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standalone raymath 

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/**********************************************************************************************
*
* 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;
}

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- 64
src/raymath.h
File diff soppresso perché troppo grande
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