#ifndef LINMATH_H

#define LINMATH_H

/**

* Linmath

* Copyright (C) 2013 Wolfgang 'datenwolf' Draxinger <code@datenwolf.net>

* Released under WTFPL license

*

* Modified by Mario Döring

*/

#include <math.h>

#define LINMATH_H_DEFINE_VEC(n) \

typedef float vec##n[n]; \

static inline void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i] + b[i]; \

} \

static inline void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i] - b[i]; \

} \

static inline void vec##n##_mul(vec##n r, vec##n const a, vec##n const b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i] * b[i]; \

} \

static inline void vec##n##_div(vec##n r, vec##n const a, vec##n const b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i] / b[i]; \

} \

static inline void vec##n##_scale(vec##n r, vec##n const v, float const s) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = v[i] * s; \

} \

static inline void vec##n##_s_add(vec##n r, vec##n const v, float const s) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = v[i] + s; \

} \

static inline void vec##n##_s_sub(vec##n r, vec##n const v, float const s) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = v[i] - s; \

} \

static inline void vec##n##_s_mul(vec##n r, vec##n const v, float const s) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = v[i] * s; \

} \

static inline void vec##n##_s_div(vec##n r, vec##n const v, float const s) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = v[i] / s; \

} \

static inline float vec##n##_mul_inner(vec##n const a, vec##n const b) \

{ \

float p = 0.; \

int i; \

for(i=0; i<n; ++i) \

p += b[i]*a[i]; \

return p; \

} \

static inline float vec##n##_len(vec##n const v) \

{ \

return sqrtf(vec##n##_mul_inner(v,v)); \

} \

static inline void vec##n##_norm(vec##n r, vec##n const v) \

{ \

float k = 1.0 / vec##n##_len(v); \

vec##n##_scale(r, v, k); \

} \

static inline void vec##n##_min(vec##n r, vec##n a, vec##n b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i]<b[i] ? a[i] : b[i]; \

} \

static inline void vec##n##_max(vec##n r, vec##n a, vec##n b) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i]>b[i] ? a[i] : b[i]; \

} \

static inline float vec##n##_distance_square(vec##n const a, vec##n const b) \

{ \

float d = 0.; \

int i; \

for(i=0; i<n; ++i) \

d += (a[i] - b[i]) * (a[i] - b[i]); \

return d; \

} \

static inline void vec##n##_abs(vec##n r, vec##n a) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = fabs(a[i]); \

} \

static inline void vec##n##_mix(vec##n r, vec##n a, vec##n b, float t) \

{ \

int i; \

for(i=0; i<n; ++i) \

r[i] = a[i] + (b[i] - a[i]) * t; \

} \

static inline void vec##n##_lerp(vec##n r, vec##n a, vec##n b, float t) \

{ \

vec##n##_mix(r, a, b, t); \

} \

static inline void vec##n##_slerp(vec##n r, vec##n a, vec##n b, float t) \

{ \

float omega, cosom, sinom, scale0, scale1; \

cosom = vec##n##_mul_inner(a, b); \

if ((1.0 + cosom) > 0.000001) { \

if ((1.0 - cosom) > 0.000001) { \

omega = acos(cosom); \

sinom = sin(omega); \

scale0 = sin((1.0 - t) * omega) / sinom; \

scale1 = sin(t * omega) / sinom; \

} else { \

scale0 = 1.0 - t; \

scale1 = t; \

} \

int i; \

for(i=0; i<n; ++i) \

r[i] = scale0 * a[i] + scale1 * b[i]; \

} else { \

r[0] = -a[1]; \

r[1] = a[0]; \

r[2] = 0.0; \

scale0 = sin((1.0 - t) * M_PI * 0.5); \

scale1 = sin(t * M_PI * 0.5); \

int i; \

for(i=0; i<n; ++i) \

r[i] = scale0 * a[i] + scale1 * r[i]; \

} \

} \

LINMATH_H_DEFINE_VEC(2)

LINMATH_H_DEFINE_VEC(3)

LINMATH_H_DEFINE_VEC(4)

static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b)

{

r[0] = a[1]*b[2] - a[2]*b[1];

r[1] = a[2]*b[0] - a[0]*b[2];

r[2] = a[0]*b[1] - a[1]*b[0];

}

static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n)

{

float p = 2.f*vec3_mul_inner(v, n);

int i;

for(i=0;i<3;++i)

r[i] = v[i] - p*n[i];

}

static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b)

{

r[0] = a[1]*b[2] - a[2]*b[1];

r[1] = a[2]*b[0] - a[0]*b[2];

r[2] = a[0]*b[1] - a[1]*b[0];

r[3] = 1.f;

}

static inline void vec4_reflect(vec4 r, vec4 v, vec4 n)

{

float p = 2.f*vec4_mul_inner(v, n);

int i;

for(i=0;i<4;++i)

r[i] = v[i] - p*n[i];

}

typedef vec4 mat4x4[4];

static inline void mat4x4_identity(mat4x4 M)

{

int i, j;

for(i=0; i<4; ++i)

for(j=0; j<4; ++j)

M[i][j] = i==j ? 1.f : 0.f;

}

static inline void mat4x4_dup(mat4x4 M, mat4x4 N)

{

int i, j;

for(i=0; i<4; ++i)

for(j=0; j<4; ++j)

M[i][j] = N[i][j];

}

static inline void mat4x4_row(vec4 r, mat4x4 M, int i)

{

int k;

for(k=0; k<4; ++k)

r[k] = M[k][i];

}

static inline void mat4x4_col(vec4 r, mat4x4 M, int i)

{

int k;

for(k=0; k<4; ++k)

r[k] = M[i][k];

}

static inline void mat4x4_transpose(mat4x4 M, mat4x4 N)

{

int i, j;

for(j=0; j<4; ++j)

for(i=0; i<4; ++i)

M[i][j] = N[j][i];

}

static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b)

{

int i;

for(i=0; i<4; ++i)

vec4_add(M[i], a[i], b[i]);

}

static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b)

{

int i;

for(i=0; i<4; ++i)

vec4_sub(M[i], a[i], b[i]);

}

static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k)

{

int i;

for(i=0; i<4; ++i)

vec4_scale(M[i], a[i], k);

}

static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z)

{

int i;

vec4_scale(M[0], a[0], x);

vec4_scale(M[1], a[1], y);

vec4_scale(M[2], a[2], z);

for(i = 0; i < 4; ++i) {

M[3][i] = a[3][i];

}

}

static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b)

{

mat4x4 temp;

int k, r, c;

for(c=0; c<4; ++c) for(r=0; r<4; ++r) {

temp[c][r] = 0.f;

for(k=0; k<4; ++k)

temp[c][r] += a[k][r] * b[c][k];

}

mat4x4_dup(M, temp);

}

static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v)

{

int i, j;

for(j=0; j<4; ++j) {

r[j] = 0.f;

for(i=0; i<4; ++i)

r[j] += M[i][j] * v[i];

}

}

static inline void mat4x4_mul_vec3(vec3 r, mat4x4 M, vec3 v)

{

vec4 v4 = {v[0], v[1], v[2], 1.0f};

vec4 r4;

mat4x4_mul_vec4(r4, M, v4);

r[0] = r4[0];

r[1] = r4[1];

r[2] = r4[2];

}

static inline void mat4x4_translate(mat4x4 T, float x, float y, float z)

{

mat4x4_identity(T);

T[3][0] = x;

T[3][1] = y;

T[3][2] = z;

}

static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z)

{

vec4 t = {x, y, z, 0};

vec4 r;

int i;

for (i = 0; i < 4; ++i) {

mat4x4_row(r, M, i);

M[3][i] += vec4_mul_inner(r, t);

}

}

static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b)

{

int i, j;

for(i=0; i<4; ++i) for(j=0; j<4; ++j)

M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.f;

}

static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle)

{

float s = sinf(angle);

float c = cosf(angle);

vec3 u = {x, y, z};

if(vec3_len(u) > 1e-4) {

vec3_norm(u, u);

mat4x4 T;

mat4x4_from_vec3_mul_outer(T, u, u);

mat4x4 S = {

{ 0, u[2], -u[1], 0},

{-u[2], 0, u[0], 0},

{ u[1], -u[0], 0, 0},

{ 0, 0, 0, 0}

};

mat4x4_scale(S, S, s);

mat4x4 C;

mat4x4_identity(C);

mat4x4_sub(C, C, T);

mat4x4_scale(C, C, c);

mat4x4_add(T, T, C);

mat4x4_add(T, T, S);

T[3][3] = 1.;

mat4x4_mul(R, M, T);

} else {

mat4x4_dup(R, M);

}

}

static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle)

{

float s = sinf(angle);

float c = cosf(angle);

mat4x4 R = {

{1.f, 0.f, 0.f, 0.f},

{0.f, c, s, 0.f},

{0.f, -s, c, 0.f},

{0.f, 0.f, 0.f, 1.f}

};

mat4x4_mul(Q, M, R);

}

static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle)

{

float s = sinf(angle);

float c = cosf(angle);

mat4x4 R = {

{ c, 0.f, s, 0.f},

{ 0.f, 1.f, 0.f, 0.f},

{ -s, 0.f, c, 0.f},

{ 0.f, 0.f, 0.f, 1.f}

};

mat4x4_mul(Q, M, R);

}

static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle)

{

float s = sinf(angle);

float c = cosf(angle);

mat4x4 R = {

{ c, s, 0.f, 0.f},

{ -s, c, 0.f, 0.f},

{ 0.f, 0.f, 1.f, 0.f},

{ 0.f, 0.f, 0.f, 1.f}

};

mat4x4_mul(Q, M, R);

}

static inline void mat4x4_invert(mat4x4 T, mat4x4 M)

{

float s[6];

float c[6];

s[0] = M[0][0]*M[1][1] - M[1][0]*M[0][1];

s[1] = M[0][0]*M[1][2] - M[1][0]*M[0][2];

s[2] = M[0][0]*M[1][3] - M[1][0]*M[0][3];

s[3] = M[0][1]*M[1][2] - M[1][1]*M[0][2];

s[4] = M[0][1]*M[1][3] - M[1][1]*M[0][3];

s[5] = M[0][2]*M[1][3] - M[1][2]*M[0][3];

c[0] = M[2][0]*M[3][1] - M[3][0]*M[2][1];

c[1] = M[2][0]*M[3][2] - M[3][0]*M[2][2];

c[2] = M[2][0]*M[3][3] - M[3][0]*M[2][3];

c[3] = M[2][1]*M[3][2] - M[3][1]*M[2][2];

c[4] = M[2][1]*M[3][3] - M[3][1]*M[2][3];

c[5] = M[2][2]*M[3][3] - M[3][2]*M[2][3];

/* Assumes it is invertible */

float idet = 1.0f/( s[0]*c[5]-s[1]*c[4]+s[2]*c[3]+s[3]*c[2]-s[4]*c[1]+s[5]*c[0] );

T[0][0] = ( M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet;

T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet;

T[0][2] = ( M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet;

T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet;

T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet;

T[1][1] = ( M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet;

T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet;

T[1][3] = ( M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet;

T[2][0] = ( M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet;

T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet;

T[2][2] = ( M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet;

T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet;

T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet;

T[3][1] = ( M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet;

T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet;

T[3][3] = ( M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet;

}

static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M)

{

mat4x4_dup(R, M);

float s = 1.;

vec3 h;

vec3_norm(R[2], R[2]);

s = vec3_mul_inner(R[1], R[2]);

vec3_scale(h, R[2], s);

vec3_sub(R[1], R[1], h);

vec3_norm(R[2], R[2]);

s = vec3_mul_inner(R[1], R[2]);

vec3_scale(h, R[2], s);

vec3_sub(R[1], R[1], h);

vec3_norm(R[1], R[1]);

s = vec3_mul_inner(R[0], R[1]);

vec3_scale(h, R[1], s);

vec3_sub(R[0], R[0], h);

vec3_norm(R[0], R[0]);

}

static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f)

{

M[0][0] = 2.f*n/(r-l);

M[0][1] = M[0][2] = M[0][3] = 0.f;

M[1][1] = 2.*n/(t-b);

M[1][0] = M[1][2] = M[1][3] = 0.f;

M[2][0] = (r+l)/(r-l);

M[2][1] = (t+b)/(t-b);

M[2][2] = -(f+n)/(f-n);

M[2][3] = -1.f;

M[3][2] = -2.f*(f*n)/(f-n);

M[3][0] = M[3][1] = M[3][3] = 0.f;

}

static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f)

{

M[0][0] = 2.f/(r-l);

M[0][1] = M[0][2] = M[0][3] = 0.f;

M[1][1] = 2.f/(t-b);

M[1][0] = M[1][2] = M[1][3] = 0.f;

M[2][2] = -2.f/(f-n);

M[2][0] = M[2][1] = M[2][3] = 0.f;

M[3][0] = -(r+l)/(r-l);

M[3][1] = -(t+b)/(t-b);

M[3][2] = -(f+n)/(f-n);

M[3][3] = 1.f;

}

static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float n, float f)

{

/* NOTE: Degrees are an unhandy unit to work with.

* linmath.h uses radians for everything! */

float const a = 1.f / tan(y_fov / 2.f);

m[0][0] = a / aspect;

m[0][1] = 0.f;

m[0][2] = 0.f;

m[0][3] = 0.f;

m[1][0] = 0.f;

m[1][1] = a;

m[1][2] = 0.f;

m[1][3] = 0.f;

m[2][0] = 0.f;

m[2][1] = 0.f;

m[2][2] = -((f + n) / (f - n));

m[2][3] = -1.f;

m[3][0] = 0.f;

m[3][1] = 0.f;

m[3][2] = -((2.f * f * n) / (f - n));

m[3][3] = 0.f;

}

static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up)

{

/* Adapted from Android's OpenGL Matrix.java. */

/* See the OpenGL GLUT documentation for gluLookAt for a description */

/* of the algorithm. We implement it in a straightforward way: */

/* TODO: The negation of of can be spared by swapping the order of

* operands in the following cross products in the right way. */

vec3 f;

vec3_sub(f, center, eye);

vec3_norm(f, f);

vec3 s;

vec3_mul_cross(s, f, up);

vec3_norm(s, s);

vec3 t;

vec3_mul_cross(t, s, f);

m[0][0] = s[0];

m[0][1] = t[0];

m[0][2] = -f[0];

m[0][3] = 0.f;

m[1][0] = s[1];

m[1][1] = t[1];

m[1][2] = -f[1];

m[1][3] = 0.f;

m[2][0] = s[2];

m[2][1] = t[2];

m[2][2] = -f[2];

m[2][3] = 0.f;

m[3][0] = 0.f;

m[3][1] = 0.f;

m[3][2] = 0.f;

m[3][3] = 1.f;

mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]);

}

static inline float mat4x4_det(mat4x4 M)

{

float a = M[0][0]*M[1][1] - M[0][1]*M[1][0];

float b = M[0][0]*M[1][2] - M[0][2]*M[1][0];

float c = M[0][0]*M[1][3] - M[0][3]*M[1][0];

float d = M[0][1]*M[1][2] - M[0][2]*M[1][1];

float e = M[0][1]*M[1][3] - M[0][3]*M[1][1];

float f = M[0][2]*M[1][3] - M[0][3]*M[1][2];

float g = M[2][0]*M[3][1] - M[2][1]*M[3][0];

float h = M[2][0]*M[3][2] - M[2][2]*M[3][0];

float i = M[2][0]*M[3][3] - M[2][3]*M[3][0];

float j = M[2][1]*M[3][2] - M[2][2]*M[3][1];

float k = M[2][1]*M[3][3] - M[2][3]*M[3][1];

float l = M[2][2]*M[3][3] - M[2][3]*M[3][2];

return a*l - b*k + c*j + d*i - e*h + f*g;

}

typedef float quat[4];

static inline void quat_identity(quat q)

{

q[1] = q[2] = q[3] = 0.f;

q[0] = 1.f;

}

static inline void quat_add(quat r, quat a, quat b)

{

int i;

for(i=0; i<4; ++i)

r[i] = a[i] + b[i];

}

static inline void quat_sub(quat r, quat a, quat b)

{

int i;

for(i=0; i<4; ++i)

r[i] = a[i] - b[i];

}

static inline void quat_mul(quat r, quat p, quat q)

{

r[0] = p[0]*q[0] - p[1]*q[1] - p[2]*q[2] - p[3]*q[3];

r[1] = p[0]*q[1] + p[1]*q[0] + p[2]*q[3] - p[3]*q[2];

r[2] = p[0]*q[2] + p[2]*q[0] + p[3]*q[1] - p[1]*q[3];

r[3] = p[0]*q[3] + p[3]*q[0] + p[1]*q[2] - p[2]*q[1];

}

static inline void quat_mul_scalar(quat r, quat q, float s)

{

int i;

for(i=0; i<4; ++i)

r[i] = q[i] * s;

}

static inline void quat_div_scalar(quat r, quat p, float s)

{

int i;

for(i=0; i<4; ++i)

r[i] = p[i] / s;

}

static inline float quat_len(quat q)

{

return sqrtf(q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3]);

}

static inline float quat_len2(quat q)

{

return q[0]*q[0] + q[1]*q[1] + q[2]*q[2] + q[3]*q[3];

}

static inline void quat_scale(quat r, quat v, float s)

{

int i;

for(i=0; i<4; ++i)

r[i] = v[i] * s;

}

static inline float quat_inner_product(quat a, quat b)

{

float p = 0.f;

int i;

for(i=0; i<4; ++i)

p += b[i]*a[i];

return p;

}

static inline void quat_conj(quat r, quat q)

{

r[0] = q[0];

r[1] = -q[1];

r[2] = -q[2];

r[3] = -q[3];

}

static inline float quat_dot(quat a, quat b)

{

return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + a[3]*b[3];

}

static inline void quat_slerp(quat r, quat a, quat b, float t)

{

float cosTheta = quat_dot(a, b);

if(cosTheta < 0.f)

{

cosTheta = -cosTheta;

b[0] = -b[0];

b[1] = -b[1];

b[2] = -b[2];

b[3] = -b[3];

}

if(cosTheta > 1.f - 1e-6f)

{

r[0] = a[0] + t * (b[0] - a[0]);

r[1] = a[1] + t * (b[1] - a[1]);

r[2] = a[2] + t * (b[2] - a[2]);

r[3] = a[3] + t * (b[3] - a[3]);

}

else

{

float angle = acosf(cosTheta);

float sinTheta = sinf(angle);

float a0 = sinf((1.f - t) * angle) / sinTheta;

float b0 = sinf(t * angle) / sinTheta;

r[0] = a0 * a[0] + b0 * b[0];

r[1] = a0 * a[1] + b0 * b[1];

r[2] = a0 * a[2] + b0 * b[2];

r[3] = a0 * a[3] + b0 * b[3];

}

}

static inline void quat_inverse(quat r, quat q)

{

float d = quat_inner_product(q, q);

r[0] = q[0] / d;

r[1] = -q[1] / d;

r[2] = -q[2] / d;

r[3] = -q[3] / d;

}

static inline void quat_rotate(quat r, float angle, vec3 axis) {

float half_angle = angle * 0.5f;

float s = sinf(half_angle);

r[0] = cosf(half_angle);

r[1] = axis[0] * s;

r[2] = axis[1] * s;

r[3] = axis[2] * s;

}

static inline void quat_rotate_by(quat r, quat q, float angle, vec3 axis) {

quat p;

quat_rotate(p, angle, axis);

quat_mul(r, q, p);

}

static inline void quat_euler_angles(vec3 r, quat q)

{

// roll (x-axis rotation)

double sinr_cosp = 2 * (q[0] * q[1] + q[2] * q[3]);

double cosr_cosp = 1 - 2 * (q[1] * q[1] + q[2] * q[2]);

r[0] = atan2(sinr_cosp, cosr_cosp);

// pitch (y-axis rotation)

double sinp = 2 * (q[0] * q[2] - q[3] * q[1]);

if (fabs(sinp) >= 1)

r[1] = copysign(M_PI / 2, sinp); // use 90 degrees if out of range

else

r[1] = asin(sinp);

// yaw (z-axis rotation)

double siny_cosp = 2 * (q[0] * q[3] + q[1] * q[2]);

double cosy_cosp = 1 - 2 * (q[2] * q[2] + q[3] * q[3]);

r[2] = atan2(siny_cosp, cosy_cosp);

}

#define quat_norm vec4_norm

#define quat_mix vec4_mix

#define quat_lerp vec4_lerp

static inline void quat_mul_vec3(vec3 r, quat q, vec3 v)

{

/**

* Method by Fabian 'ryg' Giessen (of Farbrausch)

* t = 2 * cross(q.xyz, v)

* v' = v + q.w * t + cross(q.xyz, t)

*/

// rotates a vector by a quaternion

// r = quat * vec3

vec3 t;

vec3 q_xyz = {q[1], q[2], q[3]};

vec3 u = {q[1], q[2], q[3]};

vec3_mul_cross(t, q_xyz, v);

vec3_scale(t, t, 2);

vec3_mul_cross(u, q_xyz, t);

vec3_scale(t, t, q[0]);

vec3_add(r, v, t);

vec3_add(r, r, u);

}

static inline void vec3_mul_quat(vec3 r, vec3 v, quat q)

{

// we copy the behavior of the GLM library here

// meaing that we do the inverse quaternion

// r = vec3 * quat

quat q_inv;

quat_inverse(q_inv, q);

quat_mul_vec3(r, q_inv, v);

}

static inline void mat4x4_from_quat(mat4x4 M, quat q)

{

// this is basically a direct port of the code from the GLM library

float qxx = q[1] * q[1];

float qyy = q[2] * q[2];

float qzz = q[3] * q[3];

float qxz = q[1] * q[3];

float qxy = q[1] * q[2];

float qyz = q[2] * q[3];

float qwx = q[0] * q[1];

float qwy = q[0] * q[2];

float qwz = q[0] * q[3];

M[0][0] = 1.f - 2.f * (qyy + qzz);

M[0][1] = 2.f * (qxy + qwz);

M[0][2] = 2.f * (qxz - qwy);

M[0][3] = 0.f;

M[1][0] = 2.f * (qxy - qwz);

M[1][1] = 1.f - 2.f * (qxx + qzz);

M[1][2] = 2.f * (qyz + qwx);

M[2][0] = 2.f * (qxz + qwy);

M[2][1] = 2.f * (qyz - qwx);

M[2][2] = 1.f - 2.f * (qxx + qyy);

M[2][3] = 0.f;

}

static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q)

{

/* XXX: The way this is written only works for othogonal matrices. */

/* TODO: Take care of non-orthogonal case. */

quat_mul_vec3(R[0], q, M[0]);

quat_mul_vec3(R[1], q, M[1]);

quat_mul_vec3(R[2], q, M[2]);

R[3][0] = R[3][1] = R[3][2] = 0.f;

R[3][3] = 1.f;

}

static inline void quat_from_mat4x4(quat q, mat4x4 M)

{

// this again is basically a direct port of the code from the GLM library

float fourXSquaredMinus1 = M[0][0] - M[1][1] - M[2][2];

float fourYSquaredMinus1 = M[1][1] - M[0][0] - M[2][2];

float fourZSquaredMinus1 = M[2][2] - M[0][0] - M[1][1];

float fourWSquaredMinus1 = M[0][0] + M[1][1] + M[2][2];

int biggestIndex = 0;

float fourBiggestSquaredMinus1 = fourWSquaredMinus1;

if(fourXSquaredMinus1 > fourBiggestSquaredMinus1)

{

fourBiggestSquaredMinus1 = fourXSquaredMinus1;

biggestIndex = 1;

}

if(fourYSquaredMinus1 > fourBiggestSquaredMinus1)

{

fourBiggestSquaredMinus1 = fourYSquaredMinus1;

biggestIndex = 2;

}

if(fourZSquaredMinus1 > fourBiggestSquaredMinus1)

{

fourBiggestSquaredMinus1 = fourZSquaredMinus1;

biggestIndex = 3;

}

float biggestVal = sqrt(fourBiggestSquaredMinus1 + 1.f) * 0.5f;

float mult = 0.25f / biggestVal;

switch(biggestIndex)

{

case 0:

q[0] = biggestVal;

q[1] = (M[1][2] - M[2][1]) * mult;

q[2] = (M[2][0] - M[0][2]) * mult;

q[3] = (M[0][1] - M[1][0]) * mult;

break;

case 1:

q[0] = (M[1][2] - M[2][1]) * mult;

q[1] = biggestVal;

q[2] = (M[0][1] + M[1][0]) * mult;

q[3] = (M[2][0] + M[0][2]) * mult;

break;

case 2:

q[0] = (M[2][0] - M[0][2]) * mult;

q[1] = (M[0][1] + M[1][0]) * mult;

q[2] = biggestVal;

q[3] = (M[1][2] + M[2][1]) * mult;

break;

case 3:

q[0] = (M[0][1] - M[1][0]) * mult;

q[1] = (M[2][0] + M[0][2]) * mult;

q[2] = (M[1][2] + M[2][1]) * mult;

q[3] = biggestVal;

break;

default:

q[0] = 1;

q[1] = 0;

q[2] = 0;

q[3] = 0;

break;

}

}

#endif