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Diffstat (limited to 'src/raymath.h')
| -rw-r--r-- | src/raymath.h | 1093 |
1 files changed, 1041 insertions, 52 deletions
diff --git a/src/raymath.h b/src/raymath.h index e140b74c..35cee39f 100644 --- a/src/raymath.h +++ b/src/raymath.h @@ -1,9 +1,23 @@ /********************************************************************************************** * -* raymath +* raymath (header only file) * * Some useful functions to work with Vector3, Matrix and Quaternions * +* You must: +* #define RAYMATH_IMPLEMENTATION +* before you include this file in *only one* C or C++ file to create the implementation. +* +* Example: +* #define RAYMATH_IMPLEMENTATION +* #include "raymath.h" +* +* You can also use: +* #define RAYMATH_EXTERN_INLINE // Inlines all functions code, so it runs faster. +* // This requires lots of memory on system. +* #define RAYMATH_STANDALONE // Not dependent on raylib.h structs: Vector3, Matrix. +* +* * Copyright (c) 2015 Ramon Santamaria (@raysan5) * * This software is provided "as-is", without any express or implied warranty. In no event @@ -26,10 +40,17 @@ #ifndef RAYMATH_H #define RAYMATH_H -//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line +//#define RAYMATH_STANDALONE // NOTE: To use raymath as standalone lib, just uncomment this line +//#define RAYMATH_EXTERN_INLINE // NOTE: To compile functions as static inline, uncomment this line #ifndef RAYMATH_STANDALONE - #include "raylib.h" // Required for typedef: Vector3 + #include "raylib.h" // Required for structs: Vector3, Matrix +#endif + +#if defined(RAYMATH_EXTERN_INLINE) + #define RMDEF extern inline +#else + #define RMDEF extern #endif //---------------------------------------------------------------------------------- @@ -39,14 +60,25 @@ #define PI 3.14159265358979323846 #endif -#define DEG2RAD (PI / 180.0f) -#define RAD2DEG (180.0f / PI) +#ifndef DEG2RAD + #define DEG2RAD (PI/180.0f) +#endif + +#ifndef RAD2DEG + #define RAD2DEG (180.0f/PI) +#endif //---------------------------------------------------------------------------------- // Types and Structures Definition //---------------------------------------------------------------------------------- -#ifdef RAYMATH_STANDALONE +#if defined(RAYMATH_STANDALONE) + // Vector2 type + typedef struct Vector2 { + float x; + float y; + } Vector2; + // Vector3 type typedef struct Vector3 { float x; @@ -71,69 +103,1026 @@ typedef struct Quaternion { float w; } Quaternion; +#ifndef RAYMATH_EXTERN_INLINE #ifdef __cplusplus -extern "C" { // Prevents name mangling of functions +extern "C" { #endif //------------------------------------------------------------------------------------ // Functions Declaration to work with Vector3 //------------------------------------------------------------------------------------ -Vector3 VectorAdd(Vector3 v1, Vector3 v2); // Add two vectors -Vector3 VectorSubtract(Vector3 v1, Vector3 v2); // Substract two vectors -Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2); // Calculate two vectors cross product -Vector3 VectorPerpendicular(Vector3 v); // Calculate one vector perpendicular vector -float VectorDotProduct(Vector3 v1, Vector3 v2); // Calculate two vectors dot product -float VectorLength(const Vector3 v); // Calculate vector lenght -void VectorScale(Vector3 *v, float scale); // Scale provided vector -void VectorNegate(Vector3 *v); // Negate provided vector (invert direction) -void VectorNormalize(Vector3 *v); // Normalize provided vector -float VectorDistance(Vector3 v1, Vector3 v2); // Calculate distance between two points -Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount); // Calculate linear interpolation between two vectors -Vector3 VectorReflect(Vector3 vector, Vector3 normal); // Calculate reflected vector to normal -void VectorTransform(Vector3 *v, Matrix mat); // Transforms a Vector3 by a given Matrix -Vector3 VectorZero(void); // Return a Vector3 init to zero +RMDEF Vector3 VectorAdd(Vector3 v1, Vector3 v2); // Add two vectors +RMDEF Vector3 VectorSubtract(Vector3 v1, Vector3 v2); // Substract two vectors +RMDEF Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2); // Calculate two vectors cross product +RMDEF Vector3 VectorPerpendicular(Vector3 v); // Calculate one vector perpendicular vector +RMDEF float VectorDotProduct(Vector3 v1, Vector3 v2); // Calculate two vectors dot product +RMDEF float VectorLength(const Vector3 v); // Calculate vector lenght +RMDEF void VectorScale(Vector3 *v, float scale); // Scale provided vector +RMDEF void VectorNegate(Vector3 *v); // Negate provided vector (invert direction) +RMDEF void VectorNormalize(Vector3 *v); // Normalize provided vector +RMDEF float VectorDistance(Vector3 v1, Vector3 v2); // Calculate distance between two points +RMDEF Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount); // Calculate linear interpolation between two vectors +RMDEF Vector3 VectorReflect(Vector3 vector, Vector3 normal); // Calculate reflected vector to normal +RMDEF void VectorTransform(Vector3 *v, Matrix mat); // Transforms a Vector3 by a given Matrix +RMDEF Vector3 VectorZero(void); // Return a Vector3 init to zero +RMDEF Vector3 VectorMin(Vector3 vec1, Vector3 vec2); // Return min value for each pair of components +RMDEF Vector3 VectorMax(Vector3 vec1, Vector3 vec2); // Return max value for each pair of components //------------------------------------------------------------------------------------ // Functions Declaration to work with Matrix //------------------------------------------------------------------------------------ -float *GetMatrixVector(Matrix mat); // Returns an OpenGL-ready vector (glMultMatrixf) -float MatrixDeterminant(Matrix mat); // Compute matrix determinant -float MatrixTrace(Matrix mat); // Returns the trace of the matrix (sum of the values along the diagonal) -void MatrixTranspose(Matrix *mat); // Transposes provided matrix -void MatrixInvert(Matrix *mat); // Invert provided matrix -void MatrixNormalize(Matrix *mat); // Normalize provided matrix -Matrix MatrixIdentity(void); // Returns identity matrix -Matrix MatrixAdd(Matrix left, Matrix right); // Add two matrices -Matrix MatrixSubstract(Matrix left, Matrix right); // Substract two matrices (left - right) -Matrix MatrixTranslate(float x, float y, float z); // Returns translation matrix -Matrix MatrixRotate(float angle, Vector3 axis); // Returns rotation matrix for an angle around an specified axis (angle in radians) -Matrix MatrixRotateX(float angle); // Returns x-rotation matrix (angle in radians) -Matrix MatrixRotateY(float angle); // Returns y-rotation matrix (angle in radians) -Matrix MatrixRotateZ(float angle); // Returns z-rotation matrix (angle in radians) -Matrix MatrixScale(float x, float y, float z); // Returns scaling matrix -Matrix MatrixMultiply(Matrix left, Matrix right); // Returns two matrix multiplication -Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far); // Returns perspective projection matrix -Matrix MatrixPerspective(double fovy, double aspect, double near, double far); // Returns perspective projection matrix -Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far); // Returns orthographic projection matrix -Matrix MatrixLookAt(Vector3 position, Vector3 target, Vector3 up); // Returns camera look-at matrix (view matrix) -void PrintMatrix(Matrix m); // Print matrix utility +RMDEF float MatrixDeterminant(Matrix mat); // Compute matrix determinant +RMDEF float MatrixTrace(Matrix mat); // Returns the trace of the matrix (sum of the values along the diagonal) +RMDEF void MatrixTranspose(Matrix *mat); // Transposes provided matrix +RMDEF void MatrixInvert(Matrix *mat); // Invert provided matrix +RMDEF void MatrixNormalize(Matrix *mat); // Normalize provided matrix +RMDEF Matrix MatrixIdentity(void); // Returns identity matrix +RMDEF Matrix MatrixAdd(Matrix left, Matrix right); // Add two matrices +RMDEF Matrix MatrixSubstract(Matrix left, Matrix right); // Substract two matrices (left - right) +RMDEF Matrix MatrixTranslate(float x, float y, float z); // Returns translation matrix +RMDEF Matrix MatrixRotate(Vector3 axis, float angle); // Returns rotation matrix for an angle around an specified axis (angle in radians) +RMDEF Matrix MatrixRotateX(float angle); // Returns x-rotation matrix (angle in radians) +RMDEF Matrix MatrixRotateY(float angle); // Returns y-rotation matrix (angle in radians) +RMDEF Matrix MatrixRotateZ(float angle); // Returns z-rotation matrix (angle in radians) +RMDEF Matrix MatrixScale(float x, float y, float z); // Returns scaling matrix +RMDEF Matrix MatrixMultiply(Matrix left, Matrix right); // Returns two matrix multiplication +RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far); // Returns perspective projection matrix +RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far); // Returns perspective projection matrix +RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far); // Returns orthographic projection matrix +RMDEF Matrix MatrixLookAt(Vector3 position, Vector3 target, Vector3 up); // Returns camera look-at matrix (view matrix) +RMDEF void PrintMatrix(Matrix m); // Print matrix utility //------------------------------------------------------------------------------------ // Functions Declaration to work with Quaternions //------------------------------------------------------------------------------------ -float QuaternionLength(Quaternion quat); // Compute the length of a quaternion -void QuaternionNormalize(Quaternion *q); // Normalize provided quaternion -Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); // Calculate two quaternion multiplication -Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float slerp); // Calculates spherical linear interpolation between two quaternions -Quaternion QuaternionFromMatrix(Matrix matrix); // Returns a quaternion for a given rotation matrix -Matrix QuaternionToMatrix(Quaternion q); // Returns a matrix for a given quaternion -Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis); // Returns rotation quaternion for an angle and axis -void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis); // Returns the rotation angle and axis for a given quaternion -void QuaternionTransform(Quaternion *q, Matrix mat); // Transform a quaternion given a transformation matrix +RMDEF float QuaternionLength(Quaternion quat); // Compute the length of a quaternion +RMDEF void QuaternionNormalize(Quaternion *q); // Normalize provided quaternion +RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2); // Calculate two quaternion multiplication +RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float slerp); // Calculates spherical linear interpolation between two quaternions +RMDEF Quaternion QuaternionFromMatrix(Matrix matrix); // Returns a quaternion for a given rotation matrix +RMDEF Matrix QuaternionToMatrix(Quaternion q); // Returns a matrix for a given quaternion +RMDEF Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle); // Returns rotation quaternion for an angle and axis +RMDEF void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle); // Returns the rotation angle and axis for a given quaternion +RMDEF void QuaternionTransform(Quaternion *q, Matrix mat); // Transform a quaternion given a transformation matrix #ifdef __cplusplus } #endif -#endif // RAYMATH_H
\ No newline at end of file +#endif // notdef RAYMATH_EXTERN_INLINE + +#endif // RAYMATH_H +//////////////////////////////////////////////////////////////////// end of header file + +#if defined(RAYMATH_IMPLEMENTATION) || defined(RAYMATH_EXTERN_INLINE) + +#include <stdio.h> // Used only on PrintMatrix() +#include <math.h> // Standard math libary: sin(), cos(), tan()... +#include <stdlib.h> // Used for abs() + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Vector3 math +//---------------------------------------------------------------------------------- + +// Add two vectors +RMDEF Vector3 VectorAdd(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.x + v2.x; + result.y = v1.y + v2.y; + result.z = v1.z + v2.z; + + return result; +} + +// Substract two vectors +RMDEF Vector3 VectorSubtract(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.x - v2.x; + result.y = v1.y - v2.y; + result.z = v1.z - v2.z; + + return result; +} + +// Calculate two vectors cross product +RMDEF Vector3 VectorCrossProduct(Vector3 v1, Vector3 v2) +{ + Vector3 result; + + result.x = v1.y*v2.z - v1.z*v2.y; + result.y = v1.z*v2.x - v1.x*v2.z; + result.z = v1.x*v2.y - v1.y*v2.x; + + return result; +} + +// Calculate one vector perpendicular vector +RMDEF Vector3 VectorPerpendicular(Vector3 v) +{ + Vector3 result; + + float min = fabs(v.x); + Vector3 cardinalAxis = {1.0f, 0.0f, 0.0f}; + + if (fabs(v.y) < min) + { + min = fabs(v.y); + cardinalAxis = (Vector3){0.0f, 1.0f, 0.0f}; + } + + if(fabs(v.z) < min) + { + cardinalAxis = (Vector3){0.0f, 0.0f, 1.0f}; + } + + result = VectorCrossProduct(v, cardinalAxis); + + return result; +} + +// Calculate two vectors dot product +RMDEF float VectorDotProduct(Vector3 v1, Vector3 v2) +{ + float result; + + result = v1.x*v2.x + v1.y*v2.y + v1.z*v2.z; + + return result; +} + +// Calculate vector lenght +RMDEF float VectorLength(const Vector3 v) +{ + float length; + + length = sqrt(v.x*v.x + v.y*v.y + v.z*v.z); + + return length; +} + +// Scale provided vector +RMDEF void VectorScale(Vector3 *v, float scale) +{ + v->x *= scale; + v->y *= scale; + v->z *= scale; +} + +// Negate provided vector (invert direction) +RMDEF void VectorNegate(Vector3 *v) +{ + v->x = -v->x; + v->y = -v->y; + v->z = -v->z; +} + +// Normalize provided vector +RMDEF void VectorNormalize(Vector3 *v) +{ + float length, ilength; + + length = VectorLength(*v); + + if (length == 0) length = 1.0f; + + ilength = 1.0f/length; + + v->x *= ilength; + v->y *= ilength; + v->z *= ilength; +} + +// Calculate distance between two points +RMDEF float VectorDistance(Vector3 v1, Vector3 v2) +{ + float result; + + float dx = v2.x - v1.x; + float dy = v2.y - v1.y; + float dz = v2.z - v1.z; + + result = sqrt(dx*dx + dy*dy + dz*dz); + + return result; +} + +// Calculate linear interpolation between two vectors +RMDEF Vector3 VectorLerp(Vector3 v1, Vector3 v2, float amount) +{ + Vector3 result; + + 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 VectorReflect(Vector3 vector, Vector3 normal) +{ + // I is the original vector + // N is the normal of the incident plane + // R = I - (2*N*( DotProduct[ I,N] )) + + Vector3 result; + + float dotProduct = VectorDotProduct(vector, normal); + + result.x = vector.x - (2.0f*normal.x)*dotProduct; + result.y = vector.y - (2.0f*normal.y)*dotProduct; + result.z = vector.z - (2.0f*normal.z)*dotProduct; + + return result; +} + +// Transforms a Vector3 with a given Matrix +RMDEF void VectorTransform(Vector3 *v, Matrix mat) +{ + float x = v->x; + float y = v->y; + float z = v->z; + + //MatrixTranspose(&mat); + + v->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12; + v->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13; + v->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14; +}; + +// Return a Vector3 init to zero +RMDEF Vector3 VectorZero(void) +{ + Vector3 zero = { 0.0f, 0.0f, 0.0f }; + + return zero; +} + +// Return min value for each pair of components +RMDEF Vector3 VectorMin(Vector3 vec1, Vector3 vec2) +{ + Vector3 result; + + result.x = fminf(vec1.x, vec2.x); + result.y = fminf(vec1.y, vec2.y); + result.z = fminf(vec1.z, vec2.z); + + return result; +} + +// Return max value for each pair of components +RMDEF Vector3 VectorMax(Vector3 vec1, Vector3 vec2) +{ + Vector3 result; + + result.x = fmaxf(vec1.x, vec2.x); + result.y = fmaxf(vec1.y, vec2.y); + result.z = fmaxf(vec1.z, vec2.z); + + return result; +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Matrix math +//---------------------------------------------------------------------------------- + +// Compute matrix determinant +RMDEF float MatrixDeterminant(Matrix mat) +{ + float result; + + // 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; +} + +// Returns the trace of the matrix (sum of the values along the diagonal) +RMDEF float MatrixTrace(Matrix mat) +{ + return (mat.m0 + mat.m5 + mat.m10 + mat.m15); +} + +// Transposes provided matrix +RMDEF void MatrixTranspose(Matrix *mat) +{ + Matrix temp; + + temp.m0 = mat->m0; + temp.m1 = mat->m4; + temp.m2 = mat->m8; + temp.m3 = mat->m12; + temp.m4 = mat->m1; + temp.m5 = mat->m5; + temp.m6 = mat->m9; + temp.m7 = mat->m13; + temp.m8 = mat->m2; + temp.m9 = mat->m6; + temp.m10 = mat->m10; + temp.m11 = mat->m14; + temp.m12 = mat->m3; + temp.m13 = mat->m7; + temp.m14 = mat->m11; + temp.m15 = mat->m15; + + *mat = temp; +} + +// Invert provided matrix +RMDEF void MatrixInvert(Matrix *mat) +{ + Matrix temp; + + // 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); + + temp.m0 = (a11*b11 - a12*b10 + a13*b09)*invDet; + temp.m1 = (-a01*b11 + a02*b10 - a03*b09)*invDet; + temp.m2 = (a31*b05 - a32*b04 + a33*b03)*invDet; + temp.m3 = (-a21*b05 + a22*b04 - a23*b03)*invDet; + temp.m4 = (-a10*b11 + a12*b08 - a13*b07)*invDet; + temp.m5 = (a00*b11 - a02*b08 + a03*b07)*invDet; + temp.m6 = (-a30*b05 + a32*b02 - a33*b01)*invDet; + temp.m7 = (a20*b05 - a22*b02 + a23*b01)*invDet; + temp.m8 = (a10*b10 - a11*b08 + a13*b06)*invDet; + temp.m9 = (-a00*b10 + a01*b08 - a03*b06)*invDet; + temp.m10 = (a30*b04 - a31*b02 + a33*b00)*invDet; + temp.m11 = (-a20*b04 + a21*b02 - a23*b00)*invDet; + temp.m12 = (-a10*b09 + a11*b07 - a12*b06)*invDet; + temp.m13 = (a00*b09 - a01*b07 + a02*b06)*invDet; + temp.m14 = (-a30*b03 + a31*b01 - a32*b00)*invDet; + temp.m15 = (a20*b03 - a21*b01 + a22*b00)*invDet; + + *mat = temp; +} + +// Normalize provided matrix +RMDEF void MatrixNormalize(Matrix *mat) +{ + float det = MatrixDeterminant(*mat); + + mat->m0 /= det; + mat->m1 /= det; + mat->m2 /= det; + mat->m3 /= det; + mat->m4 /= det; + mat->m5 /= det; + mat->m6 /= det; + mat->m7 /= det; + mat->m8 /= det; + mat->m9 /= det; + mat->m10 /= det; + mat->m11 /= det; + mat->m12 /= det; + mat->m13 /= det; + mat->m14 /= det; + mat->m15 /= det; +} + +// 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; +} + +// Substract two matrices (left - right) +RMDEF Matrix MatrixSubstract(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, 0.0f, + 0.0f, 1.0f, 0.0f, 0.0f, + 0.0f, 0.0f, 1.0f, 0.0f, + x, y, z, 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; + + Matrix mat = MatrixIdentity(); + + float x = axis.x, y = axis.y, z = axis.z; + + float length = sqrt(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; + + // Cache some 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; + + // Construct the elements of the rotation matrix + float b00 = x*x*t + cosres, b01 = y*x*t + z*sinres, b02 = z*x*t - y*sinres; + float b10 = x*y*t - z*sinres, b11 = y*y*t + cosres, b12 = z*y*t + x*sinres; + float b20 = x*z*t + y*sinres, b21 = y*z*t - x*sinres, b22 = z*z*t + cosres; + + // Perform rotation-specific matrix multiplication + result.m0 = a00*b00 + a10*b01 + a20*b02; + result.m1 = a01*b00 + a11*b01 + a21*b02; + result.m2 = a02*b00 + a12*b01 + a22*b02; + result.m3 = a03*b00 + a13*b01 + a23*b02; + result.m4 = a00*b10 + a10*b11 + a20*b12; + result.m5 = a01*b10 + a11*b11 + a21*b12; + result.m6 = a02*b10 + a12*b11 + a22*b12; + result.m7 = a03*b10 + a13*b11 + a23*b12; + result.m8 = a00*b20 + a10*b21 + a20*b22; + result.m9 = a01*b20 + a11*b21 + a21*b22; + result.m10 = a02*b20 + a12*b21 + a22*b22; + result.m11 = a03*b20 + a13*b21 + a23*b22; + result.m12 = mat.m12; + result.m13 = mat.m13; + result.m14 = mat.m14; + result.m15 = mat.m15; + + return result; +} + +/* +// Another implementation for MatrixRotate... +RMDEF Matrix MatrixRotate(float angle, float x, float y, float z) +{ + Matrix result = MatrixIdentity(); + + float c = cosf(angle); // cosine + float s = sinf(angle); // sine + float c1 = 1.0f - c; // 1 - c + + float m0 = result.m0, m4 = result.m4, m8 = result.m8, m12 = result.m12, + m1 = result.m1, m5 = result.m5, m9 = result.m9, m13 = result.m13, + m2 = result.m2, m6 = result.m6, m10 = result.m10, m14 = result.m14; + + // build rotation matrix + float r0 = x*x*c1 + c; + float r1 = x*y*c1 + z*s; + float r2 = x*z*c1 - y*s; + float r4 = x*y*c1 - z*s; + float r5 = y*y*c1 + c; + float r6 = y*z*c1 + x*s; + float r8 = x*z*c1 + y*s; + float r9 = y*z*c1 - x*s; + float r10= z*z*c1 + c; + + // multiply rotation matrix + result.m0 = r0*m0 + r4*m1 + r8*m2; + result.m1 = r1*m0 + r5*m1 + r9*m2; + result.m2 = r2*m0 + r6*m1 + r10*m2; + result.m4 = r0*m4 + r4*m5 + r8*m6; + result.m5 = r1*m4 + r5*m5 + r9*m6; + result.m6 = r2*m4 + r6*m5 + r10*m6; + result.m8 = r0*m8 + r4*m9 + r8*m10; + result.m9 = r1*m8 + r5*m9 + r9*m10; + result.m10 = r2*m8 + r6*m9 + r10*m10; + result.m12 = r0*m12+ r4*m13 + r8*m14; + result.m13 = r1*m12+ r5*m13 + r9*m14; + result.m14 = r2*m12+ r6*m13 + r10*m14; + + 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; + + result.m0 = right.m0*left.m0 + right.m1*left.m4 + right.m2*left.m8 + right.m3*left.m12; + result.m1 = right.m0*left.m1 + right.m1*left.m5 + right.m2*left.m9 + right.m3*left.m13; + result.m2 = right.m0*left.m2 + right.m1*left.m6 + right.m2*left.m10 + right.m3*left.m14; + result.m3 = right.m0*left.m3 + right.m1*left.m7 + right.m2*left.m11 + right.m3*left.m15; + result.m4 = right.m4*left.m0 + right.m5*left.m4 + right.m6*left.m8 + right.m7*left.m12; + result.m5 = right.m4*left.m1 + right.m5*left.m5 + right.m6*left.m9 + right.m7*left.m13; + result.m6 = right.m4*left.m2 + right.m5*left.m6 + right.m6*left.m10 + right.m7*left.m14; + result.m7 = right.m4*left.m3 + right.m5*left.m7 + right.m6*left.m11 + right.m7*left.m15; + result.m8 = right.m8*left.m0 + right.m9*left.m4 + right.m10*left.m8 + right.m11*left.m12; + result.m9 = right.m8*left.m1 + right.m9*left.m5 + right.m10*left.m9 + right.m11*left.m13; + result.m10 = right.m8*left.m2 + right.m9*left.m6 + right.m10*left.m10 + right.m11*left.m14; + result.m11 = right.m8*left.m3 + right.m9*left.m7 + right.m10*left.m11 + right.m11*left.m15; + result.m12 = right.m12*left.m0 + right.m13*left.m4 + right.m14*left.m8 + right.m15*left.m12; + result.m13 = right.m12*left.m1 + right.m13*left.m5 + right.m14*left.m9 + right.m15*left.m13; + result.m14 = right.m12*left.m2 + right.m13*left.m6 + right.m14*left.m10 + right.m15*left.m14; + result.m15 = right.m12*left.m3 + right.m13*left.m7 + right.m14*left.m11 + right.m15*left.m15; + + return result; +} + +// Returns perspective projection matrix +RMDEF Matrix MatrixFrustum(double left, double right, double bottom, double top, double near, double far) +{ + Matrix result; + + float rl = (right - left); + float tb = (top - bottom); + float fn = (far - near); + + result.m0 = (near*2.0f)/rl; + result.m1 = 0.0f; + result.m2 = 0.0f; + result.m3 = 0.0f; + + result.m4 = 0.0f; + result.m5 = (near*2.0f)/tb; + result.m6 = 0.0f; + result.m7 = 0.0f; + + result.m8 = (right + left)/rl; + result.m9 = (top + bottom)/tb; + result.m10 = -(far + near)/fn; + result.m11 = -1.0f; + + result.m12 = 0.0f; + result.m13 = 0.0f; + result.m14 = -(far*near*2.0f)/fn; + result.m15 = 0.0f; + + return result; +} + +// Returns perspective projection matrix +RMDEF Matrix MatrixPerspective(double fovy, double aspect, double near, double far) +{ + double top = near*tanf(fovy*PI/360.0f); + double right = top*aspect; + + return MatrixFrustum(-right, right, -top, top, near, far); +} + +// Returns orthographic projection matrix +RMDEF Matrix MatrixOrtho(double left, double right, double bottom, double top, double near, double far) +{ + Matrix result; + + float rl = (right - left); + float tb = (top - bottom); + float fn = (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 = -(left + right)/rl; + result.m13 = -(top + bottom)/tb; + result.m14 = -(far + 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; + + Vector3 z = VectorSubtract(eye, target); + VectorNormalize(&z); + Vector3 x = VectorCrossProduct(up, z); + VectorNormalize(&x); + Vector3 y = VectorCrossProduct(z, x); + VectorNormalize(&y); + + result.m0 = x.x; + result.m1 = x.y; + result.m2 = x.z; + result.m3 = -((x.x*eye.x) + (x.y*eye.y) + (x.z*eye.z)); + result.m4 = y.x; + result.m5 = y.y; + result.m6 = y.z; + result.m7 = -((y.x*eye.x) + (y.y*eye.y) + (y.z*eye.z)); + result.m8 = z.x; + result.m9 = z.y; + result.m10 = z.z; + result.m11 = -((z.x*eye.x) + (z.y*eye.y) + (z.z*eye.z)); + result.m12 = 0.0f; + result.m13 = 0.0f; + result.m14 = 0.0f; + result.m15 = 1.0f; + + return result; +} + +// Print matrix utility (for debug) +RMDEF void PrintMatrix(Matrix m) +{ + printf("----------------------\n"); + printf("%2.2f %2.2f %2.2f %2.2f\n", m.m0, m.m4, m.m8, m.m12); + printf("%2.2f %2.2f %2.2f %2.2f\n", m.m1, m.m5, m.m9, m.m13); + printf("%2.2f %2.2f %2.2f %2.2f\n", m.m2, m.m6, m.m10, m.m14); + printf("%2.2f %2.2f %2.2f %2.2f\n", m.m3, m.m7, m.m11, m.m15); + printf("----------------------\n"); +} + +//---------------------------------------------------------------------------------- +// Module Functions Definition - Quaternion math +//---------------------------------------------------------------------------------- + +// Computes the length of a quaternion +RMDEF float QuaternionLength(Quaternion quat) +{ + return sqrt(quat.x*quat.x + quat.y*quat.y + quat.z*quat.z + quat.w*quat.w); +} + +// Normalize provided quaternion +RMDEF void QuaternionNormalize(Quaternion *q) +{ + float length, ilength; + + length = QuaternionLength(*q); + + if (length == 0.0f) length = 1.0f; + + ilength = 1.0f/length; + + q->x *= ilength; + q->y *= ilength; + q->z *= ilength; + q->w *= ilength; +} + +// Calculate two quaternion multiplication +RMDEF Quaternion QuaternionMultiply(Quaternion q1, Quaternion q2) +{ + Quaternion result; + + 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; +} + +// Calculates spherical linear interpolation between two quaternions +RMDEF Quaternion QuaternionSlerp(Quaternion q1, Quaternion q2, float amount) +{ + Quaternion result; + + 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 + { + float halfTheta = acos(cosHalfTheta); + float sinHalfTheta = sqrt(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; +} + +// Returns a quaternion for a given rotation matrix +RMDEF Quaternion QuaternionFromMatrix(Matrix matrix) +{ + Quaternion result; + + float trace = MatrixTrace(matrix); + + if (trace > 0.0f) + { + float s = (float)sqrt(trace + 1)*2.0f; + float invS = 1.0f/s; + + result.w = s*0.25f; + result.x = (matrix.m6 - matrix.m9)*invS; + result.y = (matrix.m8 - matrix.m2)*invS; + result.z = (matrix.m1 - matrix.m4)*invS; + } + else + { + float m00 = matrix.m0, m11 = matrix.m5, m22 = matrix.m10; + + if (m00 > m11 && m00 > m22) + { + float s = (float)sqrt(1.0f + m00 - m11 - m22)*2.0f; + float invS = 1.0f/s; + + result.w = (matrix.m6 - matrix.m9)*invS; + result.x = s*0.25f; + result.y = (matrix.m4 + matrix.m1)*invS; + result.z = (matrix.m8 + matrix.m2)*invS; + } + else if (m11 > m22) + { + float s = (float)sqrt(1.0f + m11 - m00 - m22)*2.0f; + float invS = 1.0f/s; + + result.w = (matrix.m8 - matrix.m2)*invS; + result.x = (matrix.m4 + matrix.m1)*invS; + result.y = s*0.25f; + result.z = (matrix.m9 + matrix.m6)*invS; + } + else + { + float s = (float)sqrt(1.0f + m22 - m00 - m11)*2.0f; + float invS = 1.0f/s; + + result.w = (matrix.m1 - matrix.m4)*invS; + result.x = (matrix.m8 + matrix.m2)*invS; + result.y = (matrix.m9 + matrix.m6)*invS; + result.z = s*0.25f; + } + } + + return result; +} + +// Returns a matrix for a given quaternion +RMDEF Matrix QuaternionToMatrix(Quaternion q) +{ + Matrix result; + + 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 xx = x*x2; + float xy = x*y2; + float xz = x*z2; + + float yy = y*y2; + float yz = y*z2; + float zz = z*z2; + + float wx = w*x2; + float wy = w*y2; + float wz = w*z2; + + 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 (VectorLength(axis) != 0.0f) + + angle *= 0.5f; + + VectorNormalize(&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; + + 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) QuaternionNormalize(&q); + + Vector3 resAxis = { 0.0f, 0.0f, 0.0f }; + float resAngle = 0.0f; + + resAngle = 2.0f*(float)acos(q.w); + float den = (float)sqrt(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; +} + +// Transform a quaternion given a transformation matrix +RMDEF void QuaternionTransform(Quaternion *q, Matrix mat) +{ + float x = q->x; + float y = q->y; + float z = q->z; + float w = q->w; + + q->x = mat.m0*x + mat.m4*y + mat.m8*z + mat.m12*w; + q->y = mat.m1*x + mat.m5*y + mat.m9*z + mat.m13*w; + q->z = mat.m2*x + mat.m6*y + mat.m10*z + mat.m14*w; + q->w = mat.m3*x + mat.m7*y + mat.m11*z + mat.m15*w; +} + +#endif // RAYMATH_IMPLEMENTATION |