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authorRay <raysan5@gmail.com>2016-01-20 15:47:48 +0100
committerRay <raysan5@gmail.com>2016-01-20 15:47:48 +0100
commitc8e8c0a0024a2301bbcc940233cbc4e82116242c (patch)
treebf9bd71745bb9430e1e89a521043b69713f07953 /src
parent29c618a35e19c1c00be94bf423ad6af7ecf1d3f8 (diff)
parentae87a35f6eca258547c5be9d65f8d8ba3103c9c7 (diff)
downloadraylib-c8e8c0a0024a2301bbcc940233cbc4e82116242c.tar.gz
raylib-c8e8c0a0024a2301bbcc940233cbc4e82116242c.zip
Merge pull request #76 from kd7tck/develop
standalone raymath
Diffstat (limited to 'src')
-rw-r--r--src/raymath.c988
-rw-r--r--src/raymath.h1050
2 files changed, 986 insertions, 1052 deletions
diff --git a/src/raymath.c b/src/raymath.c
deleted file mode 100644
index 5feef59d..00000000
--- a/src/raymath.c
+++ /dev/null
@@ -1,988 +0,0 @@
-/**********************************************************************************************
-*
-* raymath
-*
-* Some useful functions to work with Vector3, Matrix and Quaternions
-*
-* Copyright (c) 2015 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.
-*
-**********************************************************************************************/
-
-#include "raymath.h"
-
-#include <stdio.h> // Used only on PrintMatrix()
-#include <math.h> // Standard math libary: sin(), cos(), tan()...
-#include <stdlib.h> // Used for abs()
-
-//----------------------------------------------------------------------------------
-// Defines and Macros
-//----------------------------------------------------------------------------------
-//...
-
-//----------------------------------------------------------------------------------
-// Module specific Functions Declaration
-//----------------------------------------------------------------------------------
-// ...
-
-//----------------------------------------------------------------------------------
-// Module Functions Definition - Vector3 math
-//----------------------------------------------------------------------------------
-
-// Converts Vector3 to float array
-float *VectorToFloat(Vector3 vec)
-{
- static float buffer[3];
-
- buffer[0] = vec.x;
- buffer[1] = vec.y;
- buffer[2] = vec.z;
-
- return buffer;
-}
-
-// Add two vectors
-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
-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
-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
-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
-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
-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
-void VectorScale(Vector3 *v, float scale)
-{
- v->x *= scale;
- v->y *= scale;
- v->z *= scale;
-}
-
-// Negate provided vector (invert direction)
-void VectorNegate(Vector3 *v)
-{
- v->x = -v->x;
- v->y = -v->y;
- v->z = -v->z;
-}
-
-// Normalize provided vector
-void VectorNormalize(Vector3 *v)
-{
- float length, ilength;
-
- length = VectorLength(*v);
-
- if (length == 0) length = 1;
-
- ilength = 1.0/length;
-
- v->x *= ilength;
- v->y *= ilength;
- v->z *= ilength;
-}
-
-// Calculate distance between two points
-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
-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
-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 - (2.0 * normal.x) * dotProduct;
- result.y = vector.y - (2.0 * normal.y) * dotProduct;
- result.z = vector.z - (2.0 * normal.z) * dotProduct;
-
- return result;
-}
-
-// Transforms a Vector3 with a given Matrix
-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
-Vector3 VectorZero(void)
-{
- Vector3 zero = { 0.0f, 0.0f, 0.0f };
-
- return zero;
-}
-
-//----------------------------------------------------------------------------------
-// Module Functions Definition - Matrix math
-//----------------------------------------------------------------------------------
-
-// Converts Matrix to float array
-// NOTE: Returned vector is a transposed version of the Matrix struct,
-// it should be this way because, despite raymath use OpenGL column-major convention,
-// Matrix struct memory alignment and variables naming are not coherent
-float *MatrixToFloat(Matrix mat)
-{
- static float buffer[16];
-
- buffer[0] = mat.m0;
- buffer[1] = mat.m4;
- buffer[2] = mat.m8;
- buffer[3] = mat.m12;
- buffer[4] = mat.m1;
- buffer[5] = mat.m5;
- buffer[6] = mat.m9;
- buffer[7] = mat.m13;
- buffer[8] = mat.m2;
- buffer[9] = mat.m6;
- buffer[10] = mat.m10;
- buffer[11] = mat.m14;
- buffer[12] = mat.m3;
- buffer[13] = mat.m7;
- buffer[14] = mat.m11;
- buffer[15] = mat.m15;
-
- return buffer;
-}
-
-// Compute matrix determinant
-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)
-float MatrixTrace(Matrix mat)
-{
- return (mat.m0 + mat.m5 + mat.m10 + mat.m15);
-}
-
-// Transposes provided matrix
-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
-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/(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
-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
-Matrix MatrixIdentity(void)
-{
- Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
-
- return result;
-}
-
-// Add two matrices
-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)
-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
-Matrix MatrixTranslate(float x, float y, float z)
-{
- Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 };
-
- return result;
-}
-
-// Create rotation matrix from axis and angle
-// NOTE: Angle should be provided in radians
-Matrix MatrixRotate(float angle, Vector3 axis)
-{
- 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) && (length != 0))
- {
- length = 1/length;
- x *= length;
- y *= length;
- z *= length;
- }
-
- float s = sinf(angle);
- float c = cosf(angle);
- float t = 1.0f - c;
-
- // 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 + c, b01 = y*x*t + z*s, b02 = z*x*t - y*s;
- float b10 = x*y*t - z*s, b11 = y*y*t + c, b12 = z*y*t + x*s;
- float b20 = x*z*t + y*s, b21 = y*z*t - x*s, b22 = z*z*t + c;
-
- // 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...
-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)
-Matrix MatrixRotateX(float angle)
-{
- Matrix result = MatrixIdentity();
-
- float cosres = (float)cos(angle);
- float sinres = (float)sin(angle);
-
- result.m5 = cosres;
- result.m6 = -sinres;
- result.m9 = sinres;
- result.m10 = cosres;
-
- return result;
-}
-
-// Returns y-rotation matrix (angle in radians)
-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)
-Matrix MatrixRotateZ(float angle)
-{
- Matrix result = MatrixIdentity();
-
- float cosres = (float)cos(angle);
- float sinres = (float)sin(angle);
-
- result.m0 = cosres;
- result.m1 = -sinres;
- result.m4 = sinres;
- result.m5 = cosres;
-
- return result;
-}
-
-// Returns scaling matrix
-Matrix MatrixScale(float x, float y, float z)
-{
- Matrix result = { x, 0, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 };
-
- return result;
-}
-
-// Returns two matrix multiplication
-// NOTE: When multiplying matrices... the order matters!
-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
-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;
- result.m2 = 0;
- result.m3 = 0;
-
- result.m4 = 0;
- result.m5 = (near*2.0f) / tb;
- result.m6 = 0;
- result.m7 = 0;
-
- result.m8 = (right + left) / rl;
- result.m9 = (top + bottom) / tb;
- result.m10 = -(far + near) / fn;
- result.m11 = -1.0f;
-
- result.m12 = 0;
- result.m13 = 0;
- result.m14 = -(far*near*2.0f) / fn;
- result.m15 = 0;
-
- return result;
-}
-
-// Returns perspective projection matrix
-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
-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 / rl;
- result.m1 = 0;
- result.m2 = 0;
- result.m3 = 0;
- result.m4 = 0;
- result.m5 = 2 / tb;
- result.m6 = 0;
- result.m7 = 0;
- result.m8 = 0;
- result.m9 = 0;
- result.m10 = -2 / fn;
- result.m11 = 0;
- result.m12 = -(left + right) / rl;
- result.m13 = -(top + bottom) / tb;
- result.m14 = -(far + near) / fn;
- result.m15 = 1;
-
- return result;
-}
-
-// Returns camera look-at matrix (view matrix)
-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;
- result.m13 = 0;
- result.m14 = 0;
- result.m15 = 1;
-
- return result;
-}
-
-// Print matrix utility (for debug)
-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
-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
-void QuaternionNormalize(Quaternion *q)
-{
- float length, ilength;
-
- length = QuaternionLength(*q);
-
- if (length == 0) length = 1;
-
- ilength = 1.0/length;
-
- q->x *= ilength;
- q->y *= ilength;
- q->z *= ilength;
- q->w *= ilength;
-}
-
-// Calculate two quaternion multiplication
-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
-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 = sin((1 - amount)*halfTheta) / sinHalfTheta;
- float ratioB = sin(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
-Quaternion QuaternionFromMatrix(Matrix matrix)
-{
- Quaternion result;
-
- float trace = MatrixTrace(matrix);
-
- if (trace > 0)
- {
- float s = (float)sqrt(trace + 1) * 2;
- float invS = 1 / s;
-
- result.w = s * 0.25;
- 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 + m00 - m11 - m22) * 2;
- float invS = 1 / s;
-
- result.w = (matrix.m6 - matrix.m9) * invS;
- result.x = s * 0.25;
- result.y = (matrix.m4 + matrix.m1) * invS;
- result.z = (matrix.m8 + matrix.m2) * invS;
- }
- else if (m11 > m22)
- {
- float s = (float)sqrt(1 + m11 - m00 - m22) * 2;
- float invS = 1 / s;
-
- result.w = (matrix.m8 - matrix.m2) * invS;
- result.x = (matrix.m4 + matrix.m1) * invS;
- result.y = s * 0.25;
- result.z = (matrix.m9 + matrix.m6) * invS;
- }
- else
- {
- float s = (float)sqrt(1 + m22 - m00 - m11) * 2;
- float invS = 1 / 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 * 0.25;
- }
- }
-
- return result;
-}
-
-// Returns a matrix for a given quaternion
-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 - (yy + zz);
- result.m1 = xy - wz;
- result.m2 = xz + wy;
- result.m3 = 0;
- result.m4 = xy + wz;
- result.m5 = 1 - (xx + zz);
- result.m6 = yz - wx;
- result.m7 = 0;
- result.m8 = xz - wy;
- result.m9 = yz + wx;
- result.m10 = 1 - (xx + yy);
- result.m11 = 0;
- result.m12 = 0;
- result.m13 = 0;
- result.m14 = 0;
- result.m15 = 1;
-
- return result;
-}
-
-// Returns rotation quaternion for an angle and axis
-// NOTE: angle must be provided in radians
-Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis)
-{
- Quaternion result = { 0, 0, 0, 1 };
-
- if (VectorLength(axis) != 0.0)
-
- angle *= 0.5;
-
- VectorNormalize(&axis);
-
- result.x = axis.x * (float)sin(angle);
- result.y = axis.y * (float)sin(angle);
- result.z = axis.z * (float)sin(angle);
- result.w = (float)cos(angle);
-
- QuaternionNormalize(&result);
-
- return result;
-}
-
-// Returns the rotation angle and axis for a given quaternion
-void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis)
-{
- if (fabs(q.w) > 1.0f) QuaternionNormalize(&q);
-
- Vector3 resAxis = { 0, 0, 0 };
- float resAngle = 0;
-
- resAngle = 2.0f * (float)acos(q.w);
- float den = (float)sqrt(1.0 - 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 = 1.0;
- }
-
- *outAxis = resAxis;
- *outAngle = resAngle;
-}
-
-// Transform a quaternion given a transformation matrix
-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;
-} \ No newline at end of file
diff --git a/src/raymath.h b/src/raymath.h
index 507bf52f..f5912795 100644
--- a/src/raymath.h
+++ b/src/raymath.h
@@ -22,6 +22,29 @@
* 3. This notice may not be removed or altered from any source distribution.
*
**********************************************************************************************/
+//============================================================================
+// YOU MUST
+//
+// #define RAYMATH_DEFINE
+//
+// Like:
+//
+// #define RAYMATH_DEFINE
+// #include "raymath.h"
+//
+// YOU CAN:
+// #define RAYMATH_INLINE //inlines all code, so it runs faster. This requires lots of memory on system.
+// AND
+// #define RAYMATH_STANDALONE //not dependent on outside libs
+//
+// This needs to be done for every library/source file.
+//============================================================================
+
+#ifdef RAYMATH_INLINE
+ #define RMDEF static inline
+#else
+ #define RMDEF static
+#endif
#ifndef RAYMATH_H
#define RAYMATH_H
@@ -39,14 +62,25 @@
#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
+ // Vector2 type
+ typedef struct Vector2 {
+ float x;
+ float y;
+ } Vector2;
+
// Vector3 type
typedef struct Vector3 {
float x;
@@ -71,70 +105,958 @@ typedef struct Quaternion {
float w;
} Quaternion;
+#ifdef RAYMATH_DEFINE
+#include <stdio.h> // Used only on PrintMatrix()
+#include <math.h> // Standard math libary: sin(), cos(), tan()...
+#include <stdlib.h> // Used for abs()
-#ifdef __cplusplus
-extern "C" { // Prevents name mangling of functions
-#endif
+//----------------------------------------------------------------------------------
+// Module Functions Definition - Vector3 math
+//----------------------------------------------------------------------------------
+
+// Converts Vector3 to float array
+RMDEF float *VectorToFloat(Vector3 vec)
+{
+ static float buffer[3];
-//------------------------------------------------------------------------------------
-// Functions Declaration to work with Vector3
-//------------------------------------------------------------------------------------
-float *VectorToFloat(Vector3 vec); // Converts Vector3 to float array
-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
-
-//------------------------------------------------------------------------------------
-// Functions Declaration to work with Matrix
-//------------------------------------------------------------------------------------
-float *MatrixToFloat(Matrix mat); // Converts Matrix to float array
-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
-
-//------------------------------------------------------------------------------------
-// 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
-
-#ifdef __cplusplus
+ buffer[0] = vec.x;
+ buffer[1] = vec.y;
+ buffer[2] = vec.z;
+
+ return buffer;
+}
+
+// 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;
+
+ ilength = 1.0/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 - (2.0 * normal.x) * dotProduct;
+ result.y = vector.y - (2.0 * normal.y) * dotProduct;
+ result.z = vector.z - (2.0 * 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;
+}
+
+//----------------------------------------------------------------------------------
+// Module Functions Definition - Matrix math
+//----------------------------------------------------------------------------------
+
+// Converts Matrix to float array
+// NOTE: Returned vector is a transposed version of the Matrix struct,
+// it should be this way because, despite raymath use OpenGL column-major convention,
+// Matrix struct memory alignment and variables naming are not coherent
+RMDEF float *MatrixToFloat(Matrix mat)
+{
+ static float buffer[16];
+
+ buffer[0] = mat.m0;
+ buffer[1] = mat.m4;
+ buffer[2] = mat.m8;
+ buffer[3] = mat.m12;
+ buffer[4] = mat.m1;
+ buffer[5] = mat.m5;
+ buffer[6] = mat.m9;
+ buffer[7] = mat.m13;
+ buffer[8] = mat.m2;
+ buffer[9] = mat.m6;
+ buffer[10] = mat.m10;
+ buffer[11] = mat.m14;
+ buffer[12] = mat.m3;
+ buffer[13] = mat.m7;
+ buffer[14] = mat.m11;
+ buffer[15] = mat.m15;
+
+ return buffer;
+}
+
+// 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/(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, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1 };
+
+ 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, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 };
+
+ return result;
+}
+
+// Create rotation matrix from axis and angle
+// NOTE: Angle should be provided in radians
+RMDEF Matrix MatrixRotate(float angle, Vector3 axis)
+{
+ 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) && (length != 0))
+ {
+ length = 1/length;
+ x *= length;
+ y *= length;
+ z *= length;
+ }
+
+ float s = sinf(angle);
+ float c = cosf(angle);
+ float t = 1.0f - c;
+
+ // 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 + c, b01 = y*x*t + z*s, b02 = z*x*t - y*s;
+ float b10 = x*y*t - z*s, b11 = y*y*t + c, b12 = z*y*t + x*s;
+ float b20 = x*z*t + y*s, b21 = y*z*t - x*s, b22 = z*z*t + c;
+
+ // 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 = (float)cos(angle);
+ float sinres = (float)sin(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 = (float)cos(angle);
+ float sinres = (float)sin(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, 0, 0, 0, y, 0, 0, 0, 0, z, 0, 0, 0, 0, 1 };
+
+ 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;
+ result.m2 = 0;
+ result.m3 = 0;
+
+ result.m4 = 0;
+ result.m5 = (near*2.0f) / tb;
+ result.m6 = 0;
+ result.m7 = 0;
+
+ result.m8 = (right + left) / rl;
+ result.m9 = (top + bottom) / tb;
+ result.m10 = -(far + near) / fn;
+ result.m11 = -1.0f;
+
+ result.m12 = 0;
+ result.m13 = 0;
+ result.m14 = -(far*near*2.0f) / fn;
+ result.m15 = 0;
+
+ 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 / rl;
+ result.m1 = 0;
+ result.m2 = 0;
+ result.m3 = 0;
+ result.m4 = 0;
+ result.m5 = 2 / tb;
+ result.m6 = 0;
+ result.m7 = 0;
+ result.m8 = 0;
+ result.m9 = 0;
+ result.m10 = -2 / fn;
+ result.m11 = 0;
+ result.m12 = -(left + right) / rl;
+ result.m13 = -(top + bottom) / tb;
+ result.m14 = -(far + near) / fn;
+ result.m15 = 1;
+
+ 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;
+ result.m13 = 0;
+ result.m14 = 0;
+ result.m15 = 1;
+
+ 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) length = 1;
+
+ ilength = 1.0/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 = sin((1 - amount)*halfTheta) / sinHalfTheta;
+ float ratioB = sin(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)
+ {
+ float s = (float)sqrt(trace + 1) * 2;
+ float invS = 1 / s;
+
+ result.w = s * 0.25;
+ 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 + m00 - m11 - m22) * 2;
+ float invS = 1 / s;
+
+ result.w = (matrix.m6 - matrix.m9) * invS;
+ result.x = s * 0.25;
+ result.y = (matrix.m4 + matrix.m1) * invS;
+ result.z = (matrix.m8 + matrix.m2) * invS;
+ }
+ else if (m11 > m22)
+ {
+ float s = (float)sqrt(1 + m11 - m00 - m22) * 2;
+ float invS = 1 / s;
+
+ result.w = (matrix.m8 - matrix.m2) * invS;
+ result.x = (matrix.m4 + matrix.m1) * invS;
+ result.y = s * 0.25;
+ result.z = (matrix.m9 + matrix.m6) * invS;
+ }
+ else
+ {
+ float s = (float)sqrt(1 + m22 - m00 - m11) * 2;
+ float invS = 1 / 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 * 0.25;
+ }
+ }
+
+ 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 - (yy + zz);
+ result.m1 = xy - wz;
+ result.m2 = xz + wy;
+ result.m3 = 0;
+ result.m4 = xy + wz;
+ result.m5 = 1 - (xx + zz);
+ result.m6 = yz - wx;
+ result.m7 = 0;
+ result.m8 = xz - wy;
+ result.m9 = yz + wx;
+ result.m10 = 1 - (xx + yy);
+ result.m11 = 0;
+ result.m12 = 0;
+ result.m13 = 0;
+ result.m14 = 0;
+ result.m15 = 1;
+
+ return result;
+}
+
+// Returns rotation quaternion for an angle and axis
+// NOTE: angle must be provided in radians
+RMDEF Quaternion QuaternionFromAxisAngle(float angle, Vector3 axis)
+{
+ Quaternion result = { 0, 0, 0, 1 };
+
+ if (VectorLength(axis) != 0.0)
+
+ angle *= 0.5;
+
+ VectorNormalize(&axis);
+
+ result.x = axis.x * (float)sin(angle);
+ result.y = axis.y * (float)sin(angle);
+ result.z = axis.z * (float)sin(angle);
+ result.w = (float)cos(angle);
+
+ QuaternionNormalize(&result);
+
+ return result;
+}
+
+// Returns the rotation angle and axis for a given quaternion
+RMDEF void QuaternionToAxisAngle(Quaternion q, float *outAngle, Vector3 *outAxis)
+{
+ if (fabs(q.w) > 1.0f) QuaternionNormalize(&q);
+
+ Vector3 resAxis = { 0, 0, 0 };
+ float resAngle = 0;
+
+ resAngle = 2.0f * (float)acos(q.w);
+ float den = (float)sqrt(1.0 - 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 = 1.0;
+ }
+
+ *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
+#endif // RAYMATH_DEFINE
#endif // RAYMATH_H \ No newline at end of file