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
117typedef 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
126typedef 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
136typedef 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
147typedef 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)
153typedef 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
163typedef struct float3 {
164 float v[3];
165} float3;
166
167typedef 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
178RMAPI 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
188RMAPI 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
196RMAPI 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
204RMAPI 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
212RMAPI 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
220RMAPI 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
236RMAPI Vector2 Vector2Zero(void)
237{
238 Vector2 result = { 0.0f, 0.0f };
239
240 return result;
241}
242
243// Vector with components value 1.0f
244RMAPI Vector2 Vector2One(void)
245{
246 Vector2 result = { 1.0f, 1.0f };
247
248 return result;
249}
250
251// Add two vectors (v1 + v2)
252RMAPI 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
260RMAPI 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)
268RMAPI 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
276RMAPI 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
284RMAPI 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
292RMAPI 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
300RMAPI 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
308RMAPI 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
316RMAPI 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)
325RMAPI 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
340RMAPI 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)
351RMAPI 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
359RMAPI 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
367RMAPI Vector2 Vector2Negate(Vector2 v)
368{
369 Vector2 result = { -v.x, -v.y };
370
371 return result;
372}
373
374// Divide vector by vector
375RMAPI 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
383RMAPI 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
399RMAPI 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
414RMAPI 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
425RMAPI 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
438RMAPI 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
449RMAPI 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
460RMAPI 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
474RMAPI 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
493RMAPI 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
502RMAPI 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
513RMAPI 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
540RMAPI 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
557RMAPI 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
582RMAPI 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
590RMAPI Vector3 Vector3One(void)
591{
592 Vector3 result = { 1.0f, 1.0f, 1.0f };
593
594 return result;
595}
596
597// Add two vectors
598RMAPI 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
606RMAPI 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
614RMAPI 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
622RMAPI 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
630RMAPI 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
638RMAPI 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
646RMAPI 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
654RMAPI 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
683RMAPI 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
691RMAPI 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
699RMAPI 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
707RMAPI 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
720RMAPI 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
733RMAPI 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)
746RMAPI 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
754RMAPI 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
762RMAPI 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
780RMAPI 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
797RMAPI 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
816RMAPI 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
849RMAPI 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
865RMAPI 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
877RMAPI 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
929RMAPI 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
950RMAPI 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
963RMAPI 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
978RMAPI 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
996RMAPI 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
1008RMAPI 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
1021RMAPI 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
1045RMAPI 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
1128RMAPI 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
1140RMAPI 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
1149RMAPI 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
1161RMAPI 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
1189RMAPI 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
1207RMAPI 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
1232RMAPI Vector4 Vector4Zero(void)
1233{
1234 Vector4 result = { 0.0f, 0.0f, 0.0f, 0.0f };
1235 return result;
1236}
1237
1238RMAPI Vector4 Vector4One(void)
1239{
1240 Vector4 result = { 1.0f, 1.0f, 1.0f, 1.0f };
1241 return result;
1242}
1243
1244RMAPI 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
1255RMAPI 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
1266RMAPI 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
1277RMAPI 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
1288RMAPI 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
1294RMAPI 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
1300RMAPI 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
1307RMAPI 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
1316RMAPI 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
1325RMAPI 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
1332RMAPI 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
1339RMAPI 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
1346RMAPI 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
1353RMAPI 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
1371RMAPI 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
1384RMAPI 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
1397RMAPI 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
1410RMAPI 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
1433RMAPI 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
1440RMAPI 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
1459RMAPI 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)
1480RMAPI 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
1488RMAPI 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
1513RMAPI 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
1560RMAPI 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
1571RMAPI 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)
1596RMAPI 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!
1622RMAPI 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
1647RMAPI 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
1659RMAPI 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
1704RMAPI 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
1724RMAPI 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
1744RMAPI 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
1765RMAPI 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
1796RMAPI 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
1831RMAPI 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
1842RMAPI 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
1875RMAPI 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
1901RMAPI 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)
1930RMAPI 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
1985RMAPI 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
2014RMAPI 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
2022RMAPI 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
2030RMAPI 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
2038RMAPI 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
2046RMAPI 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
2054RMAPI 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
2062RMAPI 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
2079RMAPI 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
2099RMAPI 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
2115RMAPI 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
2128RMAPI 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
2136RMAPI 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
2149RMAPI 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
2174RMAPI 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
2221RMAPI 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
2246RMAPI 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
2274RMAPI 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
2338RMAPI 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
2372RMAPI 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
2416RMAPI 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
2454RMAPI 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
2475RMAPI 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
2499RMAPI 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
2512RMAPI 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
2531RMAPI 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
2597static constexpr Vector2 Vector2Zeros = { 0, 0 };
2598static constexpr Vector2 Vector2Ones = { 1, 1 };
2599static constexpr Vector2 Vector2UnitX = { 1, 0 };
2600static constexpr Vector2 Vector2UnitY = { 0, 1 };
2601
2602inline Vector2 operator + (const Vector2& lhs, const Vector2& rhs)
2603{
2604 return Vector2Add(lhs, rhs);
2605}
2606
2607inline const Vector2& operator += (Vector2& lhs, const Vector2& rhs)
2608{
2609 lhs = Vector2Add(lhs, rhs);
2610 return lhs;
2611}
2612
2613inline Vector2 operator - (const Vector2& lhs, const Vector2& rhs)
2614{
2615 return Vector2Subtract(lhs, rhs);
2616}
2617
2618inline const Vector2& operator -= (Vector2& lhs, const Vector2& rhs)
2619{
2620 lhs = Vector2Subtract(lhs, rhs);
2621 return lhs;
2622}
2623
2624inline Vector2 operator * (const Vector2& lhs, const float& rhs)
2625{
2626 return Vector2Scale(lhs, rhs);
2627}
2628
2629inline const Vector2& operator *= (Vector2& lhs, const float& rhs)
2630{
2631 lhs = Vector2Scale(lhs, rhs);
2632 return lhs;
2633}
2634
2635inline Vector2 operator * (const Vector2& lhs, const Vector2& rhs)
2636{
2637 return Vector2Multiply(lhs, rhs);
2638}
2639
2640inline const Vector2& operator *= (Vector2& lhs, const Vector2& rhs)
2641{
2642 lhs = Vector2Multiply(lhs, rhs);
2643 return lhs;
2644}
2645
2646inline Vector2 operator * (const Vector2& lhs, const Matrix& rhs)
2647{
2648 return Vector2Transform(lhs, rhs);
2649}
2650
2651inline const Vector2& operator -= (Vector2& lhs, const Matrix& rhs)
2652{
2653 lhs = Vector2Transform(lhs, rhs);
2654 return lhs;
2655}
2656
2657inline Vector2 operator / (const Vector2& lhs, const float& rhs)
2658{
2659 return Vector2Scale(lhs, 1.0f / rhs);
2660}
2661
2662inline const Vector2& operator /= (Vector2& lhs, const float& rhs)
2663{
2664 lhs = Vector2Scale(lhs, rhs);
2665 return lhs;
2666}
2667
2668inline Vector2 operator / (const Vector2& lhs, const Vector2& rhs)
2669{
2670 return Vector2Divide(lhs, rhs);
2671}
2672
2673inline const Vector2& operator /= (Vector2& lhs, const Vector2& rhs)
2674{
2675 lhs = Vector2Divide(lhs, rhs);
2676 return lhs;
2677}
2678
2679inline bool operator == (const Vector2& lhs, const Vector2& rhs)
2680{
2681 return FloatEquals(lhs.x, rhs.x) && FloatEquals(lhs.y, rhs.y);
2682}
2683
2684inline 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
2690static constexpr Vector3 Vector3Zeros = { 0, 0, 0 };
2691static constexpr Vector3 Vector3Ones = { 1, 1, 1 };
2692static constexpr Vector3 Vector3UnitX = { 1, 0, 0 };
2693static constexpr Vector3 Vector3UnitY = { 0, 1, 0 };
2694static constexpr Vector3 Vector3UnitZ = { 0, 0, 1 };
2695
2696inline Vector3 operator + (const Vector3& lhs, const Vector3& rhs)
2697{
2698 return Vector3Add(lhs, rhs);
2699}
2700
2701inline const Vector3& operator += (Vector3& lhs, const Vector3& rhs)
2702{
2703 lhs = Vector3Add(lhs, rhs);
2704 return lhs;
2705}
2706
2707inline Vector3 operator - (const Vector3& lhs, const Vector3& rhs)
2708{
2709 return Vector3Subtract(lhs, rhs);
2710}
2711
2712inline const Vector3& operator -= (Vector3& lhs, const Vector3& rhs)
2713{
2714 lhs = Vector3Subtract(lhs, rhs);
2715 return lhs;
2716}
2717
2718inline Vector3 operator * (const Vector3& lhs, const float& rhs)
2719{
2720 return Vector3Scale(lhs, rhs);
2721}
2722
2723inline const Vector3& operator *= (Vector3& lhs, const float& rhs)
2724{
2725 lhs = Vector3Scale(lhs, rhs);
2726 return lhs;
2727}
2728
2729inline Vector3 operator * (const Vector3& lhs, const Vector3& rhs)
2730{
2731 return Vector3Multiply(lhs, rhs);
2732}
2733
2734inline const Vector3& operator *= (Vector3& lhs, const Vector3& rhs)
2735{
2736 lhs = Vector3Multiply(lhs, rhs);
2737 return lhs;
2738}
2739
2740inline Vector3 operator * (const Vector3& lhs, const Matrix& rhs)
2741{
2742 return Vector3Transform(lhs, rhs);
2743}
2744
2745inline const Vector3& operator -= (Vector3& lhs, const Matrix& rhs)
2746{
2747 lhs = Vector3Transform(lhs, rhs);
2748 return lhs;
2749}
2750
2751inline Vector3 operator / (const Vector3& lhs, const float& rhs)
2752{
2753 return Vector3Scale(lhs, 1.0f / rhs);
2754}
2755
2756inline const Vector3& operator /= (Vector3& lhs, const float& rhs)
2757{
2758 lhs = Vector3Scale(lhs, rhs);
2759 return lhs;
2760}
2761
2762inline Vector3 operator / (const Vector3& lhs, const Vector3& rhs)
2763{
2764 return Vector3Divide(lhs, rhs);
2765}
2766
2767inline const Vector3& operator /= (Vector3& lhs, const Vector3& rhs)
2768{
2769 lhs = Vector3Divide(lhs, rhs);
2770 return lhs;
2771}
2772
2773inline 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
2778inline 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
2784static constexpr Vector4 Vector4Zeros = { 0, 0, 0, 0 };
2785static constexpr Vector4 Vector4Ones = { 1, 1, 1, 1 };
2786static constexpr Vector4 Vector4UnitX = { 1, 0, 0, 0 };
2787static constexpr Vector4 Vector4UnitY = { 0, 1, 0, 0 };
2788static constexpr Vector4 Vector4UnitZ = { 0, 0, 1, 0 };
2789static constexpr Vector4 Vector4UnitW = { 0, 0, 0, 1 };
2790
2791inline Vector4 operator + (const Vector4& lhs, const Vector4& rhs)
2792{
2793 return Vector4Add(lhs, rhs);
2794}
2795
2796inline const Vector4& operator += (Vector4& lhs, const Vector4& rhs)
2797{
2798 lhs = Vector4Add(lhs, rhs);
2799 return lhs;
2800}
2801
2802inline Vector4 operator - (const Vector4& lhs, const Vector4& rhs)
2803{
2804 return Vector4Subtract(lhs, rhs);
2805}
2806
2807inline const Vector4& operator -= (Vector4& lhs, const Vector4& rhs)
2808{
2809 lhs = Vector4Subtract(lhs, rhs);
2810 return lhs;
2811}
2812
2813inline Vector4 operator * (const Vector4& lhs, const float& rhs)
2814{
2815 return Vector4Scale(lhs, rhs);
2816}
2817
2818inline const Vector4& operator *= (Vector4& lhs, const float& rhs)
2819{
2820 lhs = Vector4Scale(lhs, rhs);
2821 return lhs;
2822}
2823
2824inline Vector4 operator * (const Vector4& lhs, const Vector4& rhs)
2825{
2826 return Vector4Multiply(lhs, rhs);
2827}
2828
2829inline const Vector4& operator *= (Vector4& lhs, const Vector4& rhs)
2830{
2831 lhs = Vector4Multiply(lhs, rhs);
2832 return lhs;
2833}
2834
2835inline Vector4 operator / (const Vector4& lhs, const float& rhs)
2836{
2837 return Vector4Scale(lhs, 1.0f / rhs);
2838}
2839
2840inline const Vector4& operator /= (Vector4& lhs, const float& rhs)
2841{
2842 lhs = Vector4Scale(lhs, rhs);
2843 return lhs;
2844}
2845
2846inline Vector4 operator / (const Vector4& lhs, const Vector4& rhs)
2847{
2848 return Vector4Divide(lhs, rhs);
2849}
2850
2851inline const Vector4& operator /= (Vector4& lhs, const Vector4& rhs)
2852{
2853 lhs = Vector4Divide(lhs, rhs);
2854 return lhs;
2855}
2856
2857inline 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
2862inline 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
2868static constexpr Quaternion QuaternionZeros = { 0, 0, 0, 0 };
2869static constexpr Quaternion QuaternionOnes = { 1, 1, 1, 1 };
2870static constexpr Quaternion QuaternionUnitX = { 0, 0, 0, 1 };
2871
2872inline Quaternion operator + (const Quaternion& lhs, const float& rhs)
2873{
2874 return QuaternionAddValue(lhs, rhs);
2875}
2876
2877inline const Quaternion& operator += (Quaternion& lhs, const float& rhs)
2878{
2879 lhs = QuaternionAddValue(lhs, rhs);
2880 return lhs;
2881}
2882
2883inline Quaternion operator - (const Quaternion& lhs, const float& rhs)
2884{
2885 return QuaternionSubtractValue(lhs, rhs);
2886}
2887
2888inline const Quaternion& operator -= (Quaternion& lhs, const float& rhs)
2889{
2890 lhs = QuaternionSubtractValue(lhs, rhs);
2891 return lhs;
2892}
2893
2894inline Quaternion operator * (const Quaternion& lhs, const Matrix& rhs)
2895{
2896 return QuaternionTransform(lhs, rhs);
2897}
2898
2899inline const Quaternion& operator *= (Quaternion& lhs, const Matrix& rhs)
2900{
2901 lhs = QuaternionTransform(lhs, rhs);
2902 return lhs;
2903}
2904
2905// Matrix operators
2906inline Matrix operator + (const Matrix& lhs, const Matrix& rhs)
2907{
2908 return MatrixAdd(lhs, rhs);
2909}
2910
2911inline const Matrix& operator += (Matrix& lhs, const Matrix& rhs)
2912{
2913 lhs = MatrixAdd(lhs, rhs);
2914 return lhs;
2915}
2916
2917inline Matrix operator - (const Matrix& lhs, const Matrix& rhs)
2918{
2919 return MatrixSubtract(lhs, rhs);
2920}
2921
2922inline const Matrix& operator -= (Matrix& lhs, const Matrix& rhs)
2923{
2924 lhs = MatrixSubtract(lhs, rhs);
2925 return lhs;
2926}
2927
2928inline Matrix operator * (const Matrix& lhs, const Matrix& rhs)
2929{
2930 return MatrixMultiply(lhs, rhs);
2931}
2932
2933inline 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