3D useful maths

Some useful functions to work with Vector3, Matrix and Quaternions

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+/*********************************************************************************************
+*
+*   raymath
+*
+*   Some useful functions to work with Vector3, Matrix and Quaternions
+*
+*   Copyright (c) 2014 Ramon Santamaria (Ray San - raysan@raysanweb.com)
+*    
+*   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
+//----------------------------------------------------------------------------------
+
+// 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 = {1.0, 0.0, 0.0};
+ 
+    if (fabs(v.y) < min) 
+    {
+        min = fabs(v.y);
+        cardinalAxis = (Vector3){0.0, 1.0, 0.0};
+    }
+ 
+    if(fabs(v.z) < min) 
+    {
+        cardinalAxis = (Vector3){0.0, 0.0, 1.0};
+    }
+    
+    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;
+}
+
+//----------------------------------------------------------------------------------
+// Module Functions Definition - Matrix math
+//----------------------------------------------------------------------------------
+
+// Returns an OpenGL-ready vector (glMultMatrixf)
+float *GetMatrixVector(Matrix mat)
+{
+    static float vector[16];
+    
+    vector[0] = mat.m0;
+    vector[1] = mat.m4;
+    vector[2] = mat.m8;
+    vector[3] = mat.m12;
+    vector[4] = mat.m1;
+    vector[5] = mat.m5;
+    vector[6] = mat.m9;
+    vector[7] = mat.m13;
+    vector[8] = mat.m2;
+    vector[9] = mat.m6;
+    vector[10] = mat.m10;
+    vector[11] = mat.m14;
+    vector[12] = mat.m3;
+    vector[13] = mat.m7;
+    vector[14] = mat.m11;
+    vector[15] = mat.m15;
+  
+    return vector;
+}
+
+// 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);
+    
+    printf("%f\n", invDet);
+	
+	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;
+    
+    PrintMatrix(temp);
+	
+	*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()
+{
+    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
+// TODO: REVIEW
+Matrix MatrixTranslate(float x, float y, float z)
+{
+/*
+    For OpenGL
+        1, 0, 0, 0
+        0, 1, 0, 0
+        0, 0, 1, 0
+        x, y, z, 1
+    Is the correct Translation Matrix. Why? Opengl Uses column-major matrix ordering. 
+    Which is the Transpose of the Matrix you initially presented, which is in row-major ordering. 
+    Row major is used in most math text-books and also DirectX, so it is a common 
+    point of confusion for those new to OpenGL.
+    
+    * matrix notation used in opengl documentation does not describe in-memory layout for OpenGL matrices
+    
+    Translation matrix should be laid out in memory like this:
+    { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, trabsX, transY, transZ, 1 }
+    
+    
+    9.005 Are OpenGL matrices column-major or row-major?
+
+    For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out 
+    contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements 
+    of the 16-element matrix, where indices are numbered from 1 to 16 as described in section 
+    2.11.2 of the OpenGL 2.1 Specification.
+
+    Column-major versus row-major is purely a notational convention. Note that post-multiplying 
+    with column-major matrices produces the same result as pre-multiplying with row-major matrices. 
+    The OpenGL Specification and the OpenGL Reference Manual both use column-major notation. 
+    You can use any notation, as long as it's clearly stated.
+
+    Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion 
+    in the OpenGL programming community. Column-major notation suggests that matrices 
+    are not laid out in memory as a programmer would expect.
+*/
+
+    Matrix result = { 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, x, y, z, 1 };
+    
+    return result;
+}
+
+// Returns rotation matrix
+Matrix MatrixRotate(float angleX, float angleY, float angleZ)
+{
+    Matrix result;
+    
+    Matrix rotX = MatrixRotateX(angleX);
+    Matrix rotY = MatrixRotateY(angleY);
+    Matrix rotZ = MatrixRotateZ(angleZ);
+    
+    result = MatrixMultiply(MatrixMultiply(rotX, rotY), rotZ);
+      
+    return result;
+}
+
+// Create rotation matrix from axis and angle
+Matrix MatrixFromAxisAngle(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) && (length != 0))
+    {
+		length = 1 / length;
+		x *= length; 
+		y *= length; 
+		z *= length;
+	}
+	
+	float s = sin(angle);
+	float c = cos(angle);
+	float t = 1-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;
+};
+
+// Create rotation matrix from axis and angle
+Matrix MatrixFromAxisAngle2(Vector3 axis, float angle)
+{
+    Matrix result;
+    
+    VectorNormalize(&axis);
+    float axisX = axis.x, axisY = axis.y, axisZ = axis.y;
+
+    // Calculate angles
+    float cosres = (float)cos(-angle);
+    float sinres = (float)sin(-angle);
+    float t = 1.0f - cosres;
+
+    // Do the conversion math once
+    float tXX = t * axisX * axisX;
+    float tXY = t * axisX * axisY;
+    float tXZ = t * axisX * axisZ;
+    float tYY = t * axisY * axisY;
+    float tYZ = t * axisY * axisZ;
+    float tZZ = t * axisZ * axisZ;
+
+    float sinX = sinres * axisX;
+    float sinY = sinres * axisY;
+    float sinZ = sinres * axisZ;
+
+    result.m0 = tXX + cosres;
+    result.m1 = tXY + sinZ;
+    result.m2 = tXZ - sinY;
+    result.m3 = 0;
+    result.m4 = tXY - sinZ;
+    result.m5 = tYY + cosres;
+    result.m6 = tYZ + sinX;
+    result.m7 = 0;
+    result.m8 = tXZ + sinY;
+    result.m9 = tYZ - sinX;
+    result.m10 = tZZ + cosres;
+    result.m11 = 0;
+    result.m12 = 0;
+    result.m13 = 0;
+    result.m14 = 0;
+    result.m15 = 1;
+    
+    return result;
+}
+
+// Returns rotation matrix for a given quaternion
+Matrix MatrixFromQuaternion(Quaternion q)
+{
+    Matrix result = MatrixIdentity();
+    
+    Vector3 axis;
+    float angle;
+    
+    QuaternionToAxisAngle(q, &axis, &angle);
+    
+    result = MatrixFromAxisAngle2(axis, angle);
+    
+    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 = (float)cos(angle);
+    float sinres = (float)sin(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;
+
+	// Cache the matrix values (speed optimization)
+	float a00 = left.m0, a01 = left.m1, a02 = left.m2, a03 = left.m3;
+	float a10 = left.m4, a11 = left.m5, a12 = left.m6, a13 = left.m7;
+	float a20 = left.m8, a21 = left.m9, a22 = left.m10, a23 = left.m11;
+	float a30 = left.m12, a31 = left.m13, a32 = left.m14, a33 = left.m15;
+	
+	float b00 = right.m0, b01 = right.m1, b02 = right.m2, b03 = right.m3;
+	float b10 = right.m4, b11 = right.m5, b12 = right.m6, b13 = right.m7;
+	float b20 = right.m8, b21 = right.m9, b22 = right.m10, b23 = right.m11;
+	float b30 = right.m12, b31 = right.m13, b32 = right.m14, b33 = right.m15;
+	
+	result.m0 = b00*a00 + b01*a10 + b02*a20 + b03*a30;
+	result.m1 = b00*a01 + b01*a11 + b02*a21 + b03*a31;
+	result.m2 = b00*a02 + b01*a12 + b02*a22 + b03*a32;
+	result.m3 = b00*a03 + b01*a13 + b02*a23 + b03*a33;
+	result.m4 = b10*a00 + b11*a10 + b12*a20 + b13*a30;
+	result.m5 = b10*a01 + b11*a11 + b12*a21 + b13*a31;
+	result.m6 = b10*a02 + b11*a12 + b12*a22 + b13*a32;
+	result.m7 = b10*a03 + b11*a13 + b12*a23 + b13*a33;
+	result.m8 = b20*a00 + b21*a10 + b22*a20 + b23*a30;
+	result.m9 = b20*a01 + b21*a11 + b22*a21 + b23*a31;
+	result.m10 = b20*a02 + b21*a12 + b22*a22 + b23*a32;
+	result.m11 = b20*a03 + b21*a13 + b22*a23 + b23*a33;
+	result.m12 = b30*a00 + b31*a10 + b32*a20 + b33*a30;
+	result.m13 = b30*a01 + b31*a11 + b32*a21 + b33*a31;
+	result.m14 = b30*a02 + b31*a12 + b32*a22 + b33*a32;
+	result.m15 = b30*a03 + b31*a13 + b32*a23 + b33*a33;
+	
+	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) / rl;
+	result.m1 = 0;
+	result.m2 = 0;
+	result.m3 = 0;
+	result.m4 = 0;
+	result.m5 = (near*2) / 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;
+	result.m12 = 0;
+	result.m13 = 0;
+	result.m14 = -(far*near*2) / fn;
+	result.m15 = 0;
+        
+	return result;
+}
+
+// Returns perspective projection matrix
+Matrix MatrixPerspective(double fovy, double aspect, double near, double far)
+{
+    double top = near*tan(fovy*PI / 360.0);
+    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
+//----------------------------------------------------------------------------------
+
+// Calculates 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 (abs(cosHalfTheta) >= 1.0) result = q1;
+    else
+    {
+        float halfTheta = acos(cosHalfTheta);
+        float sinHalfTheta = sqrt(1.0 - cosHalfTheta*cosHalfTheta);
+
+        if (abs(sinHalfTheta) < 0.001)
+        {
+            result.x = (q1.x*0.5 + q2.x*0.5);
+            result.y = (q1.y*0.5 + q2.y*0.5);
+            result.z = (q1.z*0.5 + q2.z*0.5);
+            result.w = (q1.w*0.5 + q2.w*0.5);
+        }
+        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 from 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 rotation quaternion for an angle around an axis
+// NOTE: angle must be provided in radians
+Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle)
+{
+    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;
+}
+
+// Calculates the matrix from the 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 the axis and the angle for a given quaternion
+void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle)
+{
+    if (abs(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;
+}
\ No newline at end of file
diff --git a/src/raymath.h b/src/raymath.h
new file mode 100644
index 00000000..49cceafb
--- /dev/null
+++ b/src/raymath.h
@@ -0,0 +1,139 @@
+/*********************************************************************************************
+* 
+*   raymath
+*    
+*   Some useful functions to work with Vector3, Matrix and Quaternions
+* 
+*   Copyright (c) 2014 Ramon Santamaria (Ray San - raysan@raysanweb.com)
+*    
+*   This software is provided "as-is", without any express or implied warranty. In no event 
+*   will the authors be held liable for any damages arising from the use of this software.
+*
+*   Permission is granted to anyone to use this software for any purpose, including commercial 
+*   applications, and to alter it and redistribute it freely, subject to the following restrictions:
+*
+*     1. The origin of this software must not be misrepresented; you must not claim that you 
+*     wrote the original software. If you use this software in a product, an acknowledgment 
+*     in the product documentation would be appreciated but is not required.
+*
+*     2. Altered source versions must be plainly marked as such, and must not be misrepresented
+*     as being the original software.
+*
+*     3. This notice may not be removed or altered from any source distribution.
+*
+**********************************************************************************************/
+
+#ifndef RAYMATH_H
+#define RAYMATH_H
+
+//#define RAYMATH_STANDALONE    // NOTE: To use raymath as standalone lib, just uncomment this line
+
+#ifndef RAYMATH_STANDALONE
+    #include "raylib.h"         // Required for typedef: Vector3
+#endif
+
+//----------------------------------------------------------------------------------
+// Defines and Macros
+//----------------------------------------------------------------------------------
+#ifndef PI
+    #define PI 3.14159265358979323846
+#endif
+
+#define DEG2RAD (PI / 180.0)
+#define RAD2DEG (180.0 / PI)
+
+//----------------------------------------------------------------------------------
+// Types and Structures Definition
+//----------------------------------------------------------------------------------
+
+#ifdef RAYMATH_STANDALONE
+    // Vector3 type
+    typedef struct Vector3 {
+        float x;
+        float y;
+        float z;
+    } Vector3;
+#endif
+
+// Matrix type (OpenGL style 4x4 - right handed)
+typedef struct Matrix {
+    float m0, m4, m8, m12;
+    float m1, m5, m9, m13;
+    float m2, m6, m10, m14;
+    float m3, m7, m11, m15;
+} Matrix;
+
+// Quaternion type
+typedef struct Quaternion {
+    float x;
+    float y;
+    float z;
+    float w;
+} Quaternion;
+
+
+#ifdef __cplusplus
+extern "C" {            // Prevents name mangling of functions
+#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
+
+//------------------------------------------------------------------------------------
+// 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();                                // 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 angleX, float angleY, float angleZ); // Returns rotation matrix
+Matrix MatrixRotateAroundAxis(Vector3 axis, float angle);      // Returns rotation matrix for an angle around an specified axis
+Matrix MatrixRotateAroundAxis2(Vector3 axis, float angle);     // Returns rotation matrix for an angle around an specified axis (test another implemntation)
+Matrix MatrixFromQuaternion(Quaternion q);              // Returns rotation matrix for a given quaternion
+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);                // Calculates 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 from a given rotation matrix
+Quaternion QuaternionFromAxisAngle(Vector3 axis, float angle);  // Returns rotation quaternion for an angle around an axis
+Matrix QuaternionToMatrix(Quaternion q);                        // Calculates the matrix from the given quaternion
+void QuaternionToAxisAngle(Quaternion q, Vector3 *outAxis, float *outAngle); // Returns the axis and the angle for a given quaternion
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // RAYMATH_H
\ No newline at end of file