q.y*q.z; 2351 float ad = q.w*q.x; 2352 float bd = q.w*q.y; 2353 float cd = q.w*q.z; 2354 2355 result.m0 = 1 - 2*(b2 + c2); 2356 result.m1 = 2*(ab + cd); 2357 result.m2 = 2*(ac - bd); 2358 2359 result.m4 = 2*(ab - cd); 2360 result.m5 = 1 - 2*(a2 + c2); 2361 result.m6 = 2*(bc + ad); 2362 2363 result.m8 = 2*(ac + bd); 2364 result.m9 = 2*(bc - ad); 2365 result.m10 = 1 - 2*(a2 + b2); 2366 2367 return result; 2368 } 2369 2370 // Get rotation quaternion for an angle and axis 2371 // NOTE: Angle must be provided in radians 2372 RMAPI Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) 2373 { 2374 Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; 2375 2376 float axisLength = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z); 2377 2378 if (axisLength != 0.0f) 2379 { 2380 angle *= 0.5f; 2381 2382 float length = 0.0f; 2383 float ilength = 0.0f; 2384 2385 // Vector3Normalize(axis) 2386 length = axisLength; 2387 if (length == 0.0f) length = 1.0f; 2388 ilength = 1.0f/length; 2389 axis.x *= ilength; 2390 axis.y *= ilength; 2391 axis.z *= ilength; 2392 2393 float sinres = sinf(angle); 2394 float cosres = cosf(angle); 2395 2396 result.x = axis.x*sinres; 2397 result.y = axis.y*sinres; 2398 result.z = axis.z*sinres; 2399 result.w = cosres; 2400 2401 // QuaternionNormalize(q); 2402 Quaternion q = result; 2403 length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2404 if (length == 0.0f) length = 1.0f; 2405 ilength = 1.0f/length; 2406 result.x = q.x*ilength; 2407 result.y = q.y*ilength; 2408 result.z = q.z*ilength; 2409 result.w = q.w*ilength; 2410 } 2411 2412 return result; 2413 } 2414 2415 // Get the rotation angle and axis for a given quaternion 2416 RMAPI void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) 2417 { 2418 if (fabsf(q.w) > 1.0f) 2419 { 2420 // QuaternionNormalize(q); 2421 float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); 2422 if (length == 0.0f) length = 1.0f; 2423 float ilength = 1.0f/length; 2424 2425 q.x = q.x*ilength; 2426 q.y = q.y*ilength; 2427 q.z = q.z*ilength; 2428 q.w = q.w*ilength; 2429 } 2430 2431 Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; 2432 float resAngle = 2.0f*acosf(q.w); 2433 float den = sqrtf(1.0f - q.w*q.w); 2434 2435 if (den > EPSILON) 2436 { 2437 resAxis.x = q.x/den; 2438 resAxis.y = q.y/den; 2439 resAxis.z = q.z/den; 2440 } 2441 else 2442 { 2443 // This occurs when the angle is zero. 2444 // Not a problem: just set an arbitrary normalized axis. 2445 resAxis.x = 1.0f; 2446 } 2447 2448 *outAxis = resAxis; 2449 *outAngle = resAngle; 2450 } 2451 2452 // Get the quaternion equivalent to Euler angles 2453 // NOTE: Rotation order is ZYX 2454 RMAPI Quaternion QuaternionFromEuler(float pitch, float yaw, float roll) 2455 { 2456 Quaternion result = { 0 }; 2457 2458 float x0 = cosf(pitch*0.5f); 2459 float x1 = sinf(pitch*0.5f); 2460 float y0 = cosf(yaw*0.5f); 2461 float y1 = sinf(yaw*0.5f); 2462 float z0 = cosf(roll*0.5f); 2463 float z1 = sinf(roll*0.5f); 2464 2465 result.x = x1*y0*z0 - x0*y1*z1; 2466 result.y = x0*y1*z0 + x1*y0*z1; 2467 result.z = x0*y0*z1 - x1*y1*z0; 2468 result.w = x0*y0*z0 + x1*y1*z1; 2469 2470 return result; 2471 } 2472 2473 // Get the Euler angles equivalent to quaternion (roll, pitch, yaw) 2474 // NOTE: Angles are returned in a Vector3 struct in radians 2475 RMAPI Vector3 QuaternionToEuler(Quaternion q) 2476 { 2477 Vector3 result = { 0 }; 2478 2479 // Roll (x-axis rotation) 2480 float x0 = 2.0f*(q.w*q.x + q.y*q.z); 2481 float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y); 2482 result.x = atan2f(x0, x1); 2483 2484 // Pitch (y-axis rotation) 2485 float y0 = 2.0f*(q.w*q.y - q.z*q.x); 2486 y0 = y0 > 1.0f ? 1.0f : y0; 2487 y0 = y0 < -1.0f ? -1.0f : y0; 2488 result.y = asinf(y0); 2489 2490 // Yaw (z-axis rotation) 2491 float z0 = 2.0f*(q.w*q.z + q.x*q.y); 2492 float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z); 2493 result.z = atan2f(z0, z1); 2494 2495 return result; 2496 } 2497 2498 // Transform a quaternion given a transformation matrix 2499 RMAPI Quaternion QuaternionTransform(Quaternion q, Matrix mat) 2500 { 2501 Quaternion result = { 0 }; 2502 2503 result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w; 2504 result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w; 2505 result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w; 2506 result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w; 2507 2508 return result; 2509 } 2510 2511 // Check whether two given quaternions are almost equal 2512 RMAPI int QuaternionEquals(Quaternion p, Quaternion q) 2513 { 2514 #if !defined(EPSILON) 2515 #define EPSILON 0.000001f 2516 #endif 2517 2518 int result = (((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && 2519 ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && 2520 ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) && 2521 ((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))) || 2522 (((fabsf(p.x + q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && 2523 ((fabsf(p.y + q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && 2524 ((fabsf(p.z + q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) && 2525 ((fabsf(p.w + q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))); 2526 2527 return result; 2528 } 2529 2530 // Decompose a transformation matrix into its rotational, translational and scaling components 2531 RMAPI void MatrixDecompose(Matrix mat, Vector3 *translation, Quaternion *rotation, Vector3 *scale) 2532 { 2533 // Extract translation. 2534 translation->x = mat.m12; 2535 translation->y = mat.m13; 2536 translation->z = mat.m14; 2537 2538 // Extract upper-left for determinant computation 2539 const float a = mat.m0; 2540 const float b = mat.m4; 2541 const float c = mat.m8; 2542 const float d = mat.m1; 2543 const float e = mat.m5; 2544 const float f = mat.m9; 2545 const float g = mat.m2; 2546 const float h = mat.m6; 2547 const float i = mat.m10; 2548 const float A = e*i - f*h; 2549 const float B = f*g - d*i; 2550 const float C = d*h - e*g; 2551 2552 // Extract scale 2553 const float det = a*A + b*B + c*C; 2554 Vector3 abc = { a, b, c }; 2555 Vector3 def = { d, e, f }; 2556 Vector3 ghi = { g, h, i }; 2557 2558 float scalex = Vector3Length(abc); 2559 float scaley = Vector3Length(def); 2560 float scalez = Vector3Length(ghi); 2561 Vector3 s = { scalex, scaley, scalez }; 2562 2563 if (det < 0) s = Vector3Negate(s); 2564 2565 *scale = s; 2566 2567 // Remove scale from the matrix if it is not close to zero 2568 Matrix clone = mat; 2569 if (!FloatEquals(det, 0)) 2570 { 2571 clone.m0 /= s.x; 2572 clone.m4 /= s.x; 2573 clone.m8 /= s.x; 2574 clone.m1 /= s.y; 2575 clone.m5 /= s.y; 2576 clone.m9 /= s.y; 2577 clone.m2 /= s.z; 2578 clone.m6 /= s.z; 2579 clone.m10 /= s.z; 2580 2581 // Extract rotation 2582 *rotation = QuaternionFromMatrix(clone); 2583 } 2584 else 2585 { 2586 // Set to identity if close to zero 2587 *rotation = QuaternionIdentity(); 2588 } 2589 } 2590 2591 #if defined(__cplusplus) && !defined(RAYMATH_DISABLE_CPP_OPERATORS) 2592 2593 // Optional C++ math operators 2594 //------------------------------------------------------------------------------- 2595 2596 // Vector2 operators 2597 static constexpr Vector2 Vector2Zeros = { 0, 0 }; 2598 static constexpr Vector2 Vector2Ones = { 1, 1 }; 2599 static constexpr Vector2 Vector2UnitX = { 1, 0 }; 2600 static constexpr Vector2 Vector2UnitY = { 0, 1 }; 2601 2602 inline Vector2 operator + (const Vector2& lhs, const Vector2& rhs) 2603 { 2604 return Vector2Add(lhs, rhs); 2605 } 2606 2607 inline const Vector2& operator += (Vector2& lhs, const Vector2& rhs) 2608 { 2609 lhs = Vector2Add(lhs, rhs); 2610 return lhs; 2611 } 2612 2613 inline Vector2 operator - (const Vector2& lhs, const Vector2& rhs) 2614 { 2615 return Vector2Subtract(lhs, rhs); 2616 } 2617 2618 inline const Vector2& operator -= (Vector2& lhs, const Vector2& rhs) 2619 { 2620 lhs = Vector2Subtract(lhs, rhs); 2621 return lhs; 2622 } 2623 2624 inline Vector2 operator * (const Vector2& lhs, const float& rhs) 2625 { 2626 return Vector2Scale(lhs, rhs); 2627 } 2628 2629 inline const Vector2& operator *= (Vector2& lhs, const float& rhs) 2630 { 2631 lhs = Vector2Scale(lhs, rhs); 2632 return lhs; 2633 } 2634 2635 inline Vector2 operator * (const Vector2& lhs, const Vector2& rhs) 2636 { 2637 return Vector2Multiply(lhs, rhs); 2638 } 2639 2640 inline const Vector2& operator *= (Vector2& lhs, const Vector2& rhs) 2641 { 2642 lhs = Vector2Multiply(lhs, rhs); 2643 return lhs; 2644 } 2645 2646 inline Vector2 operator * (const Vector2& lhs, const Matrix& rhs) 2647 { 2648 return Vector2Transform(lhs, rhs); 2649 } 2650 2651 inline const Vector2& operator -= (Vector2& lhs, const Matrix& rhs) 2652 { 2653 lhs = Vector2Transform(lhs, rhs); 2654 return lhs; 2655 } 2656 2657 inline Vector2 operator / (const Vector2& lhs, const float& rhs) 2658 { 2659 return Vector2Scale(lhs, 1.0f / rhs); 2660 } 2661 2662 inline const Vector2& operator /= (Vector2& lhs, const float& rhs) 2663 { 2664 lhs = Vector2Scale(lhs, rhs); 2665 return lhs; 2666 } 2667 2668 inline Vector2 operator / (const Vector2& lhs, const Vector2& rhs) 2669 { 2670 return Vector2Divide(lhs, rhs); 2671 } 2672 2673 inline const Vector2& operator /= (Vector2& lhs, const Vector2& rhs) 2674 { 2675 lhs = Vector2Divide(lhs, rhs); 2676 return lhs; 2677 } 2678 2679 inline bool operator == (const Vector2& lhs, const Vector2& rhs) 2680 { 2681 return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y); 2682 } 2683 2684 inline bool operator != (const Vector2& lhs, const Vector2& rhs) 2685 { 2686 return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y); 2687 } 2688 2689 // Vector3 operators 2690 static constexpr Vector3 Vector3Zeros = { 0, 0, 0 }; 2691 static constexpr Vector3 Vector3Ones = { 1, 1, 1 }; 2692 static constexpr Vector3 Vector3UnitX = { 1, 0, 0 }; 2693 static constexpr Vector3 Vector3UnitY = { 0, 1, 0 }; 2694 static constexpr Vector3 Vector3UnitZ = { 0, 0, 1 }; 2695 2696 inline Vector3 operator + (const Vector3& lhs, const Vector3& rhs) 2697 { 2698 return Vector3Add(lhs, rhs); 2699 } 2700 2701 inline const Vector3& operator += (Vector3& lhs, const Vector3& rhs) 2702 { 2703 lhs = Vector3Add(lhs, rhs); 2704 return lhs; 2705 } 2706 2707 inline Vector3 operator - (const Vector3& lhs, const Vector3& rhs) 2708 { 2709 return Vector3Subtract(lhs, rhs); 2710 } 2711 2712 inline const Vector3& operator -= (Vector3& lhs, const Vector3& rhs) 2713 { 2714 lhs = Vector3Subtract(lhs, rhs); 2715 return lhs; 2716 } 2717 2718 inline Vector3 operator * (const Vector3& lhs, const float& rhs) 2719 { 2720 return Vector3Scale(lhs, rhs); 2721 } 2722 2723 inline const Vector3& operator *= (Vector3& lhs, const float& rhs) 2724 { 2725 lhs = Vector3Scale(lhs, rhs); 2726 return lhs; 2727 } 2728 2729 inline Vector3 operator * (const Vector3& lhs, const Vector3& rhs) 2730 { 2731 return Vector3Multiply(lhs, rhs); 2732 } 2733 2734 inline const Vector3& operator *= (Vector3& lhs, const Vector3& rhs) 2735 { 2736 lhs = Vector3Multiply(lhs, rhs); 2737 return lhs; 2738 } 2739 2740 inline Vector3 operator * (const Vector3& lhs, const Matrix& rhs) 2741 { 2742 return Vector3Transform(lhs, rhs); 2743 } 2744 2745 inline const Vector3& operator -= (Vector3& lhs, const Matrix& rhs) 2746 { 2747 lhs = Vector3Transform(lhs, rhs); 2748 return lhs; 2749 } 2750 2751 inline Vector3 operator / (const Vector3& lhs, const float& rhs) 2752 { 2753 return Vector3Scale(lhs, 1.0f / rhs); 2754 } 2755 2756 inline const Vector3& operator /= (Vector3& lhs, const float& rhs) 2757 { 2758 lhs = Vector3Scale(lhs, rhs); 2759 return lhs; 2760 } 2761 2762 inline Vector3 operator / (const Vector3& lhs, const Vector3& rhs) 2763 { 2764 return Vector3Divide(lhs, rhs); 2765 } 2766 2767 inline const Vector3& operator /= (Vector3& lhs, const Vector3& rhs) 2768 { 2769 lhs = Vector3Divide(lhs, rhs); 2770 return lhs; 2771 } 2772 2773 inline bool operator == (const Vector3& lhs, const Vector3& rhs) 2774 { 2775 return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y) && FloatEquals(lhs.z, rhs.z); 2776 } 2777 2778 inline bool operator != (const Vector3& lhs, const Vector3& rhs) 2779 { 2780 return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y) || !FloatEquals(lhs.z, rhs.z); 2781 } 2782 2783 // Vector4 operators 2784 static constexpr Vector4 Vector4Zeros = { 0, 0, 0, 0 }; 2785 static constexpr Vector4 Vector4Ones = { 1, 1, 1, 1 }; 2786 static constexpr Vector4 Vector4UnitX = { 1, 0, 0, 0 }; 2787 static constexpr Vector4 Vector4UnitY = { 0, 1, 0, 0 }; 2788 static constexpr Vector4 Vector4UnitZ = { 0, 0, 1, 0 }; 2789 static constexpr Vector4 Vector4UnitW = { 0, 0, 0, 1 }; 2790 2791 inline Vector4 operator + (const Vector4& lhs, const Vector4& rhs) 2792 { 2793 return Vector4Add(lhs, rhs); 2794 } 2795 2796 inline const Vector4& operator += (Vector4& lhs, const Vector4& rhs) 2797 { 2798 lhs = Vector4Add(lhs, rhs); 2799 return lhs; 2800 } 2801 2802 inline Vector4 operator - (const Vector4& lhs, const Vector4& rhs) 2803 { 2804 return Vector4Subtract(lhs, rhs); 2805 } 2806 2807 inline const Vector4& operator -= (Vector4& lhs, const Vector4& rhs) 2808 { 2809 lhs = Vector4Subtract(lhs, rhs); 2810 return lhs; 2811 } 2812 2813 inline Vector4 operator * (const Vector4& lhs, const float& rhs) 2814 { 2815 return Vector4Scale(lhs, rhs); 2816 } 2817 2818 inline const Vector4& operator *= (Vector4& lhs, const float& rhs) 2819 { 2820 lhs = Vector4Scale(lhs, rhs); 2821 return lhs; 2822 } 2823 2824 inline Vector4 operator * (const Vector4& lhs, const Vector4& rhs) 2825 { 2826 return Vector4Multiply(lhs, rhs); 2827 } 2828 2829 inline const Vector4& operator *= (Vector4& lhs, const Vector4& rhs) 2830 { 2831 lhs = Vector4Multiply(lhs, rhs); 2832 return lhs; 2833 } 2834 2835 inline Vector4 operator / (const Vector4& lhs, const float& rhs) 2836 { 2837 return Vector4Scale(lhs, 1.0f / rhs); 2838 } 2839 2840 inline const Vector4& operator /= (Vector4& lhs, const float& rhs) 2841 { 2842 lhs = Vector4Scale(lhs, rhs); 2843 return lhs; 2844 } 2845 2846 inline Vector4 operator / (const Vector4& lhs, const Vector4& rhs) 2847 { 2848 return Vector4Divide(lhs, rhs); 2849 } 2850 2851 inline const Vector4& operator /= (Vector4& lhs, const Vector4& rhs) 2852 { 2853 lhs = Vector4Divide(lhs, rhs); 2854 return lhs; 2855 } 2856 2857 inline bool operator == (const Vector4& lhs, const Vector4& rhs) 2858 { 2859 return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y) && FloatEquals(lhs.z, rhs.z) && FloatEquals(lhs.w, rhs.w); 2860 } 2861 2862 inline bool operator != (const Vector4& lhs, const Vector4& rhs) 2863 { 2864 return !FloatEquals(lhs.x, rhs.x) || !FloatEquals(lhs.y, rhs.y) || !FloatEquals(lhs.z, rhs.z) || !FloatEquals(lhs.w, rhs.w); 2865 } 2866 2867 // Quaternion operators 2868 static constexpr Quaternion QuaternionZeros = { 0, 0, 0, 0 }; 2869 static constexpr Quaternion QuaternionOnes = { 1, 1, 1, 1 }; 2870 static constexpr Quaternion QuaternionUnitX = { 0, 0, 0, 1 }; 2871 2872 inline Quaternion operator + (const Quaternion& lhs, const float& rhs) 2873 { 2874 return QuaternionAddValue(lhs, rhs); 2875 } 2876 2877 inline const Quaternion& operator += (Quaternion& lhs, const float& rhs) 2878 { 2879 lhs = QuaternionAddValue(lhs, rhs); 2880 return lhs; 2881 } 2882 2883 inline Quaternion operator - (const Quaternion& lhs, const float& rhs) 2884 { 2885 return QuaternionSubtractValue(lhs, rhs); 2886 } 2887 2888 inline const Quaternion& operator -= (Quaternion& lhs, const float& rhs) 2889 { 2890 lhs = QuaternionSubtractValue(lhs, rhs); 2891 return lhs; 2892 } 2893 2894 inline Quaternion operator * (const Quaternion& lhs, const Matrix& rhs) 2895 { 2896 return QuaternionTransform(lhs, rhs); 2897 } 2898 2899 inline const Quaternion& operator *= (Quaternion& lhs, const Matrix& rhs) 2900 { 2901 lhs = QuaternionTransform(lhs, rhs); 2902 return lhs; 2903 } 2904 2905 // Matrix operators 2906 inline Matrix operator + (const Matrix& lhs, const Matrix& rhs) 2907 { 2908 return MatrixAdd(lhs, rhs); 2909 } 2910 2911 inline const Matrix& operator += (Matrix& lhs, const Matrix& rhs) 2912 { 2913 lhs = MatrixAdd(lhs, rhs); 2914 return lhs; 2915 } 2916 2917 inline Matrix operator - (const Matrix& lhs, const Matrix& rhs) 2918 { 2919 return MatrixSubtract(lhs, rhs); 2920 } 2921 2922 inline const Matrix& operator -= (Matrix& lhs, const Matrix& rhs) 2923 { 2924 lhs = MatrixSubtract(lhs, rhs); 2925 return lhs; 2926 } 2927 2928 inline Matrix operator * (const Matrix& lhs, const Matrix& rhs) 2929 { 2930 return MatrixMultiply(lhs, rhs); 2931 } 2932 2933 inline const Matrix& operator *= (Matrix& lhs, const Matrix& rhs) 2934 { 2935 lhs = MatrixMultiply(lhs, rhs); 2936 return lhs; 2937 } 2938 //------------------------------------------------------------------------------- 2939 #endif // C++ operators 2940 2941 #endif // RAYMATH_H