/********************************************************************************************** * * raymath v1.2 - Math functions to work with 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_HEADER_ONLY * Define static inline functions code, so #include header suffices for use. * This may use up lots of memory. * * #define RAYMATH_STANDALONE * Avoid raylib.h header inclusion in this file. * Vector3 and Matrix data types are defined internally in raymath module. * * * LICENSE: zlib/libpng * * Copyright (c) 2015-2020 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 //#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line //#define RAYMATH_HEADER_ONLY // NOTE: To compile functions as static inline, uncomment this line #ifndef RAYMATH_STANDALONE #include "raylib.h" // Required for structs: Vector3, Matrix #endif #if defined(RAYMATH_IMPLEMENTATION) && defined(RAYMATH_HEADER_ONLY) #error "Specifying both RAYMATH_IMPLEMENTATION and RAYMATH_HEADER_ONLY is contradictory" #endif #if defined(RAYMATH_IMPLEMENTATION) #if defined(_WIN32) && defined(BUILD_LIBTYPE_SHARED) #define RMDEF __declspec(dllexport) extern inline // We are building raylib as a Win32 shared library (.dll). #elif defined(_WIN32) && defined(USE_LIBTYPE_SHARED) #define RMDEF __declspec(dllimport) // We are using raylib as a Win32 shared library (.dll) #else #define RMDEF extern inline // Provide external definition #endif #elif defined(RAYMATH_HEADER_ONLY) #define RMDEF static inline // Functions may be inlined, no external out-of-line definition #else #if defined(__TINYC__) #define RMDEF static inline // plain inline not supported by tinycc (See issue #435) #else #define RMDEF inline // Functions may be inlined or external definition used #endif #endif //---------------------------------------------------------------------------------- // Defines and Macros //---------------------------------------------------------------------------------- #ifndef PI #define PI 3.14159265358979323846 #endif #ifndef DEG2RAD #define DEG2RAD (PI/180.0f) #endif #ifndef RAD2DEG #define RAD2DEG (180.0f/PI) #endif // Return float vector for Matrix #ifndef MatrixToFloat #define MatrixToFloat(mat) (MatrixToFloatV(mat).v) #endif // Return float vector for Vector3 #ifndef Vector3ToFloat #define Vector3ToFloat(vec) (Vector3ToFloatV(vec).v) #endif //---------------------------------------------------------------------------------- // Types and Structures Definition //---------------------------------------------------------------------------------- #if defined(RAYMATH_STANDALONE) // Vector2 type typedef struct Vector2 { float x; float y; } Vector2; // Vector3 type typedef struct Vector3 { float x; float y; float z; } Vector3; // Quaternion type typedef struct Quaternion { float x; float y; float z; float w; } Quaternion; // Matrix type (OpenGL style 4x4 - right handed, column major) typedef struct Matrix { float m0, m4, m8, m12; float m1, m5, m9, m13; float m2, m6, m10, m14; float m3, m7, m11, m15; } Matrix; #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(), sqrtf(), tan(), fabs() //---------------------------------------------------------------------------------- // Module Functions Definition - Utils math //---------------------------------------------------------------------------------- // Clamp float value RMDEF float Clamp(float value, float min, float max) { const float res = value < min ? min : value; return res > max ? max : res; } // Calculate linear interpolation between two floats RMDEF float Lerp(float start, float end, float amount) { return start + amount*(end - start); } //---------------------------------------------------------------------------------- // Module Functions Definition - Vector2 math //---------------------------------------------------------------------------------- // Vector with components value 0.0f RMDEF Vector2 Vector2Zero(void) { Vector2 result = { 0.0f, 0.0f }; return result; } // Vector with components value 1.0f RMDEF Vector2 Vector2One(void) { Vector2 result = { 1.0f, 1.0f }; return result; } // Add two vectors (v1 + v2) RMDEF Vector2 Vector2Add(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x + v2.x, v1.y + v2.y }; return result; } // Add vector and float value RMDEF Vector2 Vector2AddValue(Vector2 v, float add) { Vector2 result = { v.x + add, v.y + add }; return result; } // Subtract two vectors (v1 - v2) RMDEF Vector2 Vector2Subtract(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x - v2.x, v1.y - v2.y }; return result; } // Subtract vector by float value RMDEF Vector2 Vector2SubtractValue(Vector2 v, float sub) { Vector2 result = { v.x - sub, v.y - sub }; return result; } // Calculate vector length RMDEF float Vector2Length(Vector2 v) { float result = sqrtf((v.x*v.x) + (v.y*v.y)); return result; } // Calculate two vectors dot product RMDEF float Vector2DotProduct(Vector2 v1, Vector2 v2) { float result = (v1.x*v2.x + v1.y*v2.y); return result; } // Calculate distance between two vectors RMDEF 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 angle from two vectors in X-axis RMDEF float Vector2Angle(Vector2 v1, Vector2 v2) { float result = atan2f(v2.y - v1.y, v2.x - v1.x)*(180.0f/PI); if (result < 0) result += 360.0f; return result; } // Scale vector (multiply by value) RMDEF Vector2 Vector2Scale(Vector2 v, float scale) { Vector2 result = { v.x*scale, v.y*scale }; return result; } // Multiply vector by vector RMDEF Vector2 Vector2Multiply(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x*v2.x, v1.y*v2.y }; return result; } // Negate vector RMDEF Vector2 Vector2Negate(Vector2 v) { Vector2 result = { -v.x, -v.y }; return result; } // Divide vector by vector RMDEF Vector2 Vector2Divide(Vector2 v1, Vector2 v2) { Vector2 result = { v1.x/v2.x, v1.y/v2.y }; return result; } // Normalize provided vector RMDEF Vector2 Vector2Normalize(Vector2 v) { Vector2 result = Vector2Scale(v, 1/Vector2Length(v)); return result; } // Calculate linear interpolation between two vectors RMDEF 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; } // Rotate Vector by float in Degrees. RMDEF Vector2 Vector2Rotate(Vector2 v, float degs) { float rads = degs*DEG2RAD; Vector2 result = {v.x * cosf(rads) - v.y * sinf(rads) , v.x * sinf(rads) + v.y * cosf(rads) }; return result; } //---------------------------------------------------------------------------------- // Module Functions Definition - Vector3 math //---------------------------------------------------------------------------------- // Vector with components value 0.0f RMDEF Vector3 Vector3Zero(void) { Vector3 result = { 0.0f, 0.0f, 0.0f }; return result; } // Vector with components value 1.0f RMDEF Vector3 Vector3One(void) { Vector3 result = { 1.0f, 1.0f, 1.0f }; return result; } // Add two vectors RMDEF 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 RMDEF Vector3 Vector3AddValue(Vector3 v, float add) { Vector3 result = { v.x + add, v.y + add, v.z + add }; return result; } // Subtract two vectors RMDEF 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 RMDEF Vector3 Vector3SubtractValue(Vector3 v, float sub) { Vector3 result = { v.x - sub, v.y - sub, v.z - sub }; return result; } // Multiply vector by scalar RMDEF Vector3 Vector3Scale(Vector3 v, float scalar) { Vector3 result = { v.x*scalar, v.y*scalar, v.z*scalar }; return result; } // Multiply vector by vector RMDEF 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 RMDEF 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 RMDEF 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; } result = Vector3CrossProduct(v, cardinalAxis); return result; } // Calculate vector length RMDEF float Vector3Length(const Vector3 v) { float result = sqrtf(v.x*v.x + v.y*v.y + v.z*v.z); return result; } // Calculate two vectors dot product RMDEF 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 RMDEF float Vector3Distance(Vector3 v1, Vector3 v2) { float dx = v2.x - v1.x; float dy = v2.y - v1.y; float dz = v2.z - v1.z; float result = sqrtf(dx*dx + dy*dy + dz*dz); return result; } // Negate provided vector (invert direction) RMDEF Vector3 Vector3Negate(Vector3 v) { Vector3 result = { -v.x, -v.y, -v.z }; return result; } // Divide vector by vector RMDEF 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 RMDEF Vector3 Vector3Normalize(Vector3 v) { Vector3 result = v; float length, ilength; length = Vector3Length(v); if (length == 0.0f) length = 1.0f; 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 RMDEF void Vector3OrthoNormalize(Vector3 *v1, Vector3 *v2) { *v1 = Vector3Normalize(*v1); Vector3 vn = Vector3CrossProduct(*v1, *v2); vn = Vector3Normalize(vn); *v2 = Vector3CrossProduct(vn, *v1); } // Transforms a Vector3 by a given Matrix RMDEF 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 RMDEF 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 RMDEF 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 RMDEF Vector3 Vector3Reflect(Vector3 v, Vector3 normal) { // I is the original vector // N is the normal of the incident plane // R = I - (2*N*( DotProduct[ I,N] )) Vector3 result = { 0 }; float dotProduct = Vector3DotProduct(v, normal); 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; } // Return min value for each pair of components RMDEF 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; } // Return max value for each pair of components RMDEF 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 RMDEF Vector3 Vector3Barycenter(Vector3 p, Vector3 a, Vector3 b, Vector3 c) { //Vector v0 = b - a, v1 = c - a, v2 = p - a; Vector3 v0 = Vector3Subtract(b, a); Vector3 v1 = Vector3Subtract(c, a); Vector3 v2 = Vector3Subtract(p, a); float d00 = Vector3DotProduct(v0, v0); float d01 = Vector3DotProduct(v0, v1); float d11 = Vector3DotProduct(v1, v1); float d20 = Vector3DotProduct(v2, v0); float d21 = Vector3DotProduct(v2, v1); float denom = d00*d11 - d01*d01; Vector3 result = { 0 }; result.y = (d11*d20 - d01*d21)/denom; result.z = (d00*d21 - d01*d20)/denom; result.x = 1.0f - (result.z + result.y); return result; } // Returns Vector3 as float array RMDEF 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 RMDEF float MatrixDeterminant(Matrix mat) { // 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 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; } // Returns the trace of the matrix (sum of the values along the diagonal) RMDEF float MatrixTrace(Matrix mat) { float result = (mat.m0 + mat.m5 + mat.m10 + mat.m15); return result; } // Transposes provided matrix RMDEF 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 RMDEF 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 RMDEF Matrix MatrixNormalize(Matrix mat) { Matrix result = { 0 }; float det = MatrixDeterminant(mat); 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; } // Returns identity matrix RMDEF 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 RMDEF Matrix MatrixAdd(Matrix left, Matrix right) { Matrix result = MatrixIdentity(); 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) RMDEF Matrix MatrixSubtract(Matrix left, Matrix right) { Matrix result = MatrixIdentity(); 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; } // Returns translation matrix RMDEF 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 RMDEF Matrix MatrixRotate(Vector3 axis, float angle) { Matrix result = { 0 }; float x = axis.x, y = axis.y, z = axis.z; float length = sqrtf(x*x + y*y + z*z); if ((length != 1.0f) && (length != 0.0f)) { length = 1.0f/length; x *= length; y *= length; z *= length; } 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; } // Returns xyz-rotation matrix (angles in radians) RMDEF Matrix MatrixRotateXYZ(Vector3 ang) { Matrix result = 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; } // Returns x-rotation matrix (angle in radians) RMDEF Matrix MatrixRotateX(float angle) { Matrix result = MatrixIdentity(); float cosres = cosf(angle); float sinres = sinf(angle); result.m5 = cosres; result.m6 = -sinres; result.m9 = sinres; result.m10 = cosres; return result; } // Returns y-rotation matrix (angle in radians) RMDEF Matrix MatrixRotateY(float angle) { Matrix result = MatrixIdentity(); float cosres = cosf(angle); float sinres = sinf(angle); result.m0 = cosres; result.m2 = sinres; result.m8 = -sinres; result.m10 = cosres; return result; } // Returns z-rotation matrix (angle in radians) RMDEF Matrix MatrixRotateZ(float angle) { Matrix result = MatrixIdentity(); float cosres = cosf(angle); float sinres = sinf(angle); result.m0 = cosres; result.m1 = -sinres; result.m4 = sinres; result.m5 = cosres; return result; } // Returns scaling matrix RMDEF 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; } // Returns two matrix multiplication // NOTE: When multiplying matrices... the order matters! RMDEF 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; } // Returns perspective projection matrix RMDEF 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; } // Returns perspective projection matrix // NOTE: Angle should be provided in radians RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far) { double top = near*tan(fovy*0.5); double right = top*aspect; Matrix result = MatrixFrustum(-right, right, -top, top, near, far); return result; } // Returns orthographic projection matrix RMDEF 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; } // Returns camera look-at matrix (view matrix) RMDEF Matrix MatrixLookAt(Vector3 eye, Vector3 target, Vector3 up) { Matrix result = { 0 }; Vector3 z = Vector3Subtract(eye, target); z = Vector3Normalize(z); Vector3 x = Vector3CrossProduct(up, z); x = Vector3Normalize(x); Vector3 y = Vector3CrossProduct(z, x); y = Vector3Normalize(y); result.m0 = x.x; result.m1 = x.y; result.m2 = x.z; result.m3 = 0.0f; result.m4 = y.x; result.m5 = y.y; result.m6 = y.z; result.m7 = 0.0f; result.m8 = z.x; result.m9 = z.y; result.m10 = z.z; result.m11 = 0.0f; result.m12 = eye.x; result.m13 = eye.y; result.m14 = eye.z; result.m15 = 1.0f; result = MatrixInvert(result); return result; } // Returns float array of matrix data RMDEF float16 MatrixToFloatV(Matrix mat) { float16 buffer = { 0 }; buffer.v[0] = mat.m0; buffer.v[1] = mat.m1; buffer.v[2] = mat.m2; buffer.v[3] = mat.m3; buffer.v[4] = mat.m4; buffer.v[5] = mat.m5; buffer.v[6] = mat.m6; buffer.v[7] = mat.m7; buffer.v[8] = mat.m8; buffer.v[9] = mat.m9; buffer.v[10] = mat.m10; buffer.v[11] = mat.m11; buffer.v[12] = mat.m12; buffer.v[13] = mat.m13; buffer.v[14] = mat.m14; buffer.v[15] = mat.m15; return buffer; } //---------------------------------------------------------------------------------- // Module Functions Definition - Quaternion math //---------------------------------------------------------------------------------- // Add two quaternions RMDEF 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 RMDEF 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 RMDEF 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 RMDEF Quaternion QuaternionSubtractValue(Quaternion q, float sub) { Quaternion result = {q.x - sub, q.y - sub, q.z - sub, q.w - sub}; return result; } // Returns identity quaternion RMDEF Quaternion QuaternionIdentity(void) { Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; return result; } // Computes the length of a quaternion RMDEF float QuaternionLength(Quaternion q) { float result = (float)sqrt(q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w); return result; } // Normalize provided quaternion RMDEF Quaternion QuaternionNormalize(Quaternion q) { Quaternion result = { 0 }; float length, ilength; length = QuaternionLength(q); 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; } // Invert provided quaternion RMDEF Quaternion QuaternionInvert(Quaternion q) { Quaternion result = q; float length = QuaternionLength(q); float lengthSq = length*length; if (lengthSq != 0.0) { float i = 1.0f/lengthSq; result.x *= -i; result.y *= -i; result.z *= -i; result.w *= i; } return result; } // Calculate two quaternion multiplication RMDEF 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 RMDEF 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 RMDEF 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 RMDEF 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 RMDEF Quaternion QuaternionNlerp(Quaternion q1, Quaternion q2, float amount) { Quaternion result = QuaternionLerp(q1, q2, amount); result = QuaternionNormalize(result); return result; } // Calculates spherical linear interpolation between two quaternions RMDEF 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 (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 RMDEF Quaternion QuaternionFromVector3ToVector3(Vector3 from, Vector3 to) { Quaternion result = { 0 }; float cos2Theta = Vector3DotProduct(from, to); Vector3 cross = Vector3CrossProduct(from, to); result.x = cross.x; result.y = cross.y; result.z = cross.y; result.w = 1.0f + cos2Theta; // NOTE: Added QuaternioIdentity() // Normalize to essentially nlerp the original and identity to 0.5 result = QuaternionNormalize(result); // Above lines are equivalent to: //Quaternion result = QuaternionNlerp(q, QuaternionIdentity(), 0.5f); return result; } // Returns a quaternion for a given rotation matrix RMDEF Quaternion QuaternionFromMatrix(Matrix mat) { Quaternion result = { 0 }; float trace = MatrixTrace(mat); if (trace > 0.0f) { float s = sqrtf(trace + 1)*2.0f; float invS = 1.0f/s; result.w = s*0.25f; result.x = (mat.m6 - mat.m9)*invS; result.y = (mat.m8 - mat.m2)*invS; result.z = (mat.m1 - mat.m4)*invS; } else { float m00 = mat.m0, m11 = mat.m5, m22 = mat.m10; if (m00 > m11 && m00 > m22) { float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; float invS = 1.0f/s; result.w = (mat.m6 - mat.m9)*invS; result.x = s*0.25f; result.y = (mat.m4 + mat.m1)*invS; result.z = (mat.m8 + mat.m2)*invS; } else if (m11 > m22) { float s = sqrtf(1.0f + m11 - m00 - m22)*2.0f; float invS = 1.0f/s; result.w = (mat.m8 - mat.m2)*invS; result.x = (mat.m4 + mat.m1)*invS; result.y = s*0.25f; result.z = (mat.m9 + mat.m6)*invS; } else { float s = sqrtf(1.0f + m22 - m00 - m11)*2.0f; float invS = 1.0f/s; result.w = (mat.m1 - mat.m4)*invS; result.x = (mat.m8 + mat.m2)*invS; result.y = (mat.m9 + mat.m6)*invS; result.z = s*0.25f; } } return result; } // Returns a matrix for a given quaternion RMDEF Matrix QuaternionToMatrix(Quaternion q) { Matrix result = { 0 }; float x = q.x, y = q.y, z = q.z, w = q.w; float x2 = x + x; float y2 = y + y; float z2 = z + z; float length = QuaternionLength(q); float lengthSquared = length*length; float xx = x*x2/lengthSquared; float xy = x*y2/lengthSquared; float xz = x*z2/lengthSquared; float yy = y*y2/lengthSquared; float yz = y*z2/lengthSquared; float zz = z*z2/lengthSquared; float wx = w*x2/lengthSquared; float wy = w*y2/lengthSquared; float wz = w*z2/lengthSquared; result.m0 = 1.0f - (yy + zz); result.m1 = xy - wz; result.m2 = xz + wy; result.m3 = 0.0f; result.m4 = xy + wz; result.m5 = 1.0f - (xx + zz); result.m6 = yz - wx; result.m7 = 0.0f; result.m8 = xz - wy; result.m9 = yz + wx; result.m10 = 1.0f - (xx + yy); result.m11 = 0.0f; result.m12 = 0.0f; result.m13 = 0.0f; result.m14 = 0.0f; result.m15 = 1.0f; return result; } // Returns rotation quaternion for an angle and axis // NOTE: angle must be provided in radians RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle) { Quaternion result = { 0.0f, 0.0f, 0.0f, 1.0f }; if (Vector3Length(axis) != 0.0f) angle *= 0.5f; axis = Vector3Normalize(axis); 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; result = QuaternionNormalize(result); return result; } // Returns the rotation angle and axis for a given quaternion RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle) { if (fabs(q.w) > 1.0f) q = QuaternionNormalize(q); 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; } // Returns he quaternion equivalent to Euler angles RMDEF Quaternion QuaternionFromEuler(float roll, float pitch, float yaw) { Quaternion q = { 0 }; float x0 = cosf(roll*0.5f); float x1 = sinf(roll*0.5f); float y0 = cosf(pitch*0.5f); float y1 = sinf(pitch*0.5f); float z0 = cosf(yaw*0.5f); float z1 = sinf(yaw*0.5f); q.x = x1*y0*z0 - x0*y1*z1; q.y = x0*y1*z0 + x1*y0*z1; q.z = x0*y0*z1 - x1*y1*z0; q.w = x0*y0*z0 + x1*y1*z1; return q; } // Return the Euler angles equivalent to quaternion (roll, pitch, yaw) // NOTE: Angles are returned in a Vector3 struct in degrees RMDEF 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)*RAD2DEG; // 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)*RAD2DEG; // 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)*RAD2DEG; return result; } // Transform a quaternion given a transformation matrix RMDEF 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