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Diffstat (limited to 'raylib/src/raymath.h')
-rw-r--r-- | raylib/src/raymath.h | 1888 |
1 files changed, 1888 insertions, 0 deletions
diff --git a/raylib/src/raymath.h b/raylib/src/raymath.h new file mode 100644 index 0000000..d617fdc --- /dev/null +++ b/raylib/src/raymath.h @@ -0,0 +1,1888 @@ +/********************************************************************************************** +* +* raymath v1.5 - Math functions to work with Vector2, Vector3, Matrix and Quaternions +* +* CONFIGURATION: +* +* #define RAYMATH_IMPLEMENTATION +* Generates the implementation of the library into the included file. +* If not defined, the library is in header only mode and can be included in other headers +* or source files without problems. But only ONE file should hold the implementation. +* +* #define RAYMATH_STATIC_INLINE +* Define static inline functions code, so #include header suffices for use. +* This may use up lots of memory. +* +* CONVENTIONS: +* +* - Functions are always self-contained, no function use another raymath function inside, +* required code is directly re-implemented inside +* - Functions input parameters are always received by value (2 unavoidable exceptions) +* - Functions use always a "result" anmed variable for return +* - Functions are always defined inline +* - Angles are always in radians (DEG2RAD/RAD2DEG macros provided for convenience) +* +* +* LICENSE: zlib/libpng +* +* Copyright (c) 2015-2022 Ramon Santamaria (@raysan5) +* +* This software is provided "as-is", without any express or implied warranty. In no event +* will the authors be held liable for any damages arising from the use of this software. +* +* Permission is granted to anyone to use this software for any purpose, including commercial +* applications, and to alter it and redistribute it freely, subject to the following restrictions: +* +* 1. The origin of this software must not be misrepresented; you must not claim that you +* wrote the original software. If you use this software in a product, an acknowledgment +* in the product documentation would be appreciated but is not required. +* +* 2. Altered source versions must be plainly marked as such, and must not be misrepresented +* as being the original software. +* +* 3. This notice may not be removed or altered from any source distribution. +* +**********************************************************************************************/ + +#ifndef RAYMATH_H +#define RAYMATH_H + +#if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_STATIC_INLINE) + #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_STATIC_INLINE is contradictory" +#endif + +// Function specifiers definition +#if defined(RAYMATH_IMPLEMENTATION) + #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) + #define RMAPI __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll). + #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) + #define RMAPI __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) + #else + #define RMAPI extern inline // Provide external definition + #endif +#elif defined(RAYMATH_STATIC_INLINE) + #define RMAPI static inline // Functions may be inlined, no external out-of-line definition +#else + #if defined(__TINYC__) + #define RMAPI static inline // plain inline not supported by tinycc (See issue #435) + #else + #define RMAPI inline // Functions may be inlined or external definition used + #endif +#endif + +//---------------------------------------------------------------------------------- +// Defines and Macros +//---------------------------------------------------------------------------------- +#ifndef PI + #define PI 3.14159265358979323846f +#endif + +#ifndef DEG2RAD + #define DEG2RAD (PI/180.0f) +#endif + +#ifndef RAD2DEG + #define RAD2DEG (180.0f/PI) +#endif + +// Get float vector for Matrix +#ifndef MatrixToFloat + #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) +#endif + +// Get float vector for Vector3 +#ifndef Vector3ToFloat + #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) +#endif + +//---------------------------------------------------------------------------------- +// Types and Structures Definition +//---------------------------------------------------------------------------------- +#if !defined(RL_VECTOR2_TYPE) +// Vector2 type +typedef struct Vector2 { + float x; + float y; +} Vector2; +#define RL_VECTOR2_TYPE +#endif + +#if !defined(RL_VECTOR3_TYPE) +// Vector3 type +typedef struct Vector3 { + float x; + float y; + float z; +} Vector3; +#define RL_VECTOR3_TYPE +#endif + +#if !defined(RL_VECTOR4_TYPE) +// Vector4 type +typedef struct Vector4 { + float x; + float y; + float z; + float w; +} Vector4; +#define RL_VECTOR4_TYPE +#endif + +#if !defined(RL_QUATERNION_TYPE) +// Quaternion type +typedef Vector4 Quaternion; +#define RL_QUATERNION_TYPE +#endif + +#if !defined(RL_MATRIX_TYPE) +// Matrix type (OpenGL style 4x4 - right handed, column major) +typedef struct Matrix { + float m0, m4, m8, m12; // Matrix first row (4 components) + float m1, m5, m9, m13; // Matrix second row (4 components) + float m2, m6, m10, m14; // Matrix third row (4 components) + float m3, m7, m11, m15; // Matrix fourth row (4 components) +} Matrix; +#define RL_MATRIX_TYPE +#endif + +// NOTE: Helper types to be used instead of array return types for *ToFloat functions +typedef struct float3 { + float v[3]; +} float3; + +typedef struct float16 { + float v[16]; +} float16; + +#include <math.h> // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), fminf(), fmaxf(), fabs() + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Utils math +//---------------------------------------------------------------------------------- + +// Clamp float value +RMAPI float Clamp(float value, float min, float max) +{ + float result = (value < min)? min : value; + + if (result > max) result = max; + + return result; +} + +// Calculate linear interpolation between two floats +RMAPI float Lerp(float start, float end, float amount) +{ + float result = start + amount*(end - start); + + return result; +} + +// Normalize input value within input range +RMAPI float Normalize(float value, float start, float end) +{ + float result = (value - start)/(end - start); + + return result; +} + +// Remap input value within input range to output range +RMAPI float Remap(float value, float inputStart, float inputEnd, float outputStart, float outputEnd) +{ + float result = (value - inputStart)/(inputEnd - inputStart)*(outputEnd - outputStart) + outputStart; + + return result; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Vector2 math +//---------------------------------------------------------------------------------- + +// Vector with components value 0.0f +RMAPI Vector2 Vector2Zero(void) +{ + Vector2 result = { 0.0f, 0.0f }; + + return result; +} + +// Vector with components value 1.0f +RMAPI Vector2 Vector2One(void) +{ + Vector2 result = { 1.0f, 1.0f }; + + return result; +} + +// Add two vectors (v1 + v2) +RMAPI Vector2 Vector2Add(Vector2 v1, Vector2 v2) +{ + Vector2 result = { v1.x + v2.x, v1.y + v2.y }; + + return result; +} + +// Add vector and float value +RMAPI Vector2 Vector2AddValue(Vector2 v, float add) +{ + Vector2 result = { v.x + add, v.y + add }; + + return result; +} + +// Subtract two vectors (v1 - v2) +RMAPI Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) +{ + Vector2 result = { v1.x - v2.x, v1.y - v2.y }; + + return result; +} + +// Subtract vector by float value +RMAPI Vector2 Vector2SubtractValue(Vector2 v, float sub) +{ + Vector2 result = { v.x - sub, v.y - sub }; + + return result; +} + +// Calculate vector length +RMAPI float Vector2Length(Vector2 v) +{ + float result = sqrtf((v.x*v.x) + (v.y*v.y)); + + return result; +} + +// Calculate vector square length +RMAPI float Vector2LengthSqr(Vector2 v) +{ + float result = (v.x*v.x) + (v.y*v.y); + + return result; +} + +// Calculate two vectors dot product +RMAPI float Vector2DotProduct(Vector2 v1, Vector2 v2) +{ + float result = (v1.x*v2.x + v1.y*v2.y); + + return result; +} + +// Calculate distance between two vectors +RMAPI float Vector2Distance(Vector2 v1, Vector2 v2) +{ + float result = sqrtf((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); + + return result; +} + +// Calculate square distance between two vectors +RMAPI float Vector2DistanceSqr(Vector2 v1, Vector2 v2) +{ + float result = ((v1.x - v2.x)*(v1.x - v2.x) + (v1.y - v2.y)*(v1.y - v2.y)); + + return result; +} + +// Calculate angle from two vectors +RMAPI float Vector2Angle(Vector2 v1, Vector2 v2) +{ + float result = atan2f(v2.y, v2.x) - atan2f(v1.y, v1.x); + + return result; +} + +// Scale vector (multiply by value) +RMAPI Vector2 Vector2Scale(Vector2 v, float scale) +{ + Vector2 result = { v.x*scale, v.y*scale }; + + return result; +} + +// Multiply vector by vector +RMAPI Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) +{ + Vector2 result = { v1.x*v2.x, v1.y*v2.y }; + + return result; +} + +// Negate vector +RMAPI Vector2 Vector2Negate(Vector2 v) +{ + Vector2 result = { -v.x, -v.y }; + + return result; +} + +// Divide vector by vector +RMAPI Vector2 Vector2Divide(Vector2 v1, Vector2 v2) +{ + Vector2 result = { v1.x/v2.x, v1.y/v2.y }; + + return result; +} + +// Normalize provided vector +RMAPI Vector2 Vector2Normalize(Vector2 v) +{ + Vector2 result = { 0 }; + float length = sqrtf((v.x*v.x) + (v.y*v.y)); + + if (length > 0) + { + float ilength = 1.0f/length; + result.x = v.x*ilength; + result.y = v.y*ilength; + } + + return result; +} + +// Transforms a Vector2 by a given Matrix +RMAPI Vector2 Vector2Transform(Vector2 v, Matrix mat) +{ + Vector2 result = { 0 }; + + float x = v.x; + float y = v.y; + float z = 0; + + result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; + result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; + + return result; +} + +// Calculate linear interpolation between two vectors +RMAPI Vector2 Vector2Lerp(Vector2 v1, Vector2 v2, float amount) +{ + Vector2 result = { 0 }; + + result.x = v1.x + amount*(v2.x - v1.x); + result.y = v1.y + amount*(v2.y - v1.y); + + return result; +} + +// Calculate reflected vector to normal +RMAPI Vector2 Vector2Reflect(Vector2 v, Vector2 normal) +{ + Vector2 result = { 0 }; + + float dotProduct = (v.x*normal.x + v.y*normal.y); // Dot product + + result.x = v.x - (2.0f*normal.x)*dotProduct; + result.y = v.y - (2.0f*normal.y)*dotProduct; + + return result; +} + +// Rotate vector by angle +RMAPI Vector2 Vector2Rotate(Vector2 v, float angle) +{ + Vector2 result = { 0 }; + + float cosres = cosf(angle); + float sinres = sinf(angle); + + result.x = v.x*cosres - v.y*sinres; + result.y = v.x*sinres + v.y*cosres; + + return result; +} + +// Move Vector towards target +RMAPI Vector2 Vector2MoveTowards(Vector2 v, Vector2 target, float maxDistance) +{ + Vector2 result = { 0 }; + + float dx = target.x - v.x; + float dy = target.y - v.y; + float value = (dx*dx) + (dy*dy); + + if ((value == 0) || ((maxDistance >= 0) && (value <= maxDistance*maxDistance))) return target; + + float dist = sqrtf(value); + + result.x = v.x + dx/dist*maxDistance; + result.y = v.y + dy/dist*maxDistance; + + return result; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Vector3 math +//---------------------------------------------------------------------------------- + +// Vector with components value 0.0f +RMAPI Vector3 Vector3Zero(void) +{ + Vector3 result = { 0.0f, 0.0f, 0.0f }; + + return result; +} + +// Vector with components value 1.0f +RMAPI Vector3 Vector3One(void) +{ + Vector3 result = { 1.0f, 1.0f, 1.0f }; + + return result; +} + +// Add two vectors +RMAPI Vector3 Vector3Add(Vector3 v1, Vector3 v2) +{ + Vector3 result = { v1.x + v2.x, v1.y + v2.y, v1.z + v2.z }; + + return result; +} + +// Add vector and float value +RMAPI Vector3 Vector3AddValue(Vector3 v, float add) +{ + Vector3 result = { v.x + add, v.y + add, v.z + add }; + + return result; +} + +// Subtract two vectors +RMAPI Vector3 Vector3Subtract(Vector3 v1, Vector3 v2) +{ + Vector3 result = { v1.x - v2.x, v1.y - v2.y, v1.z - v2.z }; + + return result; +} + +// Subtract vector by float value +RMAPI Vector3 Vector3SubtractValue(Vector3 v, float sub) +{ + Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; + + return result; +} + +// Multiply vector by scalar +RMAPI Vector3 Vector3Scale(Vector3 v, float scalar) +{ + Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; + + return result; +} + +// Multiply vector by vector +RMAPI Vector3 Vector3Multiply(Vector3 v1, Vector3 v2) +{ + Vector3 result = { v1.x*v2.x, v1.y*v2.y, v1.z*v2.z }; + + return result; +} + +// Calculate two vectors cross product +RMAPI Vector3 Vector3CrossProduct(Vector3 v1, Vector3 v2) +{ + 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 }; + + return result; +} + +// Calculate one vector perpendicular vector +RMAPI Vector3 Vector3Perpendicular(Vector3 v) +{ + Vector3 result = { 0 }; + + float min = (float) fabs(v.x); + Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; + + if (fabs(v.y) < min) + { + min = (float) fabs(v.y); + Vector3 tmp = {0.0f, 1.0f, 0.0f}; + cardinalAxis = tmp; + } + + if (fabs(v.z) < min) + { + Vector3 tmp = {0.0f, 0.0f, 1.0f}; + cardinalAxis = tmp; + } + + // Cross product between vectors + result.x = v.y*cardinalAxis.z - v.z*cardinalAxis.y; + result.y = v.z*cardinalAxis.x - v.x*cardinalAxis.z; + result.z = v.x*cardinalAxis.y - v.y*cardinalAxis.x; + + return result; +} + +// Calculate vector length +RMAPI float Vector3Length(const Vector3 v) +{ + float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + + return result; +} + +// Calculate vector square length +RMAPI float Vector3LengthSqr(const Vector3 v) +{ + float result = v.x*v.x + v.y*v.y + v.z*v.z; + + return result; +} + +// Calculate two vectors dot product +RMAPI float Vector3DotProduct(Vector3 v1, Vector3 v2) +{ + float result = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); + + return result; +} + +// Calculate distance between two vectors +RMAPI float Vector3Distance(Vector3 v1, Vector3 v2) +{ + float result = 0.0f; + + float dx = v2.x - v1.x; + float dy = v2.y - v1.y; + float dz = v2.z - v1.z; + result = sqrtf(dx*dx + dy*dy + dz*dz); + + return result; +} + +// Calculate square distance between two vectors +RMAPI float Vector3DistanceSqr(Vector3 v1, Vector3 v2) +{ + float result = 0.0f; + + float dx = v2.x - v1.x; + float dy = v2.y - v1.y; + float dz = v2.z - v1.z; + result = dx*dx + dy*dy + dz*dz; + + return result; +} + +// Calculate angle between two vectors +RMAPI float Vector3Angle(Vector3 v1, Vector3 v2) +{ + float result = 0.0f; + + 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 }; + float len = sqrtf(cross.x*cross.x + cross.y*cross.y + cross.z*cross.z); + float dot = (v1.x*v2.x + v1.y*v2.y + v1.z*v2.z); + result = atan2f(len, dot); + + return result; +} + +// Negate provided vector (invert direction) +RMAPI Vector3 Vector3Negate(Vector3 v) +{ + Vector3 result = { -v.x, -v.y, -v.z }; + + return result; +} + +// Divide vector by vector +RMAPI Vector3 Vector3Divide(Vector3 v1, Vector3 v2) +{ + Vector3 result = { v1.x/v2.x, v1.y/v2.y, v1.z/v2.z }; + + return result; +} + +// Normalize provided vector +RMAPI Vector3 Vector3Normalize(Vector3 v) +{ + Vector3 result = v; + + float length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + float ilength = 1.0f/length; + + result.x *= ilength; + result.y *= ilength; + result.z *= ilength; + + return result; +} + +// Orthonormalize provided vectors +// Makes vectors normalized and orthogonal to each other +// Gram-Schmidt function implementation +RMAPI void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) +{ + float length = 0.0f; + float ilength = 0.0f; + + // Vector3Normalize(*v1); + Vector3 v = *v1; + length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + v1->x *= ilength; + v1->y *= ilength; + v1->z *= ilength; + + // Vector3CrossProduct(*v1, *v2) + 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 }; + + // Vector3Normalize(vn1); + v = vn1; + length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + vn1.x *= ilength; + vn1.y *= ilength; + vn1.z *= ilength; + + // Vector3CrossProduct(vn1, *v1) + 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 }; + + *v2 = vn2; +} + +// Transforms a Vector3 by a given Matrix +RMAPI Vector3 Vector3Transform(Vector3 v, Matrix mat) +{ + Vector3 result = { 0 }; + + float x = v.x; + float y = v.y; + float z = v.z; + + result.x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; + result.y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; + result.z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; + + return result; +} + +// Transform a vector by quaternion rotation +RMAPI Vector3 Vector3RotateByQuaternion(Vector3 v, Quaternion q) +{ + Vector3 result = { 0 }; + + 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); + 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); + 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); + + return result; +} + +// Calculate linear interpolation between two vectors +RMAPI Vector3 Vector3Lerp(Vector3 v1, Vector3 v2, float amount) +{ + Vector3 result = { 0 }; + + result.x = v1.x + amount*(v2.x - v1.x); + result.y = v1.y + amount*(v2.y - v1.y); + result.z = v1.z + amount*(v2.z - v1.z); + + return result; +} + +// Calculate reflected vector to normal +RMAPI Vector3 Vector3Reflect(Vector3 v, Vector3 normal) +{ + Vector3 result = { 0 }; + + // I is the original vector + // N is the normal of the incident plane + // R = I - (2*N*(DotProduct[I, N])) + + float dotProduct = (v.x*normal.x + v.y*normal.y + v.z*normal.z); + + result.x = v.x - (2.0f*normal.x)*dotProduct; + result.y = v.y - (2.0f*normal.y)*dotProduct; + result.z = v.z - (2.0f*normal.z)*dotProduct; + + return result; +} + +// Get min value for each pair of components +RMAPI Vector3 Vector3Min(Vector3 v1, Vector3 v2) +{ + Vector3 result = { 0 }; + + result.x = fminf(v1.x, v2.x); + result.y = fminf(v1.y, v2.y); + result.z = fminf(v1.z, v2.z); + + return result; +} + +// Get max value for each pair of components +RMAPI Vector3 Vector3Max(Vector3 v1, Vector3 v2) +{ + Vector3 result = { 0 }; + + result.x = fmaxf(v1.x, v2.x); + result.y = fmaxf(v1.y, v2.y); + result.z = fmaxf(v1.z, v2.z); + + return result; +} + +// Compute barycenter coordinates (u, v, w) for point p with respect to triangle (a, b, c) +// NOTE: Assumes P is on the plane of the triangle +RMAPI Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) +{ + Vector3 result = { 0 }; + + Vector3 v0 = { b.x - a.x, b.y - a.y, b.z - a.z }; // Vector3Subtract(b, a) + Vector3 v1 = { c.x - a.x, c.y - a.y, c.z - a.z }; // Vector3Subtract(c, a) + Vector3 v2 = { p.x - a.x, p.y - a.y, p.z - a.z }; // Vector3Subtract(p, a) + float d00 = (v0.x*v0.x + v0.y*v0.y + v0.z*v0.z); // Vector3DotProduct(v0, v0) + float d01 = (v0.x*v1.x + v0.y*v1.y + v0.z*v1.z); // Vector3DotProduct(v0, v1) + float d11 = (v1.x*v1.x + v1.y*v1.y + v1.z*v1.z); // Vector3DotProduct(v1, v1) + float d20 = (v2.x*v0.x + v2.y*v0.y + v2.z*v0.z); // Vector3DotProduct(v2, v0) + float d21 = (v2.x*v1.x + v2.y*v1.y + v2.z*v1.z); // Vector3DotProduct(v2, v1) + + float denom = d00*d11 - d01*d01; + + result.y = (d11*d20 - d01*d21)/denom; + result.z = (d00*d21 - d01*d20)/denom; + result.x = 1.0f - (result.z + result.y); + + return result; +} + +// Projects a Vector3 from screen space into object space +// NOTE: We are avoiding calling other raymath functions despite available +RMAPI Vector3 Vector3Unproject(Vector3 source, Matrix projection, Matrix view) +{ + Vector3 result = { 0 }; + + // Calculate unproject matrix (multiply view patrix by projection matrix) and invert it + Matrix matViewProj = { // MatrixMultiply(view, projection); + view.m0*projection.m0 + view.m1*projection.m4 + view.m2*projection.m8 + view.m3*projection.m12, + view.m0*projection.m1 + view.m1*projection.m5 + view.m2*projection.m9 + view.m3*projection.m13, + view.m0*projection.m2 + view.m1*projection.m6 + view.m2*projection.m10 + view.m3*projection.m14, + view.m0*projection.m3 + view.m1*projection.m7 + view.m2*projection.m11 + view.m3*projection.m15, + view.m4*projection.m0 + view.m5*projection.m4 + view.m6*projection.m8 + view.m7*projection.m12, + view.m4*projection.m1 + view.m5*projection.m5 + view.m6*projection.m9 + view.m7*projection.m13, + view.m4*projection.m2 + view.m5*projection.m6 + view.m6*projection.m10 + view.m7*projection.m14, + view.m4*projection.m3 + view.m5*projection.m7 + view.m6*projection.m11 + view.m7*projection.m15, + view.m8*projection.m0 + view.m9*projection.m4 + view.m10*projection.m8 + view.m11*projection.m12, + view.m8*projection.m1 + view.m9*projection.m5 + view.m10*projection.m9 + view.m11*projection.m13, + view.m8*projection.m2 + view.m9*projection.m6 + view.m10*projection.m10 + view.m11*projection.m14, + view.m8*projection.m3 + view.m9*projection.m7 + view.m10*projection.m11 + view.m11*projection.m15, + view.m12*projection.m0 + view.m13*projection.m4 + view.m14*projection.m8 + view.m15*projection.m12, + view.m12*projection.m1 + view.m13*projection.m5 + view.m14*projection.m9 + view.m15*projection.m13, + view.m12*projection.m2 + view.m13*projection.m6 + view.m14*projection.m10 + view.m15*projection.m14, + view.m12*projection.m3 + view.m13*projection.m7 + view.m14*projection.m11 + view.m15*projection.m15 }; + + // Calculate inverted matrix -> MatrixInvert(matViewProj); + // Cache the matrix values (speed optimization) + float a00 = matViewProj.m0, a01 = matViewProj.m1, a02 = matViewProj.m2, a03 = matViewProj.m3; + float a10 = matViewProj.m4, a11 = matViewProj.m5, a12 = matViewProj.m6, a13 = matViewProj.m7; + float a20 = matViewProj.m8, a21 = matViewProj.m9, a22 = matViewProj.m10, a23 = matViewProj.m11; + float a30 = matViewProj.m12, a31 = matViewProj.m13, a32 = matViewProj.m14, a33 = matViewProj.m15; + + float b00 = a00*a11 - a01*a10; + float b01 = a00*a12 - a02*a10; + float b02 = a00*a13 - a03*a10; + float b03 = a01*a12 - a02*a11; + float b04 = a01*a13 - a03*a11; + float b05 = a02*a13 - a03*a12; + float b06 = a20*a31 - a21*a30; + float b07 = a20*a32 - a22*a30; + float b08 = a20*a33 - a23*a30; + float b09 = a21*a32 - a22*a31; + float b10 = a21*a33 - a23*a31; + float b11 = a22*a33 - a23*a32; + + // Calculate the invert determinant (inlined to avoid double-caching) + float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); + + Matrix matViewProjInv = { + (a11*b11 - a12*b10 + a13*b09)*invDet, + (-a01*b11 + a02*b10 - a03*b09)*invDet, + (a31*b05 - a32*b04 + a33*b03)*invDet, + (-a21*b05 + a22*b04 - a23*b03)*invDet, + (-a10*b11 + a12*b08 - a13*b07)*invDet, + (a00*b11 - a02*b08 + a03*b07)*invDet, + (-a30*b05 + a32*b02 - a33*b01)*invDet, + (a20*b05 - a22*b02 + a23*b01)*invDet, + (a10*b10 - a11*b08 + a13*b06)*invDet, + (-a00*b10 + a01*b08 - a03*b06)*invDet, + (a30*b04 - a31*b02 + a33*b00)*invDet, + (-a20*b04 + a21*b02 - a23*b00)*invDet, + (-a10*b09 + a11*b07 - a12*b06)*invDet, + (a00*b09 - a01*b07 + a02*b06)*invDet, + (-a30*b03 + a31*b01 - a32*b00)*invDet, + (a20*b03 - a21*b01 + a22*b00)*invDet }; + + // Create quaternion from source point + Quaternion quat = { source.x, source.y, source.z, 1.0f }; + + // Multiply quat point by unproject matrix + Quaternion qtransformed = { // QuaternionTransform(quat, matViewProjInv) + matViewProjInv.m0*quat.x + matViewProjInv.m4*quat.y + matViewProjInv.m8*quat.z + matViewProjInv.m12*quat.w, + matViewProjInv.m1*quat.x + matViewProjInv.m5*quat.y + matViewProjInv.m9*quat.z + matViewProjInv.m13*quat.w, + matViewProjInv.m2*quat.x + matViewProjInv.m6*quat.y + matViewProjInv.m10*quat.z + matViewProjInv.m14*quat.w, + matViewProjInv.m3*quat.x + matViewProjInv.m7*quat.y + matViewProjInv.m11*quat.z + matViewProjInv.m15*quat.w }; + + // Normalized world points in vectors + result.x = qtransformed.x/qtransformed.w; + result.y = qtransformed.y/qtransformed.w; + result.z = qtransformed.z/qtransformed.w; + + return result; +} + +// Get Vector3 as float array +RMAPI float3 Vector3ToFloatV(Vector3 v) +{ + float3 buffer = { 0 }; + + buffer.v[0] = v.x; + buffer.v[1] = v.y; + buffer.v[2] = v.z; + + return buffer; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Matrix math +//---------------------------------------------------------------------------------- + +// Compute matrix determinant +RMAPI float MatrixDeterminant(Matrix mat) +{ + float result = 0.0f; + + // Cache the matrix values (speed optimization) + float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3; + float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7; + float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11; + float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15; + + result = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 + + a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 + + a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 + + a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 + + a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 + + a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33; + + return result; +} + +// Get the trace of the matrix (sum of the values along the diagonal) +RMAPI float MatrixTrace(Matrix mat) +{ + float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); + + return result; +} + +// Transposes provided matrix +RMAPI Matrix MatrixTranspose(Matrix mat) +{ + Matrix result = { 0 }; + + result.m0 = mat.m0; + result.m1 = mat.m4; + result.m2 = mat.m8; + result.m3 = mat.m12; + result.m4 = mat.m1; + result.m5 = mat.m5; + result.m6 = mat.m9; + result.m7 = mat.m13; + result.m8 = mat.m2; + result.m9 = mat.m6; + result.m10 = mat.m10; + result.m11 = mat.m14; + result.m12 = mat.m3; + result.m13 = mat.m7; + result.m14 = mat.m11; + result.m15 = mat.m15; + + return result; +} + +// Invert provided matrix +RMAPI Matrix MatrixInvert(Matrix mat) +{ + Matrix result = { 0 }; + + // Cache the matrix values (speed optimization) + float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3; + float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7; + float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11; + float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15; + + float b00 = a00*a11 - a01*a10; + float b01 = a00*a12 - a02*a10; + float b02 = a00*a13 - a03*a10; + float b03 = a01*a12 - a02*a11; + float b04 = a01*a13 - a03*a11; + float b05 = a02*a13 - a03*a12; + float b06 = a20*a31 - a21*a30; + float b07 = a20*a32 - a22*a30; + float b08 = a20*a33 - a23*a30; + float b09 = a21*a32 - a22*a31; + float b10 = a21*a33 - a23*a31; + float b11 = a22*a33 - a23*a32; + + // Calculate the invert determinant (inlined to avoid double-caching) + float invDet = 1.0f/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06); + + result.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; + result.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; + result.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; + result.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; + result.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; + result.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; + result.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; + result.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; + result.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; + result.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; + result.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; + result.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; + result.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; + result.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; + result.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; + result.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; + + return result; +} + +// Normalize provided matrix +RMAPI Matrix MatrixNormalize(Matrix mat) +{ + Matrix result = { 0 }; + + // Cache the matrix values (speed optimization) + float a00 = mat.m0, a01 = mat.m1, a02 = mat.m2, a03 = mat.m3; + float a10 = mat.m4, a11 = mat.m5, a12 = mat.m6, a13 = mat.m7; + float a20 = mat.m8, a21 = mat.m9, a22 = mat.m10, a23 = mat.m11; + float a30 = mat.m12, a31 = mat.m13, a32 = mat.m14, a33 = mat.m15; + + // MatrixDeterminant(mat) + float det = a30*a21*a12*a03 - a20*a31*a12*a03 - a30*a11*a22*a03 + a10*a31*a22*a03 + + a20*a11*a32*a03 - a10*a21*a32*a03 - a30*a21*a02*a13 + a20*a31*a02*a13 + + a30*a01*a22*a13 - a00*a31*a22*a13 - a20*a01*a32*a13 + a00*a21*a32*a13 + + a30*a11*a02*a23 - a10*a31*a02*a23 - a30*a01*a12*a23 + a00*a31*a12*a23 + + a10*a01*a32*a23 - a00*a11*a32*a23 - a20*a11*a02*a33 + a10*a21*a02*a33 + + a20*a01*a12*a33 - a00*a21*a12*a33 - a10*a01*a22*a33 + a00*a11*a22*a33; + + result.m0 = mat.m0/det; + result.m1 = mat.m1/det; + result.m2 = mat.m2/det; + result.m3 = mat.m3/det; + result.m4 = mat.m4/det; + result.m5 = mat.m5/det; + result.m6 = mat.m6/det; + result.m7 = mat.m7/det; + result.m8 = mat.m8/det; + result.m9 = mat.m9/det; + result.m10 = mat.m10/det; + result.m11 = mat.m11/det; + result.m12 = mat.m12/det; + result.m13 = mat.m13/det; + result.m14 = mat.m14/det; + result.m15 = mat.m15/det; + + return result; +} + +// Get identity matrix +RMAPI Matrix MatrixIdentity(void) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; + + return result; +} + +// Add two matrices +RMAPI Matrix MatrixAdd(Matrix left, Matrix right) +{ + Matrix result = { 0 }; + + result.m0 = left.m0 + right.m0; + result.m1 = left.m1 + right.m1; + result.m2 = left.m2 + right.m2; + result.m3 = left.m3 + right.m3; + result.m4 = left.m4 + right.m4; + result.m5 = left.m5 + right.m5; + result.m6 = left.m6 + right.m6; + result.m7 = left.m7 + right.m7; + result.m8 = left.m8 + right.m8; + result.m9 = left.m9 + right.m9; + result.m10 = left.m10 + right.m10; + result.m11 = left.m11 + right.m11; + result.m12 = left.m12 + right.m12; + result.m13 = left.m13 + right.m13; + result.m14 = left.m14 + right.m14; + result.m15 = left.m15 + right.m15; + + return result; +} + +// Subtract two matrices (left - right) +RMAPI Matrix MatrixSubtract(Matrix left, Matrix right) +{ + Matrix result = { 0 }; + + result.m0 = left.m0 - right.m0; + result.m1 = left.m1 - right.m1; + result.m2 = left.m2 - right.m2; + result.m3 = left.m3 - right.m3; + result.m4 = left.m4 - right.m4; + result.m5 = left.m5 - right.m5; + result.m6 = left.m6 - right.m6; + result.m7 = left.m7 - right.m7; + result.m8 = left.m8 - right.m8; + result.m9 = left.m9 - right.m9; + result.m10 = left.m10 - right.m10; + result.m11 = left.m11 - right.m11; + result.m12 = left.m12 - right.m12; + result.m13 = left.m13 - right.m13; + result.m14 = left.m14 - right.m14; + result.m15 = left.m15 - right.m15; + + return result; +} + +// Get two matrix multiplication +// NOTE: When multiplying matrices... the order matters! +RMAPI Matrix MatrixMultiply(Matrix left, Matrix right) +{ + Matrix result = { 0 }; + + result.m0 = left.m0*right.m0 + left.m1*right.m4 + left.m2*right.m8 + left.m3*right.m12; + result.m1 = left.m0*right.m1 + left.m1*right.m5 + left.m2*right.m9 + left.m3*right.m13; + result.m2 = left.m0*right.m2 + left.m1*right.m6 + left.m2*right.m10 + left.m3*right.m14; + result.m3 = left.m0*right.m3 + left.m1*right.m7 + left.m2*right.m11 + left.m3*right.m15; + result.m4 = left.m4*right.m0 + left.m5*right.m4 + left.m6*right.m8 + left.m7*right.m12; + result.m5 = left.m4*right.m1 + left.m5*right.m5 + left.m6*right.m9 + left.m7*right.m13; + result.m6 = left.m4*right.m2 + left.m5*right.m6 + left.m6*right.m10 + left.m7*right.m14; + result.m7 = left.m4*right.m3 + left.m5*right.m7 + left.m6*right.m11 + left.m7*right.m15; + result.m8 = left.m8*right.m0 + left.m9*right.m4 + left.m10*right.m8 + left.m11*right.m12; + result.m9 = left.m8*right.m1 + left.m9*right.m5 + left.m10*right.m9 + left.m11*right.m13; + result.m10 = left.m8*right.m2 + left.m9*right.m6 + left.m10*right.m10 + left.m11*right.m14; + result.m11 = left.m8*right.m3 + left.m9*right.m7 + left.m10*right.m11 + left.m11*right.m15; + result.m12 = left.m12*right.m0 + left.m13*right.m4 + left.m14*right.m8 + left.m15*right.m12; + result.m13 = left.m12*right.m1 + left.m13*right.m5 + left.m14*right.m9 + left.m15*right.m13; + result.m14 = left.m12*right.m2 + left.m13*right.m6 + left.m14*right.m10 + left.m15*right.m14; + result.m15 = left.m12*right.m3 + left.m13*right.m7 + left.m14*right.m11 + left.m15*right.m15; + + return result; +} + +// Get translation matrix +RMAPI Matrix MatrixTranslate(float x, float y, float z) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, x, + 0.0f, 1.0f, 0.0f, y, + 0.0f, 0.0f, 1.0f, z, + 0.0f, 0.0f, 0.0f, 1.0f }; + + return result; +} + +// Create rotation matrix from axis and angle +// NOTE: Angle should be provided in radians +RMAPI Matrix MatrixRotate(Vector3 axis, float angle) +{ + Matrix result = { 0 }; + + float x = axis.x, y = axis.y, z = axis.z; + + float lengthSquared = x*x + y*y + z*z; + + if ((lengthSquared != 1.0f) && (lengthSquared != 0.0f)) + { + float ilength = 1.0f/sqrtf(lengthSquared); + x *= ilength; + y *= ilength; + z *= ilength; + } + + float sinres = sinf(angle); + float cosres = cosf(angle); + float t = 1.0f - cosres; + + result.m0 = x*x*t + cosres; + result.m1 = y*x*t + z*sinres; + result.m2 = z*x*t - y*sinres; + result.m3 = 0.0f; + + result.m4 = x*y*t - z*sinres; + result.m5 = y*y*t + cosres; + result.m6 = z*y*t + x*sinres; + result.m7 = 0.0f; + + result.m8 = x*z*t + y*sinres; + result.m9 = y*z*t - x*sinres; + result.m10 = z*z*t + cosres; + result.m11 = 0.0f; + + result.m12 = 0.0f; + result.m13 = 0.0f; + result.m14 = 0.0f; + result.m15 = 1.0f; + + return result; +} + +// Get x-rotation matrix (angle in radians) +RMAPI Matrix MatrixRotateX(float angle) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() + + float cosres = cosf(angle); + float sinres = sinf(angle); + + result.m5 = cosres; + result.m6 = -sinres; + result.m9 = sinres; + result.m10 = cosres; + + return result; +} + +// Get y-rotation matrix (angle in radians) +RMAPI Matrix MatrixRotateY(float angle) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() + + float cosres = cosf(angle); + float sinres = sinf(angle); + + result.m0 = cosres; + result.m2 = sinres; + result.m8 = -sinres; + result.m10 = cosres; + + return result; +} + +// Get z-rotation matrix (angle in radians) +RMAPI Matrix MatrixRotateZ(float angle) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() + + float cosres = cosf(angle); + float sinres = sinf(angle); + + result.m0 = cosres; + result.m1 = -sinres; + result.m4 = sinres; + result.m5 = cosres; + + return result; +} + + +// Get xyz-rotation matrix (angles in radians) +RMAPI Matrix MatrixRotateXYZ(Vector3 ang) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() + + float cosz = cosf(-ang.z); + float sinz = sinf(-ang.z); + float cosy = cosf(-ang.y); + float siny = sinf(-ang.y); + float cosx = cosf(-ang.x); + float sinx = sinf(-ang.x); + + result.m0 = cosz*cosy; + result.m4 = (cosz*siny*sinx) - (sinz*cosx); + result.m8 = (cosz*siny*cosx) + (sinz*sinx); + + result.m1 = sinz*cosy; + result.m5 = (sinz*siny*sinx) + (cosz*cosx); + result.m9 = (sinz*siny*cosx) - (cosz*sinx); + + result.m2 = -siny; + result.m6 = cosy*sinx; + result.m10= cosy*cosx; + + return result; +} + +// Get zyx-rotation matrix (angles in radians) +RMAPI Matrix MatrixRotateZYX(Vector3 ang) +{ + Matrix result = { 0 }; + + float cz = cosf(ang.z); + float sz = sinf(ang.z); + float cy = cosf(ang.y); + float sy = sinf(ang.y); + float cx = cosf(ang.x); + float sx = sinf(ang.x); + + result.m0 = cz*cy; + result.m1 = cz*sy*sx - cx*sz; + result.m2 = sz*sx + cz*cx*sy; + result.m3 = 0; + + result.m4 = cy*sz; + result.m5 = cz*cx + sz*sy*sx; + result.m6 = cx*sz*sy - cz*sx; + result.m7 = 0; + + result.m8 = -sy; + result.m9 = cy*sx; + result.m10 = cy*cx; + result.m11 = 0; + + result.m12 = 0; + result.m13 = 0; + result.m14 = 0; + result.m15 = 1; + + return result; +} + +// Get scaling matrix +RMAPI Matrix MatrixScale(float x, float y, float z) +{ + Matrix result = { x, 0.0f, 0.0f, 0.0f, + 0.0f, y, 0.0f, 0.0f, + 0.0f, 0.0f, z, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; + + return result; +} + +// Get perspective projection matrix +RMAPI Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) +{ + Matrix result = { 0 }; + + float rl = (float)(right - left); + float tb = (float)(top - bottom); + float fn = (float)(far - near); + + result.m0 = ((float)near*2.0f)/rl; + result.m1 = 0.0f; + result.m2 = 0.0f; + result.m3 = 0.0f; + + result.m4 = 0.0f; + result.m5 = ((float)near*2.0f)/tb; + result.m6 = 0.0f; + result.m7 = 0.0f; + + result.m8 = ((float)right + (float)left)/rl; + result.m9 = ((float)top + (float)bottom)/tb; + result.m10 = -((float)far + (float)near)/fn; + result.m11 = -1.0f; + + result.m12 = 0.0f; + result.m13 = 0.0f; + result.m14 = -((float)far*(float)near*2.0f)/fn; + result.m15 = 0.0f; + + return result; +} + +// Get perspective projection matrix +// NOTE: Angle should be provided in radians +RMAPI Matrix MatrixPerspective(double fovy, double aspect, double near, double far) +{ + Matrix result = { 0 }; + + double top = near*tan(fovy*0.5); + double bottom = -top; + double right = top*aspect; + double left = -right; + + // MatrixFrustum(-right, right, -top, top, near, far); + float rl = (float)(right - left); + float tb = (float)(top - bottom); + float fn = (float)(far - near); + + result.m0 = ((float)near*2.0f)/rl; + result.m5 = ((float)near*2.0f)/tb; + result.m8 = ((float)right + (float)left)/rl; + result.m9 = ((float)top + (float)bottom)/tb; + result.m10 = -((float)far + (float)near)/fn; + result.m11 = -1.0f; + result.m14 = -((float)far*(float)near*2.0f)/fn; + + return result; +} + +// Get orthographic projection matrix +RMAPI Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far) +{ + Matrix result = { 0 }; + + float rl = (float)(right - left); + float tb = (float)(top - bottom); + float fn = (float)(far - near); + + result.m0 = 2.0f/rl; + result.m1 = 0.0f; + result.m2 = 0.0f; + result.m3 = 0.0f; + result.m4 = 0.0f; + result.m5 = 2.0f/tb; + result.m6 = 0.0f; + result.m7 = 0.0f; + result.m8 = 0.0f; + result.m9 = 0.0f; + result.m10 = -2.0f/fn; + result.m11 = 0.0f; + result.m12 = -((float)left + (float)right)/rl; + result.m13 = -((float)top + (float)bottom)/tb; + result.m14 = -((float)far + (float)near)/fn; + result.m15 = 1.0f; + + return result; +} + +// Get camera look-at matrix (view matrix) +RMAPI Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) +{ + Matrix result = { 0 }; + + float length = 0.0f; + float ilength = 0.0f; + + // Vector3Subtract(eye, target) + Vector3 vz = { eye.x - target.x, eye.y - target.y, eye.z - target.z }; + + // Vector3Normalize(vz) + Vector3 v = vz; + length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + vz.x *= ilength; + vz.y *= ilength; + vz.z *= ilength; + + // Vector3CrossProduct(up, vz) + 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 }; + + // Vector3Normalize(x) + v = vx; + length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + vx.x *= ilength; + vx.y *= ilength; + vx.z *= ilength; + + // Vector3CrossProduct(vz, vx) + 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 }; + + result.m0 = vx.x; + result.m1 = vy.x; + result.m2 = vz.x; + result.m3 = 0.0f; + result.m4 = vx.y; + result.m5 = vy.y; + result.m6 = vz.y; + result.m7 = 0.0f; + result.m8 = vx.z; + result.m9 = vy.z; + result.m10 = vz.z; + result.m11 = 0.0f; + result.m12 = -(vx.x*eye.x + vx.y*eye.y + vx.z*eye.z); // Vector3DotProduct(vx, eye) + result.m13 = -(vy.x*eye.x + vy.y*eye.y + vy.z*eye.z); // Vector3DotProduct(vy, eye) + result.m14 = -(vz.x*eye.x + vz.y*eye.y + vz.z*eye.z); // Vector3DotProduct(vz, eye) + result.m15 = 1.0f; + + return result; +} + +// Get float array of matrix data +RMAPI float16 MatrixToFloatV(Matrix mat) +{ + float16 result = { 0 }; + + result.v[0] = mat.m0; + result.v[1] = mat.m1; + result.v[2] = mat.m2; + result.v[3] = mat.m3; + result.v[4] = mat.m4; + result.v[5] = mat.m5; + result.v[6] = mat.m6; + result.v[7] = mat.m7; + result.v[8] = mat.m8; + result.v[9] = mat.m9; + result.v[10] = mat.m10; + result.v[11] = mat.m11; + result.v[12] = mat.m12; + result.v[13] = mat.m13; + result.v[14] = mat.m14; + result.v[15] = mat.m15; + + return result; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Quaternion math +//---------------------------------------------------------------------------------- + +// Add two quaternions +RMAPI Quaternion QuaternionAdd(Quaternion q1, Quaternion q2) +{ + Quaternion result = {q1.x + q2.x, q1.y + q2.y, q1.z + q2.z, q1.w + q2.w}; + + return result; +} + +// Add quaternion and float value +RMAPI Quaternion QuaternionAddValue(Quaternion q, float add) +{ + Quaternion result = {q.x + add, q.y + add, q.z + add, q.w + add}; + + return result; +} + +// Subtract two quaternions +RMAPI Quaternion QuaternionSubtract(Quaternion q1, Quaternion q2) +{ + Quaternion result = {q1.x - q2.x, q1.y - q2.y, q1.z - q2.z, q1.w - q2.w}; + + return result; +} + +// Subtract quaternion and float value +RMAPI Quaternion QuaternionSubtractValue(Quaternion q, float sub) +{ + Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; + + return result; +} + +// Get identity quaternion +RMAPI Quaternion QuaternionIdentity(void) +{ + Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; + + return result; +} + +// Computes the length of a quaternion +RMAPI float QuaternionLength(Quaternion q) +{ + float result = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + + return result; +} + +// Normalize provided quaternion +RMAPI Quaternion QuaternionNormalize(Quaternion q) +{ + Quaternion result = { 0 }; + + float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + if (length == 0.0f) length = 1.0f; + float ilength = 1.0f/length; + + result.x = q.x*ilength; + result.y = q.y*ilength; + result.z = q.z*ilength; + result.w = q.w*ilength; + + return result; +} + +// Invert provided quaternion +RMAPI Quaternion QuaternionInvert(Quaternion q) +{ + Quaternion result = q; + + float lengthSq = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w; + + if (lengthSq != 0.0) + { + float invLength = 1.0f/lengthSq; + + result.x *= -invLength; + result.y *= -invLength; + result.z *= -invLength; + result.w *= invLength; + } + + return result; +} + +// Calculate two quaternion multiplication +RMAPI Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) +{ + Quaternion result = { 0 }; + + float qax = q1.x, qay = q1.y, qaz = q1.z, qaw = q1.w; + float qbx = q2.x, qby = q2.y, qbz = q2.z, qbw = q2.w; + + result.x = qax*qbw + qaw*qbx + qay*qbz - qaz*qby; + result.y = qay*qbw + qaw*qby + qaz*qbx - qax*qbz; + result.z = qaz*qbw + qaw*qbz + qax*qby - qay*qbx; + result.w = qaw*qbw - qax*qbx - qay*qby - qaz*qbz; + + return result; +} + +// Scale quaternion by float value +RMAPI Quaternion QuaternionScale(Quaternion q, float mul) +{ + Quaternion result = { 0 }; + + float qax = q.x, qay = q.y, qaz = q.z, qaw = q.w; + + result.x = qax*mul + qaw*mul + qay*mul - qaz*mul; + result.y = qay*mul + qaw*mul + qaz*mul - qax*mul; + result.z = qaz*mul + qaw*mul + qax*mul - qay*mul; + result.w = qaw*mul - qax*mul - qay*mul - qaz*mul; + + return result; +} + +// Divide two quaternions +RMAPI Quaternion QuaternionDivide(Quaternion q1, Quaternion q2) +{ + Quaternion result = { q1.x/q2.x, q1.y/q2.y, q1.z/q2.z, q1.w/q2.w }; + + return result; +} + +// Calculate linear interpolation between two quaternions +RMAPI Quaternion QuaternionLerp(Quaternion q1, Quaternion q2, float amount) +{ + Quaternion result = { 0 }; + + result.x = q1.x + amount*(q2.x - q1.x); + result.y = q1.y + amount*(q2.y - q1.y); + result.z = q1.z + amount*(q2.z - q1.z); + result.w = q1.w + amount*(q2.w - q1.w); + + return result; +} + +// Calculate slerp-optimized interpolation between two quaternions +RMAPI Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) +{ + Quaternion result = { 0 }; + + // QuaternionLerp(q1, q2, amount) + result.x = q1.x + amount*(q2.x - q1.x); + result.y = q1.y + amount*(q2.y - q1.y); + result.z = q1.z + amount*(q2.z - q1.z); + result.w = q1.w + amount*(q2.w - q1.w); + + // QuaternionNormalize(q); + Quaternion q = result; + float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + if (length == 0.0f) length = 1.0f; + float ilength = 1.0f/length; + + result.x = q.x*ilength; + result.y = q.y*ilength; + result.z = q.z*ilength; + result.w = q.w*ilength; + + return result; +} + +// Calculates spherical linear interpolation between two quaternions +RMAPI Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) +{ + Quaternion result = { 0 }; + + float cosHalfTheta = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z + q1.w*q2.w; + + if (cosHalfTheta < 0) + { + q2.x = -q2.x; q2.y = -q2.y; q2.z = -q2.z; q2.w = -q2.w; + cosHalfTheta = -cosHalfTheta; + } + + if (fabs(cosHalfTheta) >= 1.0f) result = q1; + else if (cosHalfTheta > 0.95f) result = QuaternionNlerp(q1, q2, amount); + else + { + float halfTheta = acosf(cosHalfTheta); + float sinHalfTheta = sqrtf(1.0f - cosHalfTheta*cosHalfTheta); + + if (fabs(sinHalfTheta) < 0.001f) + { + result.x = (q1.x*0.5f + q2.x*0.5f); + result.y = (q1.y*0.5f + q2.y*0.5f); + result.z = (q1.z*0.5f + q2.z*0.5f); + result.w = (q1.w*0.5f + q2.w*0.5f); + } + else + { + float ratioA = sinf((1 - amount)*halfTheta)/sinHalfTheta; + float ratioB = sinf(amount*halfTheta)/sinHalfTheta; + + result.x = (q1.x*ratioA + q2.x*ratioB); + result.y = (q1.y*ratioA + q2.y*ratioB); + result.z = (q1.z*ratioA + q2.z*ratioB); + result.w = (q1.w*ratioA + q2.w*ratioB); + } + } + + return result; +} + +// Calculate quaternion based on the rotation from one vector to another +RMAPI Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) +{ + Quaternion result = { 0 }; + + float cos2Theta = (from.x*to.x + from.y*to.y + from.z*to.z); // Vector3DotProduct(from, to) + 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) + + result.x = cross.x; + result.y = cross.y; + result.z = cross.z; + result.w = 1.0f + cos2Theta; + + // QuaternionNormalize(q); + // NOTE: Normalize to essentially nlerp the original and identity to 0.5 + Quaternion q = result; + float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + if (length == 0.0f) length = 1.0f; + float ilength = 1.0f/length; + + result.x = q.x*ilength; + result.y = q.y*ilength; + result.z = q.z*ilength; + result.w = q.w*ilength; + + return result; +} + +// Get a quaternion for a given rotation matrix +RMAPI Quaternion QuaternionFromMatrix(Matrix mat) +{ + Quaternion result = { 0 }; + + if ((mat.m0 > mat.m5) && (mat.m0 > mat.m10)) + { + float s = sqrtf(1.0f + mat.m0 - mat.m5 - mat.m10)*2; + + result.x = 0.25f*s; + result.y = (mat.m4 + mat.m1)/s; + result.z = (mat.m2 + mat.m8)/s; + result.w = (mat.m9 - mat.m6)/s; + } + else if (mat.m5 > mat.m10) + { + float s = sqrtf(1.0f + mat.m5 - mat.m0 - mat.m10)*2; + result.x = (mat.m4 + mat.m1)/s; + result.y = 0.25f*s; + result.z = (mat.m9 + mat.m6)/s; + result.w = (mat.m2 - mat.m8)/s; + } + else + { + float s = sqrtf(1.0f + mat.m10 - mat.m0 - mat.m5)*2; + result.x = (mat.m2 + mat.m8)/s; + result.y = (mat.m9 + mat.m6)/s; + result.z = 0.25f*s; + result.w = (mat.m4 - mat.m1)/s; + } + + return result; +} + +// Get a matrix for a given quaternion +RMAPI Matrix QuaternionToMatrix(Quaternion q) +{ + Matrix result = { 1.0f, 0.0f, 0.0f, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + 0.0f, 0.0f, 0.0f, 1.0f }; // MatrixIdentity() + + float a2 = q.x*q.x; + float b2 = q.y*q.y; + float c2 = q.z*q.z; + float ac = q.x*q.z; + float ab = q.x*q.y; + float bc = q.y*q.z; + float ad = q.w*q.x; + float bd = q.w*q.y; + float cd = q.w*q.z; + + result.m0 = 1 - 2*(b2 + c2); + result.m1 = 2*(ab + cd); + result.m2 = 2*(ac - bd); + + result.m4 = 2*(ab - cd); + result.m5 = 1 - 2*(a2 + c2); + result.m6 = 2*(bc + ad); + + result.m8 = 2*(ac + bd); + result.m9 = 2*(bc - ad); + result.m10 = 1 - 2*(a2 + b2); + + return result; +} + +// Get rotation quaternion for an angle and axis +// NOTE: angle must be provided in radians +RMAPI Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) +{ + Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; + + float axisLength = sqrtf(axis.x*axis.x + axis.y*axis.y + axis.z*axis.z); + + if (axisLength != 0.0f) + { + angle *= 0.5f; + + float length = 0.0f; + float ilength = 0.0f; + + // Vector3Normalize(axis) + Vector3 v = axis; + length = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + axis.x *= ilength; + axis.y *= ilength; + axis.z *= ilength; + + float sinres = sinf(angle); + float cosres = cosf(angle); + + result.x = axis.x*sinres; + result.y = axis.y*sinres; + result.z = axis.z*sinres; + result.w = cosres; + + // QuaternionNormalize(q); + Quaternion q = result; + length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + if (length == 0.0f) length = 1.0f; + ilength = 1.0f/length; + result.x = q.x*ilength; + result.y = q.y*ilength; + result.z = q.z*ilength; + result.w = q.w*ilength; + } + + return result; +} + +// Get the rotation angle and axis for a given quaternion +RMAPI void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) +{ + if (fabs(q.w) > 1.0f) + { + // QuaternionNormalize(q); + float length = sqrtf(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); + if (length == 0.0f) length = 1.0f; + float ilength = 1.0f/length; + + q.x = q.x*ilength; + q.y = q.y*ilength; + q.z = q.z*ilength; + q.w = q.w*ilength; + } + + Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; + float resAngle = 2.0f*acosf(q.w); + float den = sqrtf(1.0f - q.w*q.w); + + if (den > 0.0001f) + { + resAxis.x = q.x/den; + resAxis.y = q.y/den; + resAxis.z = q.z/den; + } + else + { + // This occurs when the angle is zero. + // Not a problem: just set an arbitrary normalized axis. + resAxis.x = 1.0f; + } + + *outAxis = resAxis; + *outAngle = resAngle; +} + +// Get the quaternion equivalent to Euler angles +// NOTE: Rotation order is ZYX +RMAPI Quaternion QuaternionFromEuler(float pitch, float yaw, float roll) +{ + Quaternion result = { 0 }; + + float x0 = cosf(pitch*0.5f); + float x1 = sinf(pitch*0.5f); + float y0 = cosf(yaw*0.5f); + float y1 = sinf(yaw*0.5f); + float z0 = cosf(roll*0.5f); + float z1 = sinf(roll*0.5f); + + result.x = x1*y0*z0 - x0*y1*z1; + result.y = x0*y1*z0 + x1*y0*z1; + result.z = x0*y0*z1 - x1*y1*z0; + result.w = x0*y0*z0 + x1*y1*z1; + + return result; +} + +// Get the Euler angles equivalent to quaternion (roll, pitch, yaw) +// NOTE: Angles are returned in a Vector3 struct in radians +RMAPI Vector3 QuaternionToEuler(Quaternion q) +{ + Vector3 result = { 0 }; + + // Roll (x-axis rotation) + float x0 = 2.0f*(q.w*q.x + q.y*q.z); + float x1 = 1.0f - 2.0f*(q.x*q.x + q.y*q.y); + result.x = atan2f(x0, x1); + + // Pitch (y-axis rotation) + float y0 = 2.0f*(q.w*q.y - q.z*q.x); + y0 = y0 > 1.0f ? 1.0f : y0; + y0 = y0 < -1.0f ? -1.0f : y0; + result.y = asinf(y0); + + // Yaw (z-axis rotation) + float z0 = 2.0f*(q.w*q.z + q.x*q.y); + float z1 = 1.0f - 2.0f*(q.y*q.y + q.z*q.z); + result.z = atan2f(z0, z1); + + return result; +} + +// Transform a quaternion given a transformation matrix +RMAPI Quaternion QuaternionTransform(Quaternion q, Matrix mat) +{ + Quaternion result = { 0 }; + + result.x = mat.m0*q.x + mat.m4*q.y + mat.m8*q.z + mat.m12*q.w; + result.y = mat.m1*q.x + mat.m5*q.y + mat.m9*q.z + mat.m13*q.w; + result.z = mat.m2*q.x + mat.m6*q.y + mat.m10*q.z + mat.m14*q.w; + result.w = mat.m3*q.x + mat.m7*q.y + mat.m11*q.z + mat.m15*q.w; + + return result; +} + +#endif // RAYMATH_H |