so://phie

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   1/**********************************************************************************************
   2*
   3*   raymath v1.5 - 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
  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*
  31*   LICENSE: zlib/libpng
  32*
  33*   Copyright (c) 2015-2024 Ramon Santamaria (@raysan5)
  34*
  35*   This software is provided "as-is", without any express or implied warranty. In no event
  36*   will the authors be held liable for any damages arising from the use of this software.
  37*
  38*   Permission is granted to anyone to use this software for any purpose, including commercial
  39*   applications, and to alter it and redistribute it freely, subject to the following restrictions:
  40*
  41*     1. The origin of this software must not be misrepresented; you must not claim that you
  42*     wrote the original software. If you use this software in a product, an acknowledgment
  43*     in the product documentation would be appreciated but is not required.
  44*
  45*     2. Altered source versions must be plainly marked as such, and must not be misrepresented
  46*     as being the original software.
  47*
  48*     3. This notice may not be removed or altered from any source distribution.
  49*
  50**********************************************************************************************/
  51
  52#ifndef RAYMATH_H
  53#define RAYMATH_H
  54
  55#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_STATIC_INLINE)
  56    #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_STATIC_INLINE is contradictory"
  57#endif
  58
  59// Function specifiers definition
  60#if defined(RAYMATH_IMPLEMENTATION)
  61    #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED)
  62        #define RMAPI __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll)
  63    #elif defined(BUILD_LIBTYPE_SHARED)
  64        #define RMAPI __attribute__((visibility("default"))) // We are building raylib as a Unix shared library (.so/.dylib)
  65    #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED)
  66        #define RMAPI __declspec(dllimport)         // We are using raylib as a Win32 shared library (.dll)
  67    #else
  68        #define RMAPI extern inline // Provide external definition
  69    #endif
  70#elif defined(RAYMATH_STATIC_INLINE)
  71    #define RMAPI static inline // Functions may be inlined, no external out-of-line definition
  72#else
  73    #if defined(__TINYC__)
  74        #define RMAPI static inline // plain inline not supported by tinycc (See issue #435)
  75    #else
  76        #define RMAPI inline        // Functions may be inlined or external definition used
  77    #endif
  78#endif
  79
  80//----------------------------------------------------------------------------------
  81// Defines and Macros
  82//----------------------------------------------------------------------------------
  83#ifndef PI
  84    #define PI 3.14159265358979323846f
  85#endif
  86
  87#ifndef EPSILON
  88    #define EPSILON 0.000001f
  89#endif
  90
  91#ifndef DEG2RAD
  92    #define DEG2RAD (PI/180.0f)
  93#endif
  94
  95#ifndef RAD2DEG
  96    #define RAD2DEG (180.0f/PI)
  97#endif
  98
  99// Get float vector for Matrix
 100#ifndef MatrixToFloat
 101    #define MatrixToFloat(mat) (MatrixToFloatV(mat).v)
 102#endif
 103
 104// Get float vector for Vector3
 105#ifndef Vector3ToFloat
 106    #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v)
 107#endif
 108
 109//----------------------------------------------------------------------------------
 110// Types and Structures Definition
 111//----------------------------------------------------------------------------------
 112#if !defined(RL_VECTOR2_TYPE)
 113// Vector2 type
 114typedef struct Vector2 {
 115    float x;
 116    float y;
 117} Vector2;
 118#define RL_VECTOR2_TYPE
 119#endif
 120
 121#if !defined(RL_VECTOR3_TYPE)
 122// Vector3 type
 123typedef struct Vector3 {
 124    float x;
 125    float y;
 126    float z;
 127} Vector3;
 128#define RL_VECTOR3_TYPE
 129#endif
 130
 131#if !defined(RL_VECTOR4_TYPE)
 132// Vector4 type
 133typedef struct Vector4 {
 134    float x;
 135    float y;
 136    float z;
 137    float w;
 138} Vector4;
 139#define RL_VECTOR4_TYPE
 140#endif
 141
 142#if !defined(RL_QUATERNION_TYPE)
 143// Quaternion type
 144typedef Vector4 Quaternion;
 145#define RL_QUATERNION_TYPE
 146#endif
 147
 148#if !defined(RL_MATRIX_TYPE)
 149// Matrix type (OpenGL style 4x4 - right handed, column major)
 150typedef struct Matrix {
 151    float m0, m4, m8, m12;      // Matrix first row (4 components)
 152    float m1, m5, m9, m13;      // Matrix second row (4 components)
 153    float m2, m6, m10, m14;     // Matrix third row (4 components)
 154    float m3, m7, m11, m15;     // Matrix fourth row (4 components)
 155} Matrix;
 156#define RL_MATRIX_TYPE
 157#endif
 158
 159// NOTE: Helper types to be used instead of array return types for *ToFloat functions
 160typedef struct float3 {
 161    float v[3];
 162} float3;
 163
 164typedef struct float16 {
 165    float v[16];
 166} float16;
 167
 168#include <math.h>       // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), fminf(), fmaxf(), fabsf()
 169
 170//----------------------------------------------------------------------------------
 171// Module Functions Definition - Utils math
 172//----------------------------------------------------------------------------------
 173
 174// Clamp float value
 175RMAPI float Clamp(float value, float min, float max)
 176{
 177    float result = (value < min) ? min : value;
 178
 179    if (result > max) result = max;
 180
 181    return result;
 182}
 183
 184// Calculate linear interpolation between two floats
 185RMAPI float Lerp(float start, float end, float amount)
 186{
 187    float result = start + amount*(end - start);
 188
 189    return result;
 190}
 191
 192// Normalize input value within input range
 193RMAPI float Normalize(float value, float start, float end)
 194{
 195    float result = (value - start)/(end - start);
 196
 197    return result;
 198}
 199
 200// Remap input value within input range to output range
 201RMAPI float Remap(float value, float inputStart, float inputEnd, float outputStart, float outputEnd)
 202{
 203    float result = (value - inputStart)/(inputEnd - inputStart)*(outputEnd - outputStart) + outputStart;
 204
 205    return result;
 206}
 207
 208// Wrap input value from min to max
 209RMAPI float Wrap(float value, float min, float max)
 210{
 211    float result = value - (max - min)*floorf((value - min)/(max - min));
 212
 213    return result;
 214}
 215
 216// Check whether two given floats are almost equal
 217RMAPI int FloatEquals(float x, float y)
 218{
 219#if !defined(EPSILON)
 220    #define EPSILON 0.000001f
 221#endif
 222
 223    int result = (fabsf(x - y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(x), fabsf(y))));
 224
 225    return result;
 226}
 227
 228//----------------------------------------------------------------------------------
 229// Module Functions Definition - Vector2 math
 230//----------------------------------------------------------------------------------
 231
 232// Vector with components value 0.0f
 233RMAPI Vector2 Vector2Zero(void)
 234{
 235    Vector2 result = { 0.0f, 0.0f };
 236
 237    return result;
 238}
 239
 240// Vector with components value 1.0f
 241RMAPI Vector2 Vector2One(void)
 242{
 243    Vector2 result = { 1.0f, 1.0f };
 244
 245    return result;
 246}
 247
 248// Add two vectors (v1 + v2)
 249RMAPI Vector2 Vector2Add(Vector2 v1, Vector2 v2)
 250{
 251    Vector2 result = { v1.x + v2.x, v1.y + v2.y };
 252
 253    return result;
 254}
 255
 256// Add vector and float value
 257RMAPI Vector2 Vector2AddValue(Vector2 v, float add)
 258{
 259    Vector2 result = { v.x + add, v.y + add };
 260
 261    return result;
 262}
 263
 264// Subtract two vectors (v1 - v2)
 265RMAPI Vector2 Vector2Subtract(Vector2 v1, Vector2 v2)
 266{
 267    Vector2 result = { v1.x - v2.x, v1.y - v2.y };
 268
 269    return result;
 270}
 271
 272// Subtract vector by float value
 273RMAPI Vector2 Vector2SubtractValue(Vector2 v, float sub)
 274{
 275    Vector2 result = { v.x - sub, v.y - sub };
 276
 277    return result;
 278}
 279
 280// Calculate vector length
 281RMAPI float Vector2Length(Vector2 v)
 282{
 283    float result = sqrtf((v.x*v.x) + (v.y*v.y));
 284
 285    return result;
 286}
 287
 288// Calculate vector square length
 289RMAPI float Vector2LengthSqr(Vector2 v)
 290{
 291    float result = (v.x*v.x) + (v.y*v.y);
 292
 293    return result;
 294}
 295
 296// Calculate two vectors dot product
 297RMAPI float Vector2DotProduct(Vector2 v1, Vector2 v2)
 298{
 299    float result = (v1.x*v2.x + v1.y*v2.y);
 300
 301    return result;
 302}
 303
 304// Calculate distance between two vectors
 305RMAPI float Vector2Distance(Vector2 v1, Vector2 v2)
 306{
 307    float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
 308
 309    return result;
 310}
 311
 312// Calculate square distance between two vectors
 313RMAPI float Vector2DistanceSqr(Vector2 v1, Vector2 v2)
 314{
 315    float result = ((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y));
 316
 317    return result;
 318}
 319
 320// Calculate angle between two vectors
 321// NOTE: Angle is calculated from origin point (0, 0)
 322RMAPI float Vector2Angle(Vector2 v1, Vector2 v2)
 323{
 324    float result = 0.0f;
 325
 326    float dot = v1.x*v2.x + v1.y*v2.y;
 327    float det = v1.x*v2.y - v1.y*v2.x;
 328
 329    result = atan2f(det, dot);
 330
 331    return result;
 332}
 333
 334// Calculate angle defined by a two vectors line
 335// NOTE: Parameters need to be normalized
 336// Current implementation should be aligned with glm::angle
 337RMAPI float Vector2LineAngle(Vector2 start, Vector2 end)
 338{
 339    float result = 0.0f;
 340
 341    // TODO(10/9/2023): Currently angles move clockwise, determine if this is wanted behavior
 342    result = -atan2f(end.y - start.y, end.x - start.x);
 343
 344    return result;
 345}
 346
 347// Scale vector (multiply by value)
 348RMAPI Vector2 Vector2Scale(Vector2 v, float scale)
 349{
 350    Vector2 result = { v.x*scale, v.y*scale };
 351
 352    return result;
 353}
 354
 355// Multiply vector by vector
 356RMAPI Vector2 Vector2Multiply(Vector2 v1, Vector2 v2)
 357{
 358    Vector2 result = { v1.x*v2.x, v1.y*v2.y };
 359
 360    return result;
 361}
 362
 363// Negate vector
 364RMAPI Vector2 Vector2Negate(Vector2 v)
 365{
 366    Vector2 result = { -v.x, -v.y };
 367
 368    return result;
 369}
 370
 371// Divide vector by vector
 372RMAPI Vector2 Vector2Divide(Vector2 v1, Vector2 v2)
 373{
 374    Vector2 result = { v1.x/v2.x, v1.y/v2.y };
 375
 376    return result;
 377}
 378
 379// Normalize provided vector
 380RMAPI Vector2 Vector2Normalize(Vector2 v)
 381{
 382    Vector2 result = { 0 };
 383    float length = sqrtf((v.x*v.x) + (v.y*v.y));
 384
 385    if (length > 0)
 386    {
 387        float ilength = 1.0f/length;
 388        result.x = v.x*ilength;
 389        result.y = v.y*ilength;
 390    }
 391
 392    return result;
 393}
 394
 395// Transforms a Vector2 by a given Matrix
 396RMAPI Vector2 Vector2Transform(Vector2 v, Matrix mat)
 397{
 398    Vector2 result = { 0 };
 399
 400    float x = v.x;
 401    float y = v.y;
 402    float z = 0;
 403
 404    result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12;
 405    result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13;
 406
 407    return result;
 408}
 409
 410// Calculate linear interpolation between two vectors
 411RMAPI Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount)
 412{
 413    Vector2 result = { 0 };
 414
 415    result.x = v1.x + amount*(v2.x - v1.x);
 416    result.y = v1.y + amount*(v2.y - v1.y);
 417
 418    return result;
 419}
 420
 421// Calculate reflected vector to normal
 422RMAPI Vector2 Vector2Reflect(Vector2 v, Vector2 normal)
 423{
 424    Vector2 result = { 0 };
 425
 426    float dotProduct = (v.x*normal.x + v.y*normal.y); // Dot product
 427
 428    result.x = v.x - (2.0f*normal.x)*dotProduct;
 429    result.y = v.y - (2.0f*normal.y)*dotProduct;
 430
 431    return result;
 432}
 433
 434// Rotate vector by angle
 435RMAPI Vector2 Vector2Rotate(Vector2 v, float angle)
 436{
 437    Vector2 result = { 0 };
 438
 439    float cosres = cosf(angle);
 440    float sinres = sinf(angle);
 441
 442    result.x = v.x*cosres - v.y*sinres;
 443    result.y = v.x*sinres + v.y*cosres;
 444
 445    return result;
 446}
 447
 448// Move Vector towards target
 449RMAPI Vector2 Vector2MoveTowards(Vector2 v, Vector2 target, float maxDistance)
 450{
 451    Vector2 result = { 0 };
 452
 453    float dx = target.x - v.x;
 454    float dy = target.y - v.y;
 455    float value = (dx*dx) + (dy*dy);
 456
 457    if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target;
 458
 459    float dist = sqrtf(value);
 460
 461    result.x = v.x + dx/dist*maxDistance;
 462    result.y = v.y + dy/dist*maxDistance;
 463
 464    return result;
 465}
 466
 467// Invert the given vector
 468RMAPI Vector2 Vector2Invert(Vector2 v)
 469{
 470    Vector2 result = { 1.0f/v.x, 1.0f/v.y };
 471
 472    return result;
 473}
 474
 475// Clamp the components of the vector between
 476// min and max values specified by the given vectors
 477RMAPI Vector2 Vector2Clamp(Vector2 v, Vector2 min, Vector2 max)
 478{
 479    Vector2 result = { 0 };
 480
 481    result.x = fminf(max.x, fmaxf(min.x, v.x));
 482    result.y = fminf(max.y, fmaxf(min.y, v.y));
 483
 484    return result;
 485}
 486
 487// Clamp the magnitude of the vector between two min and max values
 488RMAPI Vector2 Vector2ClampValue(Vector2 v, float min, float max)
 489{
 490    Vector2 result = v;
 491
 492    float length = (v.x*v.x) + (v.y*v.y);
 493    if (length > 0.0f)
 494    {
 495        length = sqrtf(length);
 496
 497        float scale = 1;    // By default, 1 as the neutral element.
 498        if (length < min)
 499        {
 500            scale = min/length;
 501        }
 502        else if (length > max)
 503        {
 504            scale = max/length;
 505        }
 506
 507        result.x = v.x*scale;
 508        result.y = v.y*scale;
 509    }
 510
 511    return result;
 512}
 513
 514// Check whether two given vectors are almost equal
 515RMAPI int Vector2Equals(Vector2 p, Vector2 q)
 516{
 517#if !defined(EPSILON)
 518    #define EPSILON 0.000001f
 519#endif
 520
 521    int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
 522                  ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y)))));
 523
 524    return result;
 525}
 526
 527//----------------------------------------------------------------------------------
 528// Module Functions Definition - Vector3 math
 529//----------------------------------------------------------------------------------
 530
 531// Vector with components value 0.0f
 532RMAPI Vector3 Vector3Zero(void)
 533{
 534    Vector3 result = { 0.0f, 0.0f, 0.0f };
 535
 536    return result;
 537}
 538
 539// Vector with components value 1.0f
 540RMAPI Vector3 Vector3One(void)
 541{
 542    Vector3 result = { 1.0f, 1.0f, 1.0f };
 543
 544    return result;
 545}
 546
 547// Add two vectors
 548RMAPI Vector3 Vector3Add(Vector3 v1, Vector3 v2)
 549{
 550    Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z };
 551
 552    return result;
 553}
 554
 555// Add vector and float value
 556RMAPI Vector3 Vector3AddValue(Vector3 v, float add)
 557{
 558    Vector3 result = { v.x + add, v.y + add, v.z + add };
 559
 560    return result;
 561}
 562
 563// Subtract two vectors
 564RMAPI Vector3 Vector3Subtract(Vector3 v1, Vector3 v2)
 565{
 566    Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z };
 567
 568    return result;
 569}
 570
 571// Subtract vector by float value
 572RMAPI Vector3 Vector3SubtractValue(Vector3 v, float sub)
 573{
 574    Vector3 result = { v.x - sub, v.y - sub, v.z - sub };
 575
 576    return result;
 577}
 578
 579// Multiply vector by scalar
 580RMAPI Vector3 Vector3Scale(Vector3 v, float scalar)
 581{
 582    Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar };
 583
 584    return result;
 585}
 586
 587// Multiply vector by vector
 588RMAPI Vector3 Vector3Multiply(Vector3 v1, Vector3 v2)
 589{
 590    Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z };
 591
 592    return result;
 593}
 594
 595// Calculate two vectors cross product
 596RMAPI Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2)
 597{
 598    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 };
 599
 600    return result;
 601}
 602
 603// Calculate one vector perpendicular vector
 604RMAPI Vector3 Vector3Perpendicular(Vector3 v)
 605{
 606    Vector3 result = { 0 };
 607
 608    float min = fabsf(v.x);
 609    Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f};
 610
 611    if (fabsf(v.y) < min)
 612    {
 613        min = fabsf(v.y);
 614        Vector3 tmp = {0.0f, 1.0f, 0.0f};
 615        cardinalAxis = tmp;
 616    }
 617
 618    if (fabsf(v.z) < min)
 619    {
 620        Vector3 tmp = {0.0f, 0.0f, 1.0f};
 621        cardinalAxis = tmp;
 622    }
 623
 624    // Cross product between vectors
 625    result.x = v.y*cardinalAxis.z - v.z*cardinalAxis.y;
 626    result.y = v.z*cardinalAxis.x - v.x*cardinalAxis.z;
 627    result.z = v.x*cardinalAxis.y - v.y*cardinalAxis.x;
 628
 629    return result;
 630}
 631
 632// Calculate vector length
 633RMAPI float Vector3Length(const Vector3 v)
 634{
 635    float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
 636
 637    return result;
 638}
 639
 640// Calculate vector square length
 641RMAPI float Vector3LengthSqr(const Vector3 v)
 642{
 643    float result = v.x*v.x + v.y*v.y + v.z*v.z;
 644
 645    return result;
 646}
 647
 648// Calculate two vectors dot product
 649RMAPI float Vector3DotProduct(Vector3 v1, Vector3 v2)
 650{
 651    float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
 652
 653    return result;
 654}
 655
 656// Calculate distance between two vectors
 657RMAPI float Vector3Distance(Vector3 v1, Vector3 v2)
 658{
 659    float result = 0.0f;
 660
 661    float dx = v2.x - v1.x;
 662    float dy = v2.y - v1.y;
 663    float dz = v2.z - v1.z;
 664    result = sqrtf(dx*dx + dy*dy + dz*dz);
 665
 666    return result;
 667}
 668
 669// Calculate square distance between two vectors
 670RMAPI float Vector3DistanceSqr(Vector3 v1, Vector3 v2)
 671{
 672    float result = 0.0f;
 673
 674    float dx = v2.x - v1.x;
 675    float dy = v2.y - v1.y;
 676    float dz = v2.z - v1.z;
 677    result = dx*dx + dy*dy + dz*dz;
 678
 679    return result;
 680}
 681
 682// Calculate angle between two vectors
 683RMAPI float Vector3Angle(Vector3 v1, Vector3 v2)
 684{
 685    float result = 0.0f;
 686
 687    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 };
 688    float len = sqrtf(cross.x*cross.x + cross.y*cross.y + cross.z*cross.z);
 689    float dot = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
 690    result = atan2f(len, dot);
 691
 692    return result;
 693}
 694
 695// Negate provided vector (invert direction)
 696RMAPI Vector3 Vector3Negate(Vector3 v)
 697{
 698    Vector3 result = { -v.x, -v.y, -v.z };
 699
 700    return result;
 701}
 702
 703// Divide vector by vector
 704RMAPI Vector3 Vector3Divide(Vector3 v1, Vector3 v2)
 705{
 706    Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z };
 707
 708    return result;
 709}
 710
 711// Normalize provided vector
 712RMAPI Vector3 Vector3Normalize(Vector3 v)
 713{
 714    Vector3 result = v;
 715
 716    float length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
 717    if (length != 0.0f)
 718    {
 719        float ilength = 1.0f/length;
 720
 721        result.x *= ilength;
 722        result.y *= ilength;
 723        result.z *= ilength;
 724    }
 725
 726    return result;
 727}
 728
 729//Calculate the projection of the vector v1 on to v2
 730RMAPI Vector3 Vector3Project(Vector3 v1, Vector3 v2)
 731{
 732    Vector3 result = { 0 };
 733    
 734    float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
 735    float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z);
 736
 737    float mag = v1dv2/v2dv2;
 738
 739    result.x = v2.x*mag;
 740    result.y = v2.y*mag;
 741    result.z = v2.z*mag;
 742
 743    return result;
 744}
 745
 746//Calculate the rejection of the vector v1 on to v2
 747RMAPI Vector3 Vector3Reject(Vector3 v1, Vector3 v2)
 748{
 749    Vector3 result = { 0 };
 750    
 751    float v1dv2 = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z);
 752    float v2dv2 = (v2.x*v2.x + v2.y*v2.y + v2.z*v2.z);
 753
 754    float mag = v1dv2/v2dv2;
 755
 756    result.x = v1.x - (v2.x*mag);
 757    result.y = v1.y - (v2.y*mag);
 758    result.z = v1.z - (v2.z*mag);
 759
 760    return result;
 761}
 762
 763// Orthonormalize provided vectors
 764// Makes vectors normalized and orthogonal to each other
 765// Gram-Schmidt function implementation
 766RMAPI void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2)
 767{
 768    float length = 0.0f;
 769    float ilength = 0.0f;
 770
 771    // Vector3Normalize(*v1);
 772    Vector3 v = *v1;
 773    length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
 774    if (length == 0.0f) length = 1.0f;
 775    ilength = 1.0f/length;
 776    v1->x *= ilength;
 777    v1->y *= ilength;
 778    v1->z *= ilength;
 779
 780    // Vector3CrossProduct(*v1, *v2)
 781    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 };
 782
 783    // Vector3Normalize(vn1);
 784    v = vn1;
 785    length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
 786    if (length == 0.0f) length = 1.0f;
 787    ilength = 1.0f/length;
 788    vn1.x *= ilength;
 789    vn1.y *= ilength;
 790    vn1.z *= ilength;
 791
 792    // Vector3CrossProduct(vn1, *v1)
 793    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 };
 794
 795    *v2 = vn2;
 796}
 797
 798// Transforms a Vector3 by a given Matrix
 799RMAPI Vector3 Vector3Transform(Vector3 v, Matrix mat)
 800{
 801    Vector3 result = { 0 };
 802
 803    float x = v.x;
 804    float y = v.y;
 805    float z = v.z;
 806
 807    result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12;
 808    result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13;
 809    result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14;
 810
 811    return result;
 812}
 813
 814// Transform a vector by quaternion rotation
 815RMAPI Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q)
 816{
 817    Vector3 result = { 0 };
 818
 819    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);
 820    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);
 821    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);
 822
 823    return result;
 824}
 825
 826// Rotates a vector around an axis
 827RMAPI Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle)
 828{
 829    // Using Euler-Rodrigues Formula
 830    // Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula
 831
 832    Vector3 result = v;
 833
 834    // Vector3Normalize(axis);
 835    float length = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
 836    if (length == 0.0f) length = 1.0f;
 837    float ilength = 1.0f/length;
 838    axis.x *= ilength;
 839    axis.y *= ilength;
 840    axis.z *= ilength;
 841
 842    angle /= 2.0f;
 843    float a = sinf(angle);
 844    float b = axis.x*a;
 845    float c = axis.y*a;
 846    float d = axis.z*a;
 847    a = cosf(angle);
 848    Vector3 w = { b, c, d };
 849
 850    // Vector3CrossProduct(w, v)
 851    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 };
 852
 853    // Vector3CrossProduct(w, wv)
 854    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 };
 855
 856    // Vector3Scale(wv, 2*a)
 857    a *= 2;
 858    wv.x *= a;
 859    wv.y *= a;
 860    wv.z *= a;
 861
 862    // Vector3Scale(wwv, 2)
 863    wwv.x *= 2;
 864    wwv.y *= 2;
 865    wwv.z *= 2;
 866
 867    result.x += wv.x;
 868    result.y += wv.y;
 869    result.z += wv.z;
 870
 871    result.x += wwv.x;
 872    result.y += wwv.y;
 873    result.z += wwv.z;
 874
 875    return result;
 876}
 877
 878// Calculate linear interpolation between two vectors
 879RMAPI Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount)
 880{
 881    Vector3 result = { 0 };
 882
 883    result.x = v1.x + amount*(v2.x - v1.x);
 884    result.y = v1.y + amount*(v2.y - v1.y);
 885    result.z = v1.z + amount*(v2.z - v1.z);
 886
 887    return result;
 888}
 889
 890// Calculate reflected vector to normal
 891RMAPI Vector3 Vector3Reflect(Vector3 v, Vector3 normal)
 892{
 893    Vector3 result = { 0 };
 894
 895    // I is the original vector
 896    // N is the normal of the incident plane
 897    // R = I - (2*N*(DotProduct[I, N]))
 898
 899    float dotProduct = (v.x*normal.x + v.y*normal.y + v.z*normal.z);
 900
 901    result.x = v.x - (2.0f*normal.x)*dotProduct;
 902    result.y = v.y - (2.0f*normal.y)*dotProduct;
 903    result.z = v.z - (2.0f*normal.z)*dotProduct;
 904
 905    return result;
 906}
 907
 908// Get min value for each pair of components
 909RMAPI Vector3 Vector3Min(Vector3 v1, Vector3 v2)
 910{
 911    Vector3 result = { 0 };
 912
 913    result.x = fminf(v1.x, v2.x);
 914    result.y = fminf(v1.y, v2.y);
 915    result.z = fminf(v1.z, v2.z);
 916
 917    return result;
 918}
 919
 920// Get max value for each pair of components
 921RMAPI Vector3 Vector3Max(Vector3 v1, Vector3 v2)
 922{
 923    Vector3 result = { 0 };
 924
 925    result.x = fmaxf(v1.x, v2.x);
 926    result.y = fmaxf(v1.y, v2.y);
 927    result.z = fmaxf(v1.z, v2.z);
 928
 929    return result;
 930}
 931
 932// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c)
 933// NOTE: Assumes P is on the plane of the triangle
 934RMAPI Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c)
 935{
 936    Vector3 result = { 0 };
 937
 938    Vector3 v0 = { b.x - a.x, b.y - a.y, b.z - a.z };   // Vector3Subtract(b, a)
 939    Vector3 v1 = { c.x - a.x, c.y - a.y, c.z - a.z };   // Vector3Subtract(c, a)
 940    Vector3 v2 = { p.x - a.x, p.y - a.y, p.z - a.z };   // Vector3Subtract(p, a)
 941    float d00 = (v0.x*v0.x + v0.y*v0.y + v0.z*v0.z);    // Vector3DotProduct(v0, v0)
 942    float d01 = (v0.x*v1.x + v0.y*v1.y + v0.z*v1.z);    // Vector3DotProduct(v0, v1)
 943    float d11 = (v1.x*v1.x + v1.y*v1.y + v1.z*v1.z);    // Vector3DotProduct(v1, v1)
 944    float d20 = (v2.x*v0.x + v2.y*v0.y + v2.z*v0.z);    // Vector3DotProduct(v2, v0)
 945    float d21 = (v2.x*v1.x + v2.y*v1.y + v2.z*v1.z);    // Vector3DotProduct(v2, v1)
 946
 947    float denom = d00*d11 - d01*d01;
 948
 949    result.y = (d11*d20 - d01*d21)/denom;
 950    result.z = (d00*d21 - d01*d20)/denom;
 951    result.x = 1.0f - (result.z + result.y);
 952
 953    return result;
 954}
 955
 956// Projects a Vector3 from screen space into object space
 957// NOTE: We are avoiding calling other raymath functions despite available
 958RMAPI Vector3 Vector3Unproject(Vector3 source, Matrix projection, Matrix view)
 959{
 960    Vector3 result = { 0 };
 961
 962    // Calculate unprojected matrix (multiply view matrix by projection matrix) and invert it
 963    Matrix matViewProj = {      // MatrixMultiply(view, projection);
 964        view.m0*projection.m0 + view.m1*projection.m4 + view.m2*projection.m8 + view.m3*projection.m12,
 965        view.m0*projection.m1 + view.m1*projection.m5 + view.m2*projection.m9 + view.m3*projection.m13,
 966        view.m0*projection.m2 + view.m1*projection.m6 + view.m2*projection.m10 + view.m3*projection.m14,
 967        view.m0*projection.m3 + view.m1*projection.m7 + view.m2*projection.m11 + view.m3*projection.m15,
 968        view.m4*projection.m0 + view.m5*projection.m4 + view.m6*projection.m8 + view.m7*projection.m12,
 969        view.m4*projection.m1 + view.m5*projection.m5 + view.m6*projection.m9 + view.m7*projection.m13,
 970        view.m4*projection.m2 + view.m5*projection.m6 + view.m6*projection.m10 + view.m7*projection.m14,
 971        view.m4*projection.m3 + view.m5*projection.m7 + view.m6*projection.m11 + view.m7*projection.m15,
 972        view.m8*projection.m0 + view.m9*projection.m4 + view.m10*projection.m8 + view.m11*projection.m12,
 973        view.m8*projection.m1 + view.m9*projection.m5 + view.m10*projection.m9 + view.m11*projection.m13,
 974        view.m8*projection.m2 + view.m9*projection.m6 + view.m10*projection.m10 + view.m11*projection.m14,
 975        view.m8*projection.m3 + view.m9*projection.m7 + view.m10*projection.m11 + view.m11*projection.m15,
 976        view.m12*projection.m0 + view.m13*projection.m4 + view.m14*projection.m8 + view.m15*projection.m12,
 977        view.m12*projection.m1 + view.m13*projection.m5 + view.m14*projection.m9 + view.m15*projection.m13,
 978        view.m12*projection.m2 + view.m13*projection.m6 + view.m14*projection.m10 + view.m15*projection.m14,
 979        view.m12*projection.m3 + view.m13*projection.m7 + view.m14*projection.m11 + view.m15*projection.m15 };
 980
 981    // Calculate inverted matrix -> MatrixInvert(matViewProj);
 982    // Cache the matrix values (speed optimization)
 983    float a00 = matViewProj.m0, a01 = matViewProj.m1, a02 = matViewProj.m2, a03 = matViewProj.m3;
 984    float a10 = matViewProj.m4, a11 = matViewProj.m5, a12 = matViewProj.m6, a13 = matViewProj.m7;
 985    float a20 = matViewProj.m8, a21 = matViewProj.m9, a22 = matViewProj.m10, a23 = matViewProj.m11;
 986    float a30 = matViewProj.m12, a31 = matViewProj.m13, a32 = matViewProj.m14, a33 = matViewProj.m15;
 987
 988    float b00 = a00*a11 - a01*a10;
 989    float b01 = a00*a12 - a02*a10;
 990    float b02 = a00*a13 - a03*a10;
 991    float b03 = a01*a12 - a02*a11;
 992    float b04 = a01*a13 - a03*a11;
 993    float b05 = a02*a13 - a03*a12;
 994    float b06 = a20*a31 - a21*a30;
 995    float b07 = a20*a32 - a22*a30;
 996    float b08 = a20*a33 - a23*a30;
 997    float b09 = a21*a32 - a22*a31;
 998    float b10 = a21*a33 - a23*a31;
 999    float b11 = a22*a33 - a23*a32;
1000
1001    // Calculate the invert determinant (inlined to avoid double-caching)
1002    float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
1003
1004    Matrix matViewProjInv = {
1005        (a11*b11 - a12*b10 + a13*b09)*invDet,
1006        (-a01*b11 + a02*b10 - a03*b09)*invDet,
1007        (a31*b05 - a32*b04 + a33*b03)*invDet,
1008        (-a21*b05 + a22*b04 - a23*b03)*invDet,
1009        (-a10*b11 + a12*b08 - a13*b07)*invDet,
1010        (a00*b11 - a02*b08 + a03*b07)*invDet,
1011        (-a30*b05 + a32*b02 - a33*b01)*invDet,
1012        (a20*b05 - a22*b02 + a23*b01)*invDet,
1013        (a10*b10 - a11*b08 + a13*b06)*invDet,
1014        (-a00*b10 + a01*b08 - a03*b06)*invDet,
1015        (a30*b04 - a31*b02 + a33*b00)*invDet,
1016        (-a20*b04 + a21*b02 - a23*b00)*invDet,
1017        (-a10*b09 + a11*b07 - a12*b06)*invDet,
1018        (a00*b09 - a01*b07 + a02*b06)*invDet,
1019        (-a30*b03 + a31*b01 - a32*b00)*invDet,
1020        (a20*b03 - a21*b01 + a22*b00)*invDet };
1021
1022    // Create quaternion from source point
1023    Quaternion quat = { source.x, source.y, source.z, 1.0f };
1024
1025    // Multiply quat point by unprojecte matrix
1026    Quaternion qtransformed = {     // QuaternionTransform(quat, matViewProjInv)
1027        matViewProjInv.m0*quat.x + matViewProjInv.m4*quat.y + matViewProjInv.m8*quat.z + matViewProjInv.m12*quat.w,
1028        matViewProjInv.m1*quat.x + matViewProjInv.m5*quat.y + matViewProjInv.m9*quat.z + matViewProjInv.m13*quat.w,
1029        matViewProjInv.m2*quat.x + matViewProjInv.m6*quat.y + matViewProjInv.m10*quat.z + matViewProjInv.m14*quat.w,
1030        matViewProjInv.m3*quat.x + matViewProjInv.m7*quat.y + matViewProjInv.m11*quat.z + matViewProjInv.m15*quat.w };
1031
1032    // Normalized world points in vectors
1033    result.x = qtransformed.x/qtransformed.w;
1034    result.y = qtransformed.y/qtransformed.w;
1035    result.z = qtransformed.z/qtransformed.w;
1036
1037    return result;
1038}
1039
1040// Get Vector3 as float array
1041RMAPI float3 Vector3ToFloatV(Vector3 v)
1042{
1043    float3 buffer = { 0 };
1044
1045    buffer.v[0] = v.x;
1046    buffer.v[1] = v.y;
1047    buffer.v[2] = v.z;
1048
1049    return buffer;
1050}
1051
1052// Invert the given vector
1053RMAPI Vector3 Vector3Invert(Vector3 v)
1054{
1055    Vector3 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z };
1056
1057    return result;
1058}
1059
1060// Clamp the components of the vector between
1061// min and max values specified by the given vectors
1062RMAPI Vector3 Vector3Clamp(Vector3 v, Vector3 min, Vector3 max)
1063{
1064    Vector3 result = { 0 };
1065
1066    result.x = fminf(max.x, fmaxf(min.x, v.x));
1067    result.y = fminf(max.y, fmaxf(min.y, v.y));
1068    result.z = fminf(max.z, fmaxf(min.z, v.z));
1069
1070    return result;
1071}
1072
1073// Clamp the magnitude of the vector between two values
1074RMAPI Vector3 Vector3ClampValue(Vector3 v, float min, float max)
1075{
1076    Vector3 result = v;
1077
1078    float length = (v.x*v.x) + (v.y*v.y) + (v.z*v.z);
1079    if (length > 0.0f)
1080    {
1081        length = sqrtf(length);
1082
1083        float scale = 1;    // By default, 1 as the neutral element.
1084        if (length < min)
1085        {
1086            scale = min/length;
1087        }
1088        else if (length > max)
1089        {
1090            scale = max/length;
1091        }
1092
1093        result.x = v.x*scale;
1094        result.y = v.y*scale;
1095        result.z = v.z*scale;
1096    }
1097
1098    return result;
1099}
1100
1101// Check whether two given vectors are almost equal
1102RMAPI int Vector3Equals(Vector3 p, Vector3 q)
1103{
1104#if !defined(EPSILON)
1105    #define EPSILON 0.000001f
1106#endif
1107
1108    int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
1109                 ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
1110                 ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z)))));
1111
1112    return result;
1113}
1114
1115// Compute the direction of a refracted ray
1116// v: normalized direction of the incoming ray
1117// n: normalized normal vector of the interface of two optical media
1118// r: ratio of the refractive index of the medium from where the ray comes
1119//    to the refractive index of the medium on the other side of the surface
1120RMAPI Vector3 Vector3Refract(Vector3 v, Vector3 n, float r)
1121{
1122    Vector3 result = { 0 };
1123
1124    float dot = v.x*n.x + v.y*n.y + v.z*n.z;
1125    float d = 1.0f - r*r*(1.0f - dot*dot);
1126
1127    if (d >= 0.0f)
1128    {
1129        d = sqrtf(d);
1130        v.x = r*v.x - (r*dot + d)*n.x;
1131        v.y = r*v.y - (r*dot + d)*n.y;
1132        v.z = r*v.z - (r*dot + d)*n.z;
1133
1134        result = v;
1135    }
1136
1137    return result;
1138}
1139
1140//----------------------------------------------------------------------------------
1141// Module Functions Definition - Matrix math
1142//----------------------------------------------------------------------------------
1143
1144// Compute matrix determinant
1145RMAPI float MatrixDeterminant(Matrix mat)
1146{
1147    float result = 0.0f;
1148
1149    // Cache the matrix values (speed optimization)
1150    float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
1151    float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
1152    float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
1153    float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
1154
1155    result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 +
1156             a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 +
1157             a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 +
1158             a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 +
1159             a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 +
1160             a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33;
1161
1162    return result;
1163}
1164
1165// Get the trace of the matrix (sum of the values along the diagonal)
1166RMAPI float MatrixTrace(Matrix mat)
1167{
1168    float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15);
1169
1170    return result;
1171}
1172
1173// Transposes provided matrix
1174RMAPI Matrix MatrixTranspose(Matrix mat)
1175{
1176    Matrix result = { 0 };
1177
1178    result.m0 = mat.m0;
1179    result.m1 = mat.m4;
1180    result.m2 = mat.m8;
1181    result.m3 = mat.m12;
1182    result.m4 = mat.m1;
1183    result.m5 = mat.m5;
1184    result.m6 = mat.m9;
1185    result.m7 = mat.m13;
1186    result.m8 = mat.m2;
1187    result.m9 = mat.m6;
1188    result.m10 = mat.m10;
1189    result.m11 = mat.m14;
1190    result.m12 = mat.m3;
1191    result.m13 = mat.m7;
1192    result.m14 = mat.m11;
1193    result.m15 = mat.m15;
1194
1195    return result;
1196}
1197
1198// Invert provided matrix
1199RMAPI Matrix MatrixInvert(Matrix mat)
1200{
1201    Matrix result = { 0 };
1202
1203    // Cache the matrix values (speed optimization)
1204    float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3;
1205    float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7;
1206    float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11;
1207    float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15;
1208
1209    float b00 = a00*a11 - a01*a10;
1210    float b01 = a00*a12 - a02*a10;
1211    float b02 = a00*a13 - a03*a10;
1212    float b03 = a01*a12 - a02*a11;
1213    float b04 = a01*a13 - a03*a11;
1214    float b05 = a02*a13 - a03*a12;
1215    float b06 = a20*a31 - a21*a30;
1216    float b07 = a20*a32 - a22*a30;
1217    float b08 = a20*a33 - a23*a30;
1218    float b09 = a21*a32 - a22*a31;
1219    float b10 = a21*a33 - a23*a31;
1220    float b11 = a22*a33 - a23*a32;
1221
1222    // Calculate the invert determinant (inlined to avoid double-caching)
1223    float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
1224
1225    result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet;
1226    result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet;
1227    result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet;
1228    result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet;
1229    result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet;
1230    result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet;
1231    result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet;
1232    result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet;
1233    result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet;
1234    result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet;
1235    result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet;
1236    result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet;
1237    result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet;
1238    result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet;
1239    result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet;
1240    result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet;
1241
1242    return result;
1243}
1244
1245// Get identity matrix
1246RMAPI Matrix MatrixIdentity(void)
1247{
1248    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
1249                      0.0f, 1.0f, 0.0f, 0.0f,
1250                      0.0f, 0.0f, 1.0f, 0.0f,
1251                      0.0f, 0.0f, 0.0f, 1.0f };
1252
1253    return result;
1254}
1255
1256// Add two matrices
1257RMAPI Matrix MatrixAdd(Matrix left, Matrix right)
1258{
1259    Matrix result = { 0 };
1260
1261    result.m0 = left.m0 + right.m0;
1262    result.m1 = left.m1 + right.m1;
1263    result.m2 = left.m2 + right.m2;
1264    result.m3 = left.m3 + right.m3;
1265    result.m4 = left.m4 + right.m4;
1266    result.m5 = left.m5 + right.m5;
1267    result.m6 = left.m6 + right.m6;
1268    result.m7 = left.m7 + right.m7;
1269    result.m8 = left.m8 + right.m8;
1270    result.m9 = left.m9 + right.m9;
1271    result.m10 = left.m10 + right.m10;
1272    result.m11 = left.m11 + right.m11;
1273    result.m12 = left.m12 + right.m12;
1274    result.m13 = left.m13 + right.m13;
1275    result.m14 = left.m14 + right.m14;
1276    result.m15 = left.m15 + right.m15;
1277
1278    return result;
1279}
1280
1281// Subtract two matrices (left - right)
1282RMAPI Matrix MatrixSubtract(Matrix left, Matrix right)
1283{
1284    Matrix result = { 0 };
1285
1286    result.m0 = left.m0 - right.m0;
1287    result.m1 = left.m1 - right.m1;
1288    result.m2 = left.m2 - right.m2;
1289    result.m3 = left.m3 - right.m3;
1290    result.m4 = left.m4 - right.m4;
1291    result.m5 = left.m5 - right.m5;
1292    result.m6 = left.m6 - right.m6;
1293    result.m7 = left.m7 - right.m7;
1294    result.m8 = left.m8 - right.m8;
1295    result.m9 = left.m9 - right.m9;
1296    result.m10 = left.m10 - right.m10;
1297    result.m11 = left.m11 - right.m11;
1298    result.m12 = left.m12 - right.m12;
1299    result.m13 = left.m13 - right.m13;
1300    result.m14 = left.m14 - right.m14;
1301    result.m15 = left.m15 - right.m15;
1302
1303    return result;
1304}
1305
1306// Get two matrix multiplication
1307// NOTE: When multiplying matrices... the order matters!
1308RMAPI Matrix MatrixMultiply(Matrix left, Matrix right)
1309{
1310    Matrix result = { 0 };
1311
1312    result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12;
1313    result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13;
1314    result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14;
1315    result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15;
1316    result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12;
1317    result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13;
1318    result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14;
1319    result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15;
1320    result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12;
1321    result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13;
1322    result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14;
1323    result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15;
1324    result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12;
1325    result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13;
1326    result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14;
1327    result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15;
1328
1329    return result;
1330}
1331
1332// Get translation matrix
1333RMAPI Matrix MatrixTranslate(float x, float y, float z)
1334{
1335    Matrix result = { 1.0f, 0.0f, 0.0f, x,
1336                      0.0f, 1.0f, 0.0f, y,
1337                      0.0f, 0.0f, 1.0f, z,
1338                      0.0f, 0.0f, 0.0f, 1.0f };
1339
1340    return result;
1341}
1342
1343// Create rotation matrix from axis and angle
1344// NOTE: Angle should be provided in radians
1345RMAPI Matrix MatrixRotate(Vector3 axis, float angle)
1346{
1347    Matrix result = { 0 };
1348
1349    float x = axis.x, y = axis.y, z = axis.z;
1350
1351    float lengthSquared = x*x + y*y + z*z;
1352
1353    if ((lengthSquared != 1.0f) && (lengthSquared != 0.0f))
1354    {
1355        float ilength = 1.0f/sqrtf(lengthSquared);
1356        x *= ilength;
1357        y *= ilength;
1358        z *= ilength;
1359    }
1360
1361    float sinres = sinf(angle);
1362    float cosres = cosf(angle);
1363    float t = 1.0f - cosres;
1364
1365    result.m0 = x*x*t + cosres;
1366    result.m1 = y*x*t + z*sinres;
1367    result.m2 = z*x*t - y*sinres;
1368    result.m3 = 0.0f;
1369
1370    result.m4 = x*y*t - z*sinres;
1371    result.m5 = y*y*t + cosres;
1372    result.m6 = z*y*t + x*sinres;
1373    result.m7 = 0.0f;
1374
1375    result.m8 = x*z*t + y*sinres;
1376    result.m9 = y*z*t - x*sinres;
1377    result.m10 = z*z*t + cosres;
1378    result.m11 = 0.0f;
1379
1380    result.m12 = 0.0f;
1381    result.m13 = 0.0f;
1382    result.m14 = 0.0f;
1383    result.m15 = 1.0f;
1384
1385    return result;
1386}
1387
1388// Get x-rotation matrix
1389// NOTE: Angle must be provided in radians
1390RMAPI Matrix MatrixRotateX(float angle)
1391{
1392    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
1393                      0.0f, 1.0f, 0.0f, 0.0f,
1394                      0.0f, 0.0f, 1.0f, 0.0f,
1395                      0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity()
1396
1397    float cosres = cosf(angle);
1398    float sinres = sinf(angle);
1399
1400    result.m5 = cosres;
1401    result.m6 = sinres;
1402    result.m9 = -sinres;
1403    result.m10 = cosres;
1404
1405    return result;
1406}
1407
1408// Get y-rotation matrix
1409// NOTE: Angle must be provided in radians
1410RMAPI Matrix MatrixRotateY(float angle)
1411{
1412    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
1413                      0.0f, 1.0f, 0.0f, 0.0f,
1414                      0.0f, 0.0f, 1.0f, 0.0f,
1415                      0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity()
1416
1417    float cosres = cosf(angle);
1418    float sinres = sinf(angle);
1419
1420    result.m0 = cosres;
1421    result.m2 = -sinres;
1422    result.m8 = sinres;
1423    result.m10 = cosres;
1424
1425    return result;
1426}
1427
1428// Get z-rotation matrix
1429// NOTE: Angle must be provided in radians
1430RMAPI Matrix MatrixRotateZ(float angle)
1431{
1432    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
1433                      0.0f, 1.0f, 0.0f, 0.0f,
1434                      0.0f, 0.0f, 1.0f, 0.0f,
1435                      0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity()
1436
1437    float cosres = cosf(angle);
1438    float sinres = sinf(angle);
1439
1440    result.m0 = cosres;
1441    result.m1 = sinres;
1442    result.m4 = -sinres;
1443    result.m5 = cosres;
1444
1445    return result;
1446}
1447
1448
1449// Get xyz-rotation matrix
1450// NOTE: Angle must be provided in radians
1451RMAPI Matrix MatrixRotateXYZ(Vector3 angle)
1452{
1453    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
1454                      0.0f, 1.0f, 0.0f, 0.0f,
1455                      0.0f, 0.0f, 1.0f, 0.0f,
1456                      0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity()
1457
1458    float cosz = cosf(-angle.z);
1459    float sinz = sinf(-angle.z);
1460    float cosy = cosf(-angle.y);
1461    float siny = sinf(-angle.y);
1462    float cosx = cosf(-angle.x);
1463    float sinx = sinf(-angle.x);
1464
1465    result.m0 = cosz*cosy;
1466    result.m1 = (cosz*siny*sinx) - (sinz*cosx);
1467    result.m2 = (cosz*siny*cosx) + (sinz*sinx);
1468
1469    result.m4 = sinz*cosy;
1470    result.m5 = (sinz*siny*sinx) + (cosz*cosx);
1471    result.m6 = (sinz*siny*cosx) - (cosz*sinx);
1472
1473    result.m8 = -siny;
1474    result.m9 = cosy*sinx;
1475    result.m10= cosy*cosx;
1476
1477    return result;
1478}
1479
1480// Get zyx-rotation matrix
1481// NOTE: Angle must be provided in radians
1482RMAPI Matrix MatrixRotateZYX(Vector3 angle)
1483{
1484    Matrix result = { 0 };
1485
1486    float cz = cosf(angle.z);
1487    float sz = sinf(angle.z);
1488    float cy = cosf(angle.y);
1489    float sy = sinf(angle.y);
1490    float cx = cosf(angle.x);
1491    float sx = sinf(angle.x);
1492
1493    result.m0 = cz*cy;
1494    result.m4 = cz*sy*sx - cx*sz;
1495    result.m8 = sz*sx + cz*cx*sy;
1496    result.m12 = 0;
1497
1498    result.m1 = cy*sz;
1499    result.m5 = cz*cx + sz*sy*sx;
1500    result.m9 = cx*sz*sy - cz*sx;
1501    result.m13 = 0;
1502
1503    result.m2 = -sy;
1504    result.m6 = cy*sx;
1505    result.m10 = cy*cx;
1506    result.m14 = 0;
1507
1508    result.m3 = 0;
1509    result.m7 = 0;
1510    result.m11 = 0;
1511    result.m15 = 1;
1512
1513    return result;
1514}
1515
1516// Get scaling matrix
1517RMAPI Matrix MatrixScale(float x, float y, float z)
1518{
1519    Matrix result = { x, 0.0f, 0.0f, 0.0f,
1520                      0.0f, y, 0.0f, 0.0f,
1521                      0.0f, 0.0f, z, 0.0f,
1522                      0.0f, 0.0f, 0.0f, 1.0f };
1523
1524    return result;
1525}
1526
1527// Get perspective projection matrix
1528RMAPI Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far)
1529{
1530    Matrix result = { 0 };
1531
1532    float rl = (float)(right - left);
1533    float tb = (float)(top - bottom);
1534    float fn = (float)(far - near);
1535
1536    result.m0 = ((float)near*2.0f)/rl;
1537    result.m1 = 0.0f;
1538    result.m2 = 0.0f;
1539    result.m3 = 0.0f;
1540
1541    result.m4 = 0.0f;
1542    result.m5 = ((float)near*2.0f)/tb;
1543    result.m6 = 0.0f;
1544    result.m7 = 0.0f;
1545
1546    result.m8 = ((float)right + (float)left)/rl;
1547    result.m9 = ((float)top + (float)bottom)/tb;
1548    result.m10 = -((float)far + (float)near)/fn;
1549    result.m11 = -1.0f;
1550
1551    result.m12 = 0.0f;
1552    result.m13 = 0.0f;
1553    result.m14 = -((float)far*(float)near*2.0f)/fn;
1554    result.m15 = 0.0f;
1555
1556    return result;
1557}
1558
1559// Get perspective projection matrix
1560// NOTE: Fovy angle must be provided in radians
1561RMAPI Matrix MatrixPerspective(double fovY, double aspect, double nearPlane, double farPlane)
1562{
1563    Matrix result = { 0 };
1564
1565    double top = nearPlane*tan(fovY*0.5);
1566    double bottom = -top;
1567    double right = top*aspect;
1568    double left = -right;
1569
1570    // MatrixFrustum(-right, right, -top, top, near, far);
1571    float rl = (float)(right - left);
1572    float tb = (float)(top - bottom);
1573    float fn = (float)(farPlane - nearPlane);
1574
1575    result.m0 = ((float)nearPlane*2.0f)/rl;
1576    result.m5 = ((float)nearPlane*2.0f)/tb;
1577    result.m8 = ((float)right + (float)left)/rl;
1578    result.m9 = ((float)top + (float)bottom)/tb;
1579    result.m10 = -((float)farPlane + (float)nearPlane)/fn;
1580    result.m11 = -1.0f;
1581    result.m14 = -((float)farPlane*(float)nearPlane*2.0f)/fn;
1582
1583    return result;
1584}
1585
1586// Get orthographic projection matrix
1587RMAPI Matrix MatrixOrtho(double left, double right, double bottom, double top, double nearPlane, double farPlane)
1588{
1589    Matrix result = { 0 };
1590
1591    float rl = (float)(right - left);
1592    float tb = (float)(top - bottom);
1593    float fn = (float)(farPlane - nearPlane);
1594
1595    result.m0 = 2.0f/rl;
1596    result.m1 = 0.0f;
1597    result.m2 = 0.0f;
1598    result.m3 = 0.0f;
1599    result.m4 = 0.0f;
1600    result.m5 = 2.0f/tb;
1601    result.m6 = 0.0f;
1602    result.m7 = 0.0f;
1603    result.m8 = 0.0f;
1604    result.m9 = 0.0f;
1605    result.m10 = -2.0f/fn;
1606    result.m11 = 0.0f;
1607    result.m12 = -((float)left + (float)right)/rl;
1608    result.m13 = -((float)top + (float)bottom)/tb;
1609    result.m14 = -((float)farPlane + (float)nearPlane)/fn;
1610    result.m15 = 1.0f;
1611
1612    return result;
1613}
1614
1615// Get camera look-at matrix (view matrix)
1616RMAPI Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up)
1617{
1618    Matrix result = { 0 };
1619
1620    float length = 0.0f;
1621    float ilength = 0.0f;
1622
1623    // Vector3Subtract(eye, target)
1624    Vector3 vz = { eye.x - target.x, eye.y - target.y, eye.z - target.z };
1625
1626    // Vector3Normalize(vz)
1627    Vector3 v = vz;
1628    length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
1629    if (length == 0.0f) length = 1.0f;
1630    ilength = 1.0f/length;
1631    vz.x *= ilength;
1632    vz.y *= ilength;
1633    vz.z *= ilength;
1634
1635    // Vector3CrossProduct(up, vz)
1636    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 };
1637
1638    // Vector3Normalize(x)
1639    v = vx;
1640    length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
1641    if (length == 0.0f) length = 1.0f;
1642    ilength = 1.0f/length;
1643    vx.x *= ilength;
1644    vx.y *= ilength;
1645    vx.z *= ilength;
1646
1647    // Vector3CrossProduct(vz, vx)
1648    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 };
1649
1650    result.m0 = vx.x;
1651    result.m1 = vy.x;
1652    result.m2 = vz.x;
1653    result.m3 = 0.0f;
1654    result.m4 = vx.y;
1655    result.m5 = vy.y;
1656    result.m6 = vz.y;
1657    result.m7 = 0.0f;
1658    result.m8 = vx.z;
1659    result.m9 = vy.z;
1660    result.m10 = vz.z;
1661    result.m11 = 0.0f;
1662    result.m12 = -(vx.x*eye.x + vx.y*eye.y + vx.z*eye.z);   // Vector3DotProduct(vx, eye)
1663    result.m13 = -(vy.x*eye.x + vy.y*eye.y + vy.z*eye.z);   // Vector3DotProduct(vy, eye)
1664    result.m14 = -(vz.x*eye.x + vz.y*eye.y + vz.z*eye.z);   // Vector3DotProduct(vz, eye)
1665    result.m15 = 1.0f;
1666
1667    return result;
1668}
1669
1670// Get float array of matrix data
1671RMAPI float16 MatrixToFloatV(Matrix mat)
1672{
1673    float16 result = { 0 };
1674
1675    result.v[0] = mat.m0;
1676    result.v[1] = mat.m1;
1677    result.v[2] = mat.m2;
1678    result.v[3] = mat.m3;
1679    result.v[4] = mat.m4;
1680    result.v[5] = mat.m5;
1681    result.v[6] = mat.m6;
1682    result.v[7] = mat.m7;
1683    result.v[8] = mat.m8;
1684    result.v[9] = mat.m9;
1685    result.v[10] = mat.m10;
1686    result.v[11] = mat.m11;
1687    result.v[12] = mat.m12;
1688    result.v[13] = mat.m13;
1689    result.v[14] = mat.m14;
1690    result.v[15] = mat.m15;
1691
1692    return result;
1693}
1694
1695//----------------------------------------------------------------------------------
1696// Module Functions Definition - Quaternion math
1697//----------------------------------------------------------------------------------
1698
1699// Add two quaternions
1700RMAPI Quaternion QuaternionAdd(Quaternion q1, Quaternion q2)
1701{
1702    Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w};
1703
1704    return result;
1705}
1706
1707// Add quaternion and float value
1708RMAPI Quaternion QuaternionAddValue(Quaternion q, float add)
1709{
1710    Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add};
1711
1712    return result;
1713}
1714
1715// Subtract two quaternions
1716RMAPI Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2)
1717{
1718    Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w};
1719
1720    return result;
1721}
1722
1723// Subtract quaternion and float value
1724RMAPI Quaternion QuaternionSubtractValue(Quaternion q, float sub)
1725{
1726    Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub};
1727
1728    return result;
1729}
1730
1731// Get identity quaternion
1732RMAPI Quaternion QuaternionIdentity(void)
1733{
1734    Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
1735
1736    return result;
1737}
1738
1739// Computes the length of a quaternion
1740RMAPI float QuaternionLength(Quaternion q)
1741{
1742    float result = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
1743
1744    return result;
1745}
1746
1747// Normalize provided quaternion
1748RMAPI Quaternion QuaternionNormalize(Quaternion q)
1749{
1750    Quaternion result = { 0 };
1751
1752    float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
1753    if (length == 0.0f) length = 1.0f;
1754    float ilength = 1.0f/length;
1755
1756    result.x = q.x*ilength;
1757    result.y = q.y*ilength;
1758    result.z = q.z*ilength;
1759    result.w = q.w*ilength;
1760
1761    return result;
1762}
1763
1764// Invert provided quaternion
1765RMAPI Quaternion QuaternionInvert(Quaternion q)
1766{
1767    Quaternion result = q;
1768
1769    float lengthSq = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
1770
1771    if (lengthSq != 0.0f)
1772    {
1773        float invLength = 1.0f/lengthSq;
1774
1775        result.x *= -invLength;
1776        result.y *= -invLength;
1777        result.z *= -invLength;
1778        result.w *= invLength;
1779    }
1780
1781    return result;
1782}
1783
1784// Calculate two quaternion multiplication
1785RMAPI Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2)
1786{
1787    Quaternion result = { 0 };
1788
1789    float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w;
1790    float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w;
1791
1792    result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby;
1793    result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz;
1794    result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx;
1795    result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz;
1796
1797    return result;
1798}
1799
1800// Scale quaternion by float value
1801RMAPI Quaternion QuaternionScale(Quaternion q, float mul)
1802{
1803    Quaternion result = { 0 };
1804
1805    result.x = q.x*mul;
1806    result.y = q.y*mul;
1807    result.z = q.z*mul;
1808    result.w = q.w*mul;
1809
1810    return result;
1811}
1812
1813// Divide two quaternions
1814RMAPI Quaternion QuaternionDivide(Quaternion q1, Quaternion q2)
1815{
1816    Quaternion result = { q1.x/q2.x, q1.y/q2.y, q1.z/q2.z, q1.w/q2.w };
1817
1818    return result;
1819}
1820
1821// Calculate linear interpolation between two quaternions
1822RMAPI Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount)
1823{
1824    Quaternion result = { 0 };
1825
1826    result.x = q1.x + amount*(q2.x - q1.x);
1827    result.y = q1.y + amount*(q2.y - q1.y);
1828    result.z = q1.z + amount*(q2.z - q1.z);
1829    result.w = q1.w + amount*(q2.w - q1.w);
1830
1831    return result;
1832}
1833
1834// Calculate slerp-optimized interpolation between two quaternions
1835RMAPI Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount)
1836{
1837    Quaternion result = { 0 };
1838
1839    // QuaternionLerp(q1, q2, amount)
1840    result.x = q1.x + amount*(q2.x - q1.x);
1841    result.y = q1.y + amount*(q2.y - q1.y);
1842    result.z = q1.z + amount*(q2.z - q1.z);
1843    result.w = q1.w + amount*(q2.w - q1.w);
1844
1845    // QuaternionNormalize(q);
1846    Quaternion q = result;
1847    float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
1848    if (length == 0.0f) length = 1.0f;
1849    float ilength = 1.0f/length;
1850
1851    result.x = q.x*ilength;
1852    result.y = q.y*ilength;
1853    result.z = q.z*ilength;
1854    result.w = q.w*ilength;
1855
1856    return result;
1857}
1858
1859// Calculates spherical linear interpolation between two quaternions
1860RMAPI Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount)
1861{
1862    Quaternion result = { 0 };
1863
1864#if !defined(EPSILON)
1865    #define EPSILON 0.000001f
1866#endif
1867
1868    float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w;
1869
1870    if (cosHalfTheta < 0)
1871    {
1872        q2.x = -q2.x; q2.y = -q2.y; q2.z = -q2.z; q2.w = -q2.w;
1873        cosHalfTheta = -cosHalfTheta;
1874    }
1875
1876    if (fabsf(cosHalfTheta) >= 1.0f) result = q1;
1877    else if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount);
1878    else
1879    {
1880        float halfTheta = acosf(cosHalfTheta);
1881        float sinHalfTheta = sqrtf(1.0f - cosHalfTheta*cosHalfTheta);
1882
1883        if (fabsf(sinHalfTheta) < EPSILON)
1884        {
1885            result.x = (q1.x*0.5f + q2.x*0.5f);
1886            result.y = (q1.y*0.5f + q2.y*0.5f);
1887            result.z = (q1.z*0.5f + q2.z*0.5f);
1888            result.w = (q1.w*0.5f + q2.w*0.5f);
1889        }
1890        else
1891        {
1892            float ratioA = sinf((1 - amount)*halfTheta)/sinHalfTheta;
1893            float ratioB = sinf(amount*halfTheta)/sinHalfTheta;
1894
1895            result.x = (q1.x*ratioA + q2.x*ratioB);
1896            result.y = (q1.y*ratioA + q2.y*ratioB);
1897            result.z = (q1.z*ratioA + q2.z*ratioB);
1898            result.w = (q1.w*ratioA + q2.w*ratioB);
1899        }
1900    }
1901
1902    return result;
1903}
1904
1905// Calculate quaternion based on the rotation from one vector to another
1906RMAPI Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to)
1907{
1908    Quaternion result = { 0 };
1909
1910    float cos2Theta = (from.x*to.x + from.y*to.y + from.z*to.z);    // Vector3DotProduct(from, to)
1911    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)
1912
1913    result.x = cross.x;
1914    result.y = cross.y;
1915    result.z = cross.z;
1916    result.w = 1.0f + cos2Theta;
1917
1918    // QuaternionNormalize(q);
1919    // NOTE: Normalize to essentially nlerp the original and identity to 0.5
1920    Quaternion q = result;
1921    float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
1922    if (length == 0.0f) length = 1.0f;
1923    float ilength = 1.0f/length;
1924
1925    result.x = q.x*ilength;
1926    result.y = q.y*ilength;
1927    result.z = q.z*ilength;
1928    result.w = q.w*ilength;
1929
1930    return result;
1931}
1932
1933// Get a quaternion for a given rotation matrix
1934RMAPI Quaternion QuaternionFromMatrix(Matrix mat)
1935{
1936    Quaternion result = { 0 };
1937
1938    float fourWSquaredMinus1 = mat.m0  + mat.m5 + mat.m10;
1939    float fourXSquaredMinus1 = mat.m0  - mat.m5 - mat.m10;
1940    float fourYSquaredMinus1 = mat.m5  - mat.m0 - mat.m10;
1941    float fourZSquaredMinus1 = mat.m10 - mat.m0 - mat.m5;
1942
1943    int biggestIndex = 0;
1944    float fourBiggestSquaredMinus1 = fourWSquaredMinus1;
1945    if (fourXSquaredMinus1 > fourBiggestSquaredMinus1)
1946    {
1947        fourBiggestSquaredMinus1 = fourXSquaredMinus1;
1948        biggestIndex = 1;
1949    }
1950
1951    if (fourYSquaredMinus1 > fourBiggestSquaredMinus1)
1952    {
1953        fourBiggestSquaredMinus1 = fourYSquaredMinus1;
1954        biggestIndex = 2;
1955    }
1956
1957    if (fourZSquaredMinus1 > fourBiggestSquaredMinus1)
1958    {
1959        fourBiggestSquaredMinus1 = fourZSquaredMinus1;
1960        biggestIndex = 3;
1961    }
1962
1963    float biggestVal = sqrtf(fourBiggestSquaredMinus1 + 1.0f)*0.5f;
1964    float mult = 0.25f/biggestVal;
1965
1966    switch (biggestIndex)
1967    {
1968        case 0:
1969            result.w = biggestVal;
1970            result.x = (mat.m6 - mat.m9)*mult;
1971            result.y = (mat.m8 - mat.m2)*mult;
1972            result.z = (mat.m1 - mat.m4)*mult;
1973            break;
1974        case 1:
1975            result.x = biggestVal;
1976            result.w = (mat.m6 - mat.m9)*mult;
1977            result.y = (mat.m1 + mat.m4)*mult;
1978            result.z = (mat.m8 + mat.m2)*mult;
1979            break;
1980        case 2:
1981            result.y = biggestVal;
1982            result.w = (mat.m8 - mat.m2)*mult;
1983            result.x = (mat.m1 + mat.m4)*mult;
1984            result.z = (mat.m6 + mat.m9)*mult;
1985            break;
1986        case 3:
1987            result.z = biggestVal;
1988            result.w = (mat.m1 - mat.m4)*mult;
1989            result.x = (mat.m8 + mat.m2)*mult;
1990            result.y = (mat.m6 + mat.m9)*mult;
1991            break;
1992    }
1993
1994    return result;
1995}
1996
1997// Get a matrix for a given quaternion
1998RMAPI Matrix QuaternionToMatrix(Quaternion q)
1999{
2000    Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f,
2001                      0.0f, 1.0f, 0.0f, 0.0f,
2002                      0.0f, 0.0f, 1.0f, 0.0f,
2003                      0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity()
2004
2005    float a2 = q.x*q.x;
2006    float b2 = q.y*q.y;
2007    float c2 = q.z*q.z;
2008    float ac = q.x*q.z;
2009    float ab = q.x*q.y;
2010    float bc = q.y*q.z;
2011    float ad = q.w*q.x;
2012    float bd = q.w*q.y;
2013    float cd = q.w*q.z;
2014
2015    result.m0 = 1 - 2*(b2 + c2);
2016    result.m1 = 2*(ab + cd);
2017    result.m2 = 2*(ac - bd);
2018
2019    result.m4 = 2*(ab - cd);
2020    result.m5 = 1 - 2*(a2 + c2);
2021    result.m6 = 2*(bc + ad);
2022
2023    result.m8 = 2*(ac + bd);
2024    result.m9 = 2*(bc - ad);
2025    result.m10 = 1 - 2*(a2 + b2);
2026
2027    return result;
2028}
2029
2030// Get rotation quaternion for an angle and axis
2031// NOTE: Angle must be provided in radians
2032RMAPI Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
2033{
2034    Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f };
2035
2036    float axisLength = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z);
2037
2038    if (axisLength != 0.0f)
2039    {
2040        angle *= 0.5f;
2041
2042        float length = 0.0f;
2043        float ilength = 0.0f;
2044
2045        // Vector3Normalize(axis)
2046        Vector3 v = axis;
2047        length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z);
2048        if (length == 0.0f) length = 1.0f;
2049        ilength = 1.0f/length;
2050        axis.x *= ilength;
2051        axis.y *= ilength;
2052        axis.z *= ilength;
2053
2054        float sinres = sinf(angle);
2055        float cosres = cosf(angle);
2056
2057        result.x = axis.x*sinres;
2058        result.y = axis.y*sinres;
2059        result.z = axis.z*sinres;
2060        result.w = cosres;
2061
2062        // QuaternionNormalize(q);
2063        Quaternion q = result;
2064        length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
2065        if (length == 0.0f) length = 1.0f;
2066        ilength = 1.0f/length;
2067        result.x = q.x*ilength;
2068        result.y = q.y*ilength;
2069        result.z = q.z*ilength;
2070        result.w = q.w*ilength;
2071    }
2072
2073    return result;
2074}
2075
2076// Get the rotation angle and axis for a given quaternion
2077RMAPI void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
2078{
2079    if (fabsf(q.w) > 1.0f)
2080    {
2081        // QuaternionNormalize(q);
2082        float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w);
2083        if (length == 0.0f) length = 1.0f;
2084        float ilength = 1.0f/length;
2085
2086        q.x = q.x*ilength;
2087        q.y = q.y*ilength;
2088        q.z = q.z*ilength;
2089        q.w = q.w*ilength;
2090    }
2091
2092    Vector3 resAxis = { 0.0f, 0.0f, 0.0f };
2093    float resAngle = 2.0f*acosf(q.w);
2094    float den = sqrtf(1.0f - q.w*q.w);
2095
2096    if (den > EPSILON)
2097    {
2098        resAxis.x = q.x/den;
2099        resAxis.y = q.y/den;
2100        resAxis.z = q.z/den;
2101    }
2102    else
2103    {
2104        // This occurs when the angle is zero.
2105        // Not a problem: just set an arbitrary normalized axis.
2106        resAxis.x = 1.0f;
2107    }
2108
2109    *outAxis = resAxis;
2110    *outAngle = resAngle;
2111}
2112
2113// Get the quaternion equivalent to Euler angles
2114// NOTE: Rotation order is ZYX
2115RMAPI Quaternion QuaternionFromEuler(float pitch, float yaw, float roll)
2116{
2117    Quaternion result = { 0 };
2118
2119    float x0 = cosf(pitch*0.5f);
2120    float x1 = sinf(pitch*0.5f);
2121    float y0 = cosf(yaw*0.5f);
2122    float y1 = sinf(yaw*0.5f);
2123    float z0 = cosf(roll*0.5f);
2124    float z1 = sinf(roll*0.5f);
2125
2126    result.x = x1*y0*z0 - x0*y1*z1;
2127    result.y = x0*y1*z0 + x1*y0*z1;
2128    result.z = x0*y0*z1 - x1*y1*z0;
2129    result.w = x0*y0*z0 + x1*y1*z1;
2130
2131    return result;
2132}
2133
2134// Get the Euler angles equivalent to quaternion (roll, pitch, yaw)
2135// NOTE: Angles are returned in a Vector3 struct in radians
2136RMAPI Vector3 QuaternionToEuler(Quaternion q)
2137{
2138    Vector3 result = { 0 };
2139
2140    // Roll (x-axis rotation)
2141    float x0 = 2.0f*(q.w*q.x + q.y*q.z);
2142    float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y);
2143    result.x = atan2f(x0, x1);
2144
2145    // Pitch (y-axis rotation)
2146    float y0 = 2.0f*(q.w*q.y - q.z*q.x);
2147    y0 = y0 > 1.0f ? 1.0f : y0;
2148    y0 = y0 < -1.0f ? -1.0f : y0;
2149    result.y = asinf(y0);
2150
2151    // Yaw (z-axis rotation)
2152    float z0 = 2.0f*(q.w*q.z + q.x*q.y);
2153    float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z);
2154    result.z = atan2f(z0, z1);
2155
2156    return result;
2157}
2158
2159// Transform a quaternion given a transformation matrix
2160RMAPI Quaternion QuaternionTransform(Quaternion q, Matrix mat)
2161{
2162    Quaternion result = { 0 };
2163
2164    result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w;
2165    result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w;
2166    result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w;
2167    result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w;
2168
2169    return result;
2170}
2171
2172// Check whether two given quaternions are almost equal
2173RMAPI int QuaternionEquals(Quaternion p, Quaternion q)
2174{
2175#if !defined(EPSILON)
2176    #define EPSILON 0.000001f
2177#endif
2178
2179    int result = (((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
2180                  ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
2181                  ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) &&
2182                  ((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))) ||
2183                 (((fabsf(p.x + q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) &&
2184                  ((fabsf(p.y + q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) &&
2185                  ((fabsf(p.z + q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) &&
2186                  ((fabsf(p.w + q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w))))));
2187
2188    return result;
2189}
2190
2191#endif  // RAYMATH_H