maths and bugs

[vg.git] / src / vg / vg_m.h

/* Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved */

#define VG_PIf  3.14159265358979323846264338327950288f
#define VG_TAUf 6.28318530717958647692528676655900576f

static inline float vg_minf( float a, float b )
{
        return a < b? a: b;
}

static inline float vg_maxf( float a, float b )
{
        return a > b? a: b;
}

static inline float vg_clampf( float a, float min, float max )
{
        return vg_minf( max, vg_maxf( a, min ) );
}

static inline float vg_signf( float a )
{
   return a < 0.0f? -1.0f: 1.0f;
}

static inline float vg_randf(void)
{
   return (float)rand()/(float)(RAND_MAX);
}

static inline float vg_randint(int max)
{
   return rand()%max;
}

#define VG_MIN( A, B ) ((A)<(B)?(A):(B))
#define VG_MAX( A, B ) ((A)>(B)?(A):(B))

static inline int vg_min( int a, int b )
{
        return a < b? a: b;
}

static inline int vg_max( int a, int b )
{
        return a > b? a: b;
}

static inline float vg_rad( float deg )
{
        return deg * VG_PIf / 180.0f;
}

/*
 * Vector 3
 */
static inline void v2_copy( v2f a, v2f b )
{
        b[0] = a[0]; b[1] = a[1];
}

static inline void v2i_copy( v2i a, v2i b )
{
        b[0] = a[0]; b[1] = a[1];
}

static inline int v2i_eq( v2i a, v2i b )
{
        return ((a[0] == b[0]) && (a[1] == b[1]));
}

static inline void v2i_add( v2i a, v2i b, v2i d )
{
        d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
}

static inline void v2i_sub( v2i a, v2i b, v2i d )
{
        d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
}

static inline void v2_minv( v2f a, v2f b, v2f dest ) 
{
        dest[0] = vg_minf(a[0], b[0]);
        dest[1] = vg_minf(a[1], b[1]);
}

static inline void v2_maxv( v2f a, v2f b, v2f dest ) 
{
        dest[0] = vg_maxf(a[0], b[0]);
        dest[1] = vg_maxf(a[1], b[1]);
}

static inline void v2_sub( v2f a, v2f b, v2f d )
{
        d[0] = a[0]-b[0]; d[1] = a[1]-b[1];
}

static inline float v2_dot( v2f a, v2f b )
{
        return a[0] * b[0] + a[1] * b[1];
}

static inline float v2_cross( v2f a, v2f b )
{
        return a[0] * b[1] - a[1] * b[0];
}

static inline void v2_add( v2f a, v2f b, v2f d )
{
        d[0] = a[0]+b[0]; d[1] = a[1]+b[1];
}

static inline void v2_muls( v2f a, float s, v2f d )
{
        d[0] = a[0]*s; d[1] = a[1]*s;
}

static inline void v2_divs( v2f a, float s, v2f d )
{
        d[0] = a[0]/s; d[1] = a[1]/s;
}

static inline void v2_mul( v2f a, v2f b, v2f d )
{
        d[0] = a[0]*b[0]; 
        d[1] = a[1]*b[1];
}

static inline void v2_div( v2f a, v2f b, v2f d )
{
        d[0] = a[0]/b[0]; d[1] = a[1]/b[1];
}

static inline void v2_muladd( v2f a, v2f b, v2f s, v2f d )
{
        d[0] = a[0]+b[0]*s[0]; 
        d[1] = a[1]+b[1]*s[1];
}

static inline void v2_muladds( v2f a, v2f b, float s, v2f d )
{
        d[0] = a[0]+b[0]*s; 
        d[1] = a[1]+b[1]*s;
}

static inline float v2_length2( v2f a )
{
        return a[0]*a[0] + a[1]*a[1];
}

static inline float v2_length( v2f a )
{
        return sqrtf( v2_length2( a ) );
}

static inline float v2_dist2( v2f a, v2f b )
{
        v2f delta;
        v2_sub( a, b, delta );
        return v2_length2( delta );
}

static inline float v2_dist( v2f a, v2f b )
{
        return sqrtf( v2_dist2( a, b ) );
}

static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
{
        d[0] = a[0] + t*(b[0]-a[0]);
        d[1] = a[1] + t*(b[1]-a[1]);
}

static inline void v2_normalize( v2f a )
{
        v2_muls( a, 1.f / v2_length( a ), a );
}

/*
 * Vector 3
 */
static inline void v3_zero( v3f a )
{
        a[0] = 0.f; a[1] = 0.f; a[2] = 0.f;
}

static inline void v3_copy( v3f a, v3f b )
{
        b[0] = a[0]; b[1] = a[1]; b[2] = a[2];
}

static inline void v3_add( v3f a, v3f b, v3f d )
{
        d[0] = a[0]+b[0]; d[1] = a[1]+b[1]; d[2] = a[2]+b[2];
}

static inline void v3_sub( v3f a, v3f b, v3f d )
{
        d[0] = a[0]-b[0]; d[1] = a[1]-b[1]; d[2] = a[2]-b[2];
}

static inline void v3_mul( v3f a, v3f b, v3f d )
{
        d[0] = a[0]*b[0]; d[1] = a[1]*b[1]; d[2] = a[2]*b[2];
}

static inline void v3_div( v3f a, v3f b, v3f d )
{
        d[0] = a[0]/b[0]; d[1] = a[1]/b[1];     d[2] = a[2]/b[2];
}

static inline void v3_muls( v3f a, float s, v3f d )
{
        d[0] = a[0]*s; d[1] = a[1]*s; d[2] = a[2]*s;
}

static inline void v3_divs( v3f a, float s, v3f d )
{
        d[0] = a[0]/s; d[1] = a[1]/s; d[2] = a[2]/s;
}

static inline void v3_muladds( v3f a, v3f b, float s, v3f d )
{
        d[0] = a[0]+b[0]*s; d[1] = a[1]+b[1]*s; d[2] = a[2]+b[2]*s;
}

static inline void v3_muladd( v2f a, v2f b, v2f s, v2f d )
{
        d[0] = a[0]+b[0]*s[0]; 
        d[1] = a[1]+b[1]*s[1];
        d[2] = a[2]+b[2]*s[2];
}

static inline float v3_dot( v3f a, v3f b )
{
        return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}

static inline void v3_cross( v3f a, v3f b, v3f d )
{
  d[0] = a[1] * b[2] - a[2] * b[1];
  d[1] = a[2] * b[0] - a[0] * b[2];
  d[2] = a[0] * b[1] - a[1] * b[0];
}

static inline float v3_length2( v3f a )
{
        return v3_dot( a, a );
}

static inline float v3_length( v3f a )
{
        return sqrtf( v3_length2( a ) );
}

static inline float v3_dist2( v3f a, v3f b )
{
        v3f delta;
        v3_sub( a, b, delta );
        return v3_length2( delta );
}

static inline float v3_dist( v3f a, v3f b )
{
        return sqrtf( v3_dist2( a, b ) );
}

static inline void v3_normalize( v3f a )
{
        v3_muls( a, 1.f / v3_length( a ), a );
}

static inline float vg_lerpf( float a, float b, float t )
{
        return a + t*(b-a);
}

static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
{
        d[0] = a[0] + t*(b[0]-a[0]);
        d[1] = a[1] + t*(b[1]-a[1]);
        d[2] = a[2] + t*(b[2]-a[2]);
}

static inline void v3_minv( v3f a, v3f b, v3f dest ) 
{
        dest[0] = vg_minf(a[0], b[0]);
        dest[1] = vg_minf(a[1], b[1]);
        dest[2] = vg_minf(a[2], b[2]);
}

static inline void v3_maxv( v3f a, v3f b, v3f dest ) 
{
        dest[0] = vg_maxf(a[0], b[0]);
        dest[1] = vg_maxf(a[1], b[1]);
        dest[2] = vg_maxf(a[2], b[2]);
}

static inline float v3_minf( v3f a )
{
        return vg_minf( vg_minf( a[0], a[1] ), a[2] );
}

static inline float v3_maxf( v3f a )
{
        return vg_maxf( vg_maxf( a[0], a[1] ), a[2] );
}

static inline void v3_fill( v3f a, float v )
{
        a[0] = v;
        a[1] = v;
        a[2] = v;
}

static inline void v3_floor( v3f a, v3f b )
{
   b[0] = floorf( a[0] );
   b[1] = floorf( a[1] );
   b[2] = floorf( a[2] );
}

static inline void v3_ceil( v3f a, v3f b )
{
   b[0] = ceilf( a[0] );
   b[1] = ceilf( a[1] );
   b[2] = ceilf( a[2] );
}

static inline void v3_negate( v3f a, v3f b )
{
   b[0] = -a[0];
   b[1] = -a[1];
   b[2] = -a[2];
}

static inline void v3_rotate( v3f v, float angle, v3f axis, v3f d ) 
{
  v3f v1, v2, k;
  float c, s;

  c = cosf( angle );
  s = sinf( angle );

  v3_copy( axis, k );
  v3_normalize( k );
  v3_muls( v, c, v1 );
  v3_cross( k, v, v2 );
  v3_muls( v2, s, v2 );
  v3_add( v1, v2, v1 );
  v3_muls( k, v3_dot(k, v) * (1.0f - c), v2);
  v3_add( v1, v2, d );
}

/*
 * Vector 4
 */
static inline void v4_copy( v4f a, v4f b )
{
        b[0] = a[0]; b[1] = a[1]; b[2] = a[2]; b[3] = a[3];
}

static inline void v4_zero( v4f a )
{
        a[0] = 0.f; a[1] = 0.f; a[2] = 0.f; a[3] = 0.f;
}

static inline void v4_muladds( v3f a, v3f b, float s, v3f d )
{
        d[0] = a[0]+b[0]*s; 
   d[1] = a[1]+b[1]*s;
   d[2] = a[2]+b[2]*s;
   d[3] = a[3]+b[3]*s;
}

static inline void v4_lerp( v4f a, v4f b, float t, v4f d )
{
        d[0] = a[0] + t*(b[0]-a[0]);
        d[1] = a[1] + t*(b[1]-a[1]);
        d[2] = a[2] + t*(b[2]-a[2]);
        d[3] = a[3] + t*(b[3]-a[3]);
}

static inline float v4_dot( v4f a, v4f b )
{
        return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] + a[3]*a[3];
}

static inline float v4_length( v4f a )
{
   return sqrtf( v4_dot(a,a) );
}

/*
 * Matrix 2x2
 */

#define M2X2_INDENTIY   {{1.0f, 0.0f, }, \
                                                                { 0.0f, 1.0f, }}
                                                                
#define M2X2_ZERO                       {{0.0f, 0.0f, }, \
                                                                { 0.0f, 0.0f, }}

static inline void m2x2_copy( m2x2f a, m2x2f b )
{
        v2_copy( a[0], b[0] );
        v2_copy( a[1], b[1] );
}

static inline void m2x2_identity( m2x2f a )
{
        m2x2f id = M2X2_INDENTIY;
        m2x2_copy( id, a );
}

static inline void m2x2_create_rotation( m2x2f a, float theta )
{
        float s, c;
        
        s = sinf( theta );
        c = cosf( theta );
        
        a[0][0] =  c;
        a[0][1] = -s;
        a[1][0] =  s;
        a[1][1] =  c;
}

/*
 * Matrix 3x3
 */

#define M3X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
                                                                { 0.0f, 1.0f, 0.0f, },\
                                                                { 0.0f, 0.0f, 1.0f, }}
                                                                
#define M3X3_ZERO                       {{0.0f, 0.0f, 0.0f, },\
                                                                { 0.0f, 0.0f, 0.0f, },\
                                                                { 0.0f, 0.0f, 0.0f, }}


static inline void m3x3_copy( m3x3f a, m3x3f b )
{
        v3_copy( a[0], b[0] );
        v3_copy( a[1], b[1] );
        v3_copy( a[2], b[2] );
}

static inline void m3x3_identity( m3x3f a )
{
        m3x3f id = M3X3_IDENTITY;
        m3x3_copy( id, a );
}

static inline void m3x3_zero( m3x3f a )
{
        m3x3f z = M3X3_ZERO;
        m3x3_copy( z, a );
}

static inline void m3x3_inv( m3x3f src, m3x3f dest )
{
        float a = src[0][0], b = src[0][1], c = src[0][2],
                        d = src[1][0], e = src[1][1], f = src[1][2],
                        g = src[2][0], h = src[2][1], i = src[2][2];

        float det =    1.f / 
                                        (+a*(e*i-h*f)
                -b*(d*i-f*g)
                +c*(d*h-e*g));
                
        dest[0][0] =  (e*i-h*f)*det;
        dest[0][1] = -(b*i-c*h)*det;
        dest[0][2] =  (b*f-c*e)*det;
        dest[1][0] = -(d*i-f*g)*det;
        dest[1][1] =  (a*i-c*g)*det;
        dest[1][2] = -(a*f-d*c)*det;
        dest[2][0] =  (d*h-g*e)*det;
        dest[2][1] = -(a*h-g*b)*det;
        dest[2][2] =  (a*e-d*b)*det;
}

static inline void m3x3_transpose( m3x3f src, m3x3f dest )
{
        float a = src[0][0], b = src[0][1], c = src[0][2],
                        d = src[1][0], e = src[1][1], f = src[1][2],
                        g = src[2][0], h = src[2][1], i = src[2][2];
                        
        dest[0][0] = a;
        dest[0][1] = d;
        dest[0][2] = g;
        dest[1][0] = b;
        dest[1][1] = e;
        dest[1][2] = h;
        dest[2][0] = c;
        dest[2][1] = f;
        dest[2][2] = i;
}

static inline void m3x3_mul( m3x3f a, m3x3f b, m3x3f d )
{
        float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
                        a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
                        a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],

                        b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
                        b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
                        b20 = b[2][0], b21 = b[2][1], b22 = b[2][2];

        d[0][0] = a00*b00 + a10*b01 + a20*b02;
        d[0][1] = a01*b00 + a11*b01 + a21*b02;
        d[0][2] = a02*b00 + a12*b01 + a22*b02;
        d[1][0] = a00*b10 + a10*b11 + a20*b12;
        d[1][1] = a01*b10 + a11*b11 + a21*b12;
        d[1][2] = a02*b10 + a12*b11 + a22*b12;
        d[2][0] = a00*b20 + a10*b21 + a20*b22;
        d[2][1] = a01*b20 + a11*b21 + a21*b22;
        d[2][2] = a02*b20 + a12*b21 + a22*b22;
}

static inline void m3x3_mulv( m3x3f m, v3f v, v3f d )
{
        v3f res;
        
        res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2];
        res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2];
        res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2];
        
        v3_copy( res, d );
}

static inline void m3x3_projection( m3x3f dst, 
      float const left, float const right, float const bottom, float const top )
{
        float rl, tb;
        
        m3x3_zero( dst );

        rl = 1.0f / (right - left);
        tb = 1.0f / (top   - bottom);

        dst[0][0] = 2.0f * rl;
        dst[1][1] = 2.0f * tb;
        dst[2][2] = 1.0f;
}

static inline void m3x3_translate( m3x3f m, v3f v )
{
        m[2][0] = m[0][0] * v[0] + m[1][0] * v[1] + m[2][0];
        m[2][1] = m[0][1] * v[0] + m[1][1] * v[1] + m[2][1];
        m[2][2] = m[0][2] * v[0] + m[1][2] * v[1] + m[2][2];
}

static inline void m3x3_scale( m3x3f m, v3f v )
{
        m[0][0] = m[0][0] * v[0];
        m[0][1] = m[0][1] * v[0];
        m[0][2] = m[0][2] * v[0];

        m[1][0] = m[1][0] * v[1];
        m[1][1] = m[1][1] * v[1];
        m[1][2] = m[1][2] * v[1];
}

static inline void m3x3_rotate( m3x3f m, float angle )
{
        float m00 = m[0][0], m10 = m[1][0],
                        m01 = m[0][1], m11 = m[1][1],
                        m02 = m[0][2], m12 = m[1][2];
        float c, s;

        s = sinf( angle );
        c = cosf( angle );

        m[0][0] = m00 * c + m10 * s;
        m[0][1] = m01 * c + m11 * s;
        m[0][2] = m02 * c + m12 * s;

        m[1][0] = m00 * -s + m10 * c;
        m[1][1] = m01 * -s + m11 * c;
        m[1][2] = m02 * -s + m12 * c;
}

/*
 * Matrix 4x3
 */

#define M4X3_IDENTITY   {{1.0f, 0.0f, 0.0f, },\
                                                                { 0.0f, 1.0f, 0.0f, },\
                                                                { 0.0f, 0.0f, 1.0f, },\
                                                                { 0.0f, 0.0f, 0.0f }}

static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
{
        v3_copy( a[0], b[0] );
        v3_copy( a[1], b[1] );
        v3_copy( a[2], b[2] );
}

static inline void m4x3_invert_affine( m4x3f a, m4x3f b )
{
   m3x3_transpose( a, b );
   m3x3_mulv( b, a[3], b[3] );
   v3_negate( b[3], b[3] );
}

static inline void m4x3_copy( m4x3f a, m4x3f b )
{
        v3_copy( a[0], b[0] );
        v3_copy( a[1], b[1] );
        v3_copy( a[2], b[2] );
        v3_copy( a[3], b[3] );
}

static inline void m4x3_identity( m4x3f a )
{
        m4x3f id = M4X3_IDENTITY;
        m4x3_copy( id, a );
}

static inline void m4x3_mul( m4x3f a, m4x3f b, m4x3f d ) 
{
        float 
        a00 = a[0][0], a01 = a[0][1], a02 = a[0][2],
        a10 = a[1][0], a11 = a[1][1], a12 = a[1][2],
        a20 = a[2][0], a21 = a[2][1], a22 = a[2][2],
        a30 = a[3][0], a31 = a[3][1], a32 = a[3][2],
        b00 = b[0][0], b01 = b[0][1], b02 = b[0][2],
        b10 = b[1][0], b11 = b[1][1], b12 = b[1][2],
        b20 = b[2][0], b21 = b[2][1], b22 = b[2][2],
        b30 = b[3][0], b31 = b[3][1], b32 = b[3][2];
        
        d[0][0] = a00*b00 + a10*b01 + a20*b02;
        d[0][1] = a01*b00 + a11*b01 + a21*b02;
        d[0][2] = a02*b00 + a12*b01 + a22*b02;
        d[1][0] = a00*b10 + a10*b11 + a20*b12;
        d[1][1] = a01*b10 + a11*b11 + a21*b12;
        d[1][2] = a02*b10 + a12*b11 + a22*b12;
        d[2][0] = a00*b20 + a10*b21 + a20*b22;
        d[2][1] = a01*b20 + a11*b21 + a21*b22;
        d[2][2] = a02*b20 + a12*b21 + a22*b22;
        d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30;
        d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31;
        d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32;
}

static inline void m4x3_mulv( m4x3f m, v3f v, v3f d ) 
{
        v3f res;
  
        res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0];
        res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1];
        res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2];

        v3_copy( res, d );
}

/*
 * Affine transforms
 */

static inline void m4x3_translate( m4x3f m, v3f v )
{
        v3_muladds( m[3], m[0], v[0], m[3] );
        v3_muladds( m[3], m[1], v[1], m[3] );
        v3_muladds( m[3], m[2], v[2], m[3] );
}

static inline void m4x3_scale( m4x3f m, float s )
{
        v3_muls( m[0], s, m[0] );
        v3_muls( m[1], s, m[1] );
        v3_muls( m[2], s, m[2] );
}

static inline void m4x3_rotate_x( m4x3f m, float angle )
{
        m4x3f t = M4X3_IDENTITY;
        float c, s;

        c = cosf( angle );
        s = sinf( angle );

        t[1][1] =  c;
        t[1][2] =  s;
        t[2][1] = -s;
        t[2][2] =  c;

        m4x3_mul( m, t, m );
}

static inline void m4x3_rotate_y( m4x3f m, float angle )
{
        m4x3f t = M4X3_IDENTITY;
        float c, s;

        c = cosf( angle );
        s = sinf( angle );

        t[0][0] =  c;
        t[0][2] = -s;
        t[2][0] =  s;
        t[2][2] =  c;

        m4x3_mul( m, t, m );
}

static inline void m4x3_rotate_z( m4x3f m, float angle )
{
        m4x3f t = M4X3_IDENTITY;
        float c, s;

        c = cosf( angle );
        s = sinf( angle );

        t[0][0] =  c;
        t[0][1] =  s;
        t[1][0] = -s;
        t[1][1] =  c;

        m4x3_mul( m, t, m );
}

static inline void m4x3_expand( m4x3f m, m4x4f d )
{
   v3_copy( m[0], d[0] );
   v3_copy( m[1], d[1] );
   v3_copy( m[2], d[2] );
   v3_copy( m[3], d[3] );
   d[0][3] = 0.0f;
   d[1][3] = 0.0f;
   d[2][3] = 0.0f;
   d[3][3] = 1.0f;
}

static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
{
        v3f v;
        m4x3_mulv( m, point, v );

        v3_minv( box[0], v, box[0] );
        v3_maxv( box[1], v, box[1] );
}

static inline void box_concat( boxf a, boxf b )
{
        v3_minv( a[0], b[0], a[0] );
        v3_maxv( a[1], b[1], a[1] );
}

static inline void box_copy( boxf a, boxf b )
{
        v3_copy( a[0], b[0] );
        v3_copy( a[1], b[1] );
}

static inline void m4x3_transform_aabb( m4x3f m, boxf box )
{
        v3f a; v3f b;
        
        v3_copy( box[0], a );
        v3_copy( box[1], b );
        v3_fill( box[0],  INFINITY );
        v3_fill( box[1], -INFINITY );

        m4x3_expand_aabb_point( m, box, a );
        m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], a[2] } );
        m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], a[2] } );
        m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], a[2] } );
        m4x3_expand_aabb_point( m, box, b );
        m4x3_expand_aabb_point( m, box, (v3f){ a[0], b[1], b[2] } );
        m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
        m4x3_expand_aabb_point( m, box, (v3f){ b[0], b[1], b[2] } );
}

static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up )
{
   v3f dir;
   v3_sub( target, pos, dir );
   v3_normalize( dir );

   v3_negate( dir, m[2] );

   v3_cross( up, m[2], m[0] );
   v3_normalize( m[0] );

   v3_cross( m[2], m[0], m[1] );
   v3_copy( pos, m[3] );
}

/*
 * Matrix 4x4
 */

#define M4X4_IDENTITY   {{1.0f, 0.0f, 0.0f, 0.0f },\
                                                                { 0.0f, 1.0f, 0.0f, 0.0f },\
                                                                { 0.0f, 0.0f, 1.0f, 0.0f },\
                                                                { 0.0f, 0.0f, 0.0f, 1.0f }}

static void m4x4_projection( m4x4f m, float angle,
      float ratio, float near, float far )
{
   float scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * near,
         r = ratio * scale,
         l = -r,
         t = scale,
         b = -t;

   m[0][0] =  2.0f * near / (r - l); 
   m[0][1] =  0.0f; 
   m[0][2] =  0.0f; 
   m[0][3] =  0.0f; 
   m[1][0] =  0.0f; 
   m[1][1] =  2.0f * near / (t - b); 
   m[1][2] =  0.0f; 
   m[1][3] =  0.0f; 
   m[2][0] =  (r + l) / (r - l); 
   m[2][1] =  (t + b) / (t - b); 
   m[2][2] = -(far + near) / (far - near); 
   m[2][3] = -1.0f; 
   m[3][0] =  0.0f; 
   m[3][1] =  0.0f; 
   m[3][2] = -2.0f * far * near / (far - near); 
   m[3][3] =  0.0f;
} 

static void m4x4_translate( m4x4f m, v3f v )
{
   v4_muladds( m[3], m[0], v[0], m[3] );
   v4_muladds( m[3], m[1], v[1], m[3] );
   v4_muladds( m[3], m[2], v[2], m[3] );
}

static inline void m4x4_copy( m4x4f a, m4x4f b )
{
        v4_copy( a[0], b[0] );
        v4_copy( a[1], b[1] );
        v4_copy( a[2], b[2] );
        v4_copy( a[3], b[3] );
}

static inline void m4x4_identity( m4x4f a )
{
        m4x4f id = M4X4_IDENTITY;
        m4x4_copy( id, a );
}

static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d )
{
   float a00 = a[0][0], a01 = a[0][1], a02 = a[0][2], a03 = a[0][3],
         a10 = a[1][0], a11 = a[1][1], a12 = a[1][2], a13 = a[1][3],
         a20 = a[2][0], a21 = a[2][1], a22 = a[2][2], a23 = a[2][3],
         a30 = a[3][0], a31 = a[3][1], a32 = a[3][2], a33 = a[3][3],

         b00 = b[0][0], b01 = b[0][1], b02 = b[0][2], b03 = b[0][3],
         b10 = b[1][0], b11 = b[1][1], b12 = b[1][2], b13 = b[1][3],
         b20 = b[2][0], b21 = b[2][1], b22 = b[2][2], b23 = b[2][3],
         b30 = b[3][0], b31 = b[3][1], b32 = b[3][2], b33 = b[3][3];

  d[0][0] = a00*b00 + a10*b01 + a20*b02 + a30*b03;
  d[0][1] = a01*b00 + a11*b01 + a21*b02 + a31*b03;
  d[0][2] = a02*b00 + a12*b01 + a22*b02 + a32*b03;
  d[0][3] = a03*b00 + a13*b01 + a23*b02 + a33*b03;
  d[1][0] = a00*b10 + a10*b11 + a20*b12 + a30*b13;
  d[1][1] = a01*b10 + a11*b11 + a21*b12 + a31*b13;
  d[1][2] = a02*b10 + a12*b11 + a22*b12 + a32*b13;
  d[1][3] = a03*b10 + a13*b11 + a23*b12 + a33*b13;
  d[2][0] = a00*b20 + a10*b21 + a20*b22 + a30*b23;
  d[2][1] = a01*b20 + a11*b21 + a21*b22 + a31*b23;
  d[2][2] = a02*b20 + a12*b21 + a22*b22 + a32*b23;
  d[2][3] = a03*b20 + a13*b21 + a23*b22 + a33*b23;
  d[3][0] = a00*b30 + a10*b31 + a20*b32 + a30*b33;
  d[3][1] = a01*b30 + a11*b31 + a21*b32 + a31*b33;
  d[3][2] = a02*b30 + a12*b31 + a22*b32 + a32*b33;
  d[3][3] = a03*b30 + a13*b31 + a23*b32 + a33*b33;
}

/*
 * Planes (double precision)
 */
static inline void tri_to_plane( double a[3], double b[3], 
      double c[3], double p[4] )
{
        double edge0[3];
        double edge1[3];
        double l;
        
        edge0[0] = b[0] - a[0];
        edge0[1] = b[1] - a[1];
        edge0[2] = b[2] - a[2];
        
        edge1[0] = c[0] - a[0];
        edge1[1] = c[1] - a[1];
        edge1[2] = c[2] - a[2];
        
        p[0] = edge0[1] * edge1[2] - edge0[2] * edge1[1];
        p[1] = edge0[2] * edge1[0] - edge0[0] * edge1[2];
        p[2] = edge0[0] * edge1[1] - edge0[1] * edge1[0];
        
        l = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
        p[3] = (p[0] * a[0] + p[1] * a[1] + p[2] * a[2]) / l;
        
        p[0] = p[0] / l;
        p[1] = p[1] / l;
        p[2] = p[2] / l;
}

static inline int plane_intersect( double a[4], double b[4], 
      double c[4], double p[4] )
{
        double const epsilon = 1e-8f;
        
        double x[3];
        double d;
        
        x[0] = a[1] * b[2] - a[2] * b[1];
        x[1] = a[2] * b[0] - a[0] * b[2];
        x[2] = a[0] * b[1] - a[1] * b[0];
        
        d = x[0] * c[0] + x[1] * c[1] + x[2] * c[2];
        
        if( d < epsilon && d > -epsilon ) return 0;
        
        p[0] = (b[1] * c[2] - b[2] * c[1]) * -a[3];
        p[1] = (b[2] * c[0] - b[0] * c[2]) * -a[3];
        p[2] = (b[0] * c[1] - b[1] * c[0]) * -a[3];
        
        p[0] += (c[1] * a[2] - c[2] * a[1]) * -b[3];
        p[1] += (c[2] * a[0] - c[0] * a[2]) * -b[3];
        p[2] += (c[0] * a[1] - c[1] * a[0]) * -b[3];
        
        p[0] += (a[1] * b[2] - a[2] * b[1]) * -c[3];
        p[1] += (a[2] * b[0] - a[0] * b[2]) * -c[3];
        p[2] += (a[0] * b[1] - a[1] * b[0]) * -c[3];
        
        p[0] = -p[0] / d;
        p[1] = -p[1] / d;
        p[2] = -p[2] / d;
        
        return 1;
}

static inline double plane_polarity( double p[4], double a[3] )
{
        return 
        (a[0] * p[0] + a[1] * p[1] + a[2] * p[2])
        -(p[0]*p[3] * p[0] + p[1]*p[3] * p[1] + p[2]*p[3] * p[2])
        ;
}

/* Quaternions */

static inline void q_identity( v4f q )
{
   q[0] = 0.0f; q[1] = 0.0f; q[2] = 0.0f; q[3] = 1.0f;
}

static inline void q_axis_angle( v4f q, v3f axis, float angle )
{
   float a = angle*0.5f,
         c = cosf(a),
         s = sinf(a);

   q[0] = s*axis[0];
   q[1] = s*axis[1];
   q[2] = s*axis[2];
   q[3] = c;
}

static inline void q_mul( v4f q, v4f q1, v4f d )
{
   v4f t;
   t[0] = q[3]*q1[0] + q[0]*q1[3] + q[1]*q1[2] - q[2]*q1[1];
   t[1] = q[3]*q1[1] - q[0]*q1[2] + q[1]*q1[3] + q[2]*q1[0];
   t[2] = q[3]*q1[2] + q[0]*q1[1] - q[1]*q1[0] + q[2]*q1[3];
   t[3] = q[3]*q1[3] - q[0]*q1[0] - q[1]*q1[1] - q[2]*q1[2];
   v4_copy( t, d );
}

static inline void q_normalize( v4f q )
{
   float s = 1.0f/ sqrtf(v4_dot(q,q));
   q[0] *= s;
   q[1] *= s;
   q[2] *= s;
   q[3] *= s;
}

static inline void q_inv( v4f q, v4f d )
{
   float s = 1.0f / v4_dot(q,q);
   d[0] = -q[0]*s;
   d[1] = -q[1]*s;
   d[2] = -q[2]*s;
   d[3] =  q[3]*s;
}

static inline void q_m3x3( v4f q, m3x3f d )
{
   float
      l = v4_length(q),
      s = l > 0.0f? 2.0f/l: 0.0f,

      xx = s*q[0]*q[0], xy = s*q[0]*q[1], wx = s*q[3]*q[0],
      yy = s*q[1]*q[1], yz = s*q[1]*q[2], wy = s*q[3]*q[1],
      zz = s*q[2]*q[2], xz = s*q[0]*q[2], wz = s*q[3]*q[2];

   d[0][0] = 1.0f - yy - zz;
   d[1][1] = 1.0f - xx - zz;
   d[2][2] = 1.0f - xx - yy;
   d[0][1] = xy + wz;
   d[1][2] = yz + wx;
   d[2][0] = xz + wy;
   d[1][0] = xy - wz;
   d[2][1] = yz - wx;
   d[0][2] = xz - wy;
}