/********************************************************************************************** * * 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" 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 EPSILON #define EPSILON 0.000001f #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 // Required for: sinf(), cosf(), tan(), atan2f(), sqrtf(), floor(), 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; } // Wrap input value from min to max RMAPI float Wrap(float value, float min, float max) { float result = value - (max - min)*floorf((value - min)/(max - min)); return result; } // Check whether two given floats are almost equal RMAPI int FloatEquals(float x, float y) { int result = (fabsf(x - y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(x), fabsf(y)))); 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; } // Invert the given vector RMAPI Vector2 Vector2Invert(Vector2 v) { Vector2 result = { 1.0f/v.x, 1.0f/v.y }; return result; } // Clamp the components of the vector between // min and max values specified by the given vectors RMAPI Vector2 Vector2Clamp(Vector2 v, Vector2 min, Vector2 max) { Vector2 result = { 0 }; result.x = fminf(max.x, fmaxf(min.x, v.x)); result.y = fminf(max.y, fmaxf(min.y, v.y)); return result; } // Clamp the magnitude of the vector between two min and max values RMAPI Vector2 Vector2ClampValue(Vector2 v, float min, float max) { Vector2 result = v; float length = (v.x*v.x) + (v.y*v.y); if (length > 0.0f) { length = sqrtf(length); if (length < min) { float scale = min/length; result.x = v.x*scale; result.y = v.y*scale; } else if (length > max) { float scale = max/length; result.x = v.x*scale; result.y = v.y*scale; } } return result; } // Check whether two given vectors are almost equal RMAPI int Vector2Equals(Vector2 p, Vector2 q) { int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))); 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 (fabsf(v.y) < min) { min = (float) fabs(v.y); Vector3 tmp = {0.0f, 1.0f, 0.0f}; cardinalAxis = tmp; } if (fabsf(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; } // Rotates a vector around an axis RMAPI Vector3 Vector3RotateByAxisAngle(Vector3 v, Vector3 axis, float angle) { // Using Euler-Rodrigues Formula // Ref.: https://en.wikipedia.org/w/index.php?title=Euler%E2%80%93Rodrigues_formula Vector3 result = v; // Vector3Normalize(axis); float length = sqrtf(axis.x * axis.x + axis.y * axis.y + axis.z * axis.z); if (length == 0.0f) length = 1.0f; float ilength = 1.0f / length; axis.x *= ilength; axis.y *= ilength; axis.z *= ilength; angle /= 2.0f; float a = sinf(angle); float b = axis.x * a; float c = axis.y * a; float d = axis.z * a; a = cosf(angle); Vector3 w = { b, c, d }; // Vector3CrossProduct(w, v) 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 }; // Vector3CrossProduct(w, wv) 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 }; // Vector3Scale(wv, 2 * a) a *= 2; wv.x *= a; wv.y *= a; wv.z *= a; // Vector3Scale(wwv, 2) wwv.x *= 2; wwv.y *= 2; wwv.z *= 2; result.x += wv.x; result.y += wv.y; result.z += wv.z; result.x += wwv.x; result.y += wwv.y; result.z += wwv.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; } // Invert the given vector RMAPI Vector3 Vector3Invert(Vector3 v) { Vector3 result = { 1.0f/v.x, 1.0f/v.y, 1.0f/v.z }; return result; } // Clamp the components of the vector between // min and max values specified by the given vectors RMAPI Vector3 Vector3Clamp(Vector3 v, Vector3 min, Vector3 max) { Vector3 result = { 0 }; result.x = fminf(max.x, fmaxf(min.x, v.x)); result.y = fminf(max.y, fmaxf(min.y, v.y)); result.z = fminf(max.z, fmaxf(min.z, v.z)); return result; } // Clamp the magnitude of the vector between two values RMAPI Vector3 Vector3ClampValue(Vector3 v, float min, float max) { Vector3 result = v; float length = (v.x*v.x) + (v.y*v.y) + (v.z*v.z); if (length > 0.0f) { length = sqrtf(length); if (length < min) { float scale = min/length; result.x = v.x*scale; result.y = v.y*scale; result.z = v.z*scale; } else if (length > max) { float scale = max/length; result.x = v.x*scale; result.y = v.y*scale; result.z = v.z*scale; } } return result; } // Check whether two given vectors are almost equal RMAPI int Vector3Equals(Vector3 p, Vector3 q) { int result = ((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))); return result; } // Compute the direction of a refracted ray where v specifies the // normalized direction of the incoming ray, n specifies the // normalized normal vector of the interface of two optical media, // and r specifies the ratio of the refractive index of the medium // from where the ray comes to the refractive index of the medium // on the other side of the surface RMAPI Vector3 Vector3Refract(Vector3 v, Vector3 n, float r) { Vector3 result = { 0 }; float dot = v.x*n.x + v.y*n.y + v.z*n.z; float d = 1.0f - r*r*(1.0f - dot*dot); if (d >= 0.0f) { d = sqrtf(d); v.x = r*v.x - (r*dot + d)*n.x; v.y = r*v.y - (r*dot + d)*n.y; v.z = r*v.z - (r*dot + d)*n.z; result = v; } return result; } //---------------------------------------------------------------------------------- // 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; } // 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 // NOTE: Angle must be provided 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 // NOTE: Angle must be provided 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 // NOTE: Angle must be provided 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 // NOTE: Angle must be provided in radians RMAPI Matrix MatrixRotateXYZ(Vector3 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 cosz = cosf(-angle.z); float sinz = sinf(-angle.z); float cosy = cosf(-angle.y); float siny = sinf(-angle.y); float cosx = cosf(-angle.x); float sinx = sinf(-angle.x); result.m0 = cosz*cosy; result.m1 = (cosz*siny*sinx) - (sinz*cosx); result.m2 = (cosz*siny*cosx) + (sinz*sinx); result.m4 = sinz*cosy; result.m5 = (sinz*siny*sinx) + (cosz*cosx); result.m6 = (sinz*siny*cosx) - (cosz*sinx); result.m8 = -siny; result.m9 = cosy*sinx; result.m10= cosy*cosx; return result; } // Get zyx-rotation matrix // NOTE: Angle must be provided in radians RMAPI Matrix MatrixRotateZYX(Vector3 angle) { Matrix result = { 0 }; float cz = cosf(angle.z); float sz = sinf(angle.z); float cy = cosf(angle.y); float sy = sinf(angle.y); float cx = cosf(angle.x); float sx = sinf(angle.x); result.m0 = cz*cy; result.m4 = cz*sy*sx - cx*sz; result.m8 = sz*sx + cz*cx*sy; result.m12 = 0; result.m1 = cy*sz; result.m5 = cz*cx + sz*sy*sx; result.m9 = cx*sz*sy - cz*sx; result.m13 = 0; result.m2 = -sy; result.m6 = cy*sx; result.m10 = cy*cx; result.m14 = 0; result.m3 = 0; result.m7 = 0; result.m11 = 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: Fovy angle must 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 != 0.0f) { 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 }; result.x = q.x*mul; result.y = q.y*mul; result.z = q.z*mul; result.w = q.w*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 (fabsf(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 (fabsf(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 }; float fourWSquaredMinus1 = mat.m0 + mat.m5 + mat.m10; float fourXSquaredMinus1 = mat.m0 - mat.m5 - mat.m10; float fourYSquaredMinus1 = mat.m5 - mat.m0 - mat.m10; float fourZSquaredMinus1 = mat.m10 - mat.m0 - mat.m5; int biggestIndex = 0; float fourBiggestSquaredMinus1 = fourWSquaredMinus1; if (fourXSquaredMinus1 > fourBiggestSquaredMinus1) { fourBiggestSquaredMinus1 = fourXSquaredMinus1; biggestIndex = 1; } if (fourYSquaredMinus1 > fourBiggestSquaredMinus1) { fourBiggestSquaredMinus1 = fourYSquaredMinus1; biggestIndex = 2; } if (fourZSquaredMinus1 > fourBiggestSquaredMinus1) { fourBiggestSquaredMinus1 = fourZSquaredMinus1; biggestIndex = 3; } float biggestVal = sqrtf(fourBiggestSquaredMinus1 + 1.0f) * 0.5f; float mult = 0.25f / biggestVal; switch (biggestIndex) { case 0: result.w = biggestVal; result.x = (mat.m6 - mat.m9) * mult; result.y = (mat.m8 - mat.m2) * mult; result.z = (mat.m1 - mat.m4) * mult; break; case 1: result.x = biggestVal; result.w = (mat.m6 - mat.m9) * mult; result.y = (mat.m1 + mat.m4) * mult; result.z = (mat.m8 + mat.m2) * mult; break; case 2: result.y = biggestVal; result.w = (mat.m8 - mat.m2) * mult; result.x = (mat.m1 + mat.m4) * mult; result.z = (mat.m6 + mat.m9) * mult; break; case 3: result.z = biggestVal; result.w = (mat.m1 - mat.m4) * mult; result.x = (mat.m8 + mat.m2) * mult; result.y = (mat.m6 + mat.m9) * mult; break; } 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 (fabsf(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; } // Check whether two given quaternions are almost equal RMAPI int QuaternionEquals(Quaternion p, Quaternion q) { int result = (((fabsf(p.x - q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && ((fabsf(p.y - q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && ((fabsf(p.z - q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) && ((fabsf(p.w - q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))) || (((fabsf(p.x + q.x)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.x), fabsf(q.x))))) && ((fabsf(p.y + q.y)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.y), fabsf(q.y))))) && ((fabsf(p.z + q.z)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.z), fabsf(q.z))))) && ((fabsf(p.w + q.w)) <= (EPSILON*fmaxf(1.0f, fmaxf(fabsf(p.w), fabsf(q.w)))))); return result; } #endif // RAYMATH_H