X-Git-Url: https://harrygodden.com/git/?a=blobdiff_plain;f=src%2Fvg%2Fvg_m.h;h=8e49fe55e330f4adb99d2291ae552c56fbf55274;hb=3dd767bb10e6fee9cbffeb185d1a9685810c17b5;hp=b46a33176db74ad6626cda75837f31db10b3e1e7;hpb=a153af7a16d9d4f81e9ebe4cfb2c99a028755189;p=vg.git

diff --git a/src/vg/vg_m.h b/src/vg/vg_m.h
index b46a331..8e49fe5 100644
--- a/src/vg/vg_m.h
+++ b/src/vg/vg_m.h
@@ -1,4 +1,11 @@
-/* Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved */
+/* Copyright (C) 2021-2022 Harry Godden (hgn) - All Rights Reserved */
+
+#ifndef VG_M_H
+#define VG_M_H
+
+#include "vg_platform.h"
+#include <math.h>
+#include <stdlib.h>
 
 #define VG_PIf  3.14159265358979323846264338327950288f
 #define VG_TAUf 6.28318530717958647692528676655900576f
@@ -23,8 +30,20 @@ static inline float vg_signf( float a )
    return a < 0.0f? -1.0f: 1.0f;
 }
 
-#define VG_MIN( A, B ) ((A)<(B)?(A):(B))
-#define VG_MAX( A, B ) ((A)>(B)?(A):(B))
+static inline float vg_fractf( float a )
+{
+   return a - floorf( a );
+}
+
+static float stable_force( float current, float diff )
+{
+   float fnew = current + diff;
+
+   if( fnew * current < 0.0f )
+      return 0.0f;
+
+   return fnew;
+}
 
 static inline int vg_min( int a, int b )
 {
@@ -49,6 +68,11 @@ static inline void v2_copy( v2f a, v2f b )
 	b[0] = a[0]; b[1] = a[1];
 }
 
+static inline void v2_zero( v2f a )
+{
+	a[0] = 0.f; a[1] = 0.f;
+}
+
 static inline void v2i_copy( v2i a, v2i b )
 {
 	b[0] = a[0]; b[1] = a[1];
@@ -86,9 +110,14 @@ 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];
+	return a[0]*b[1] - a[1]*b[0];
 }
 
 static inline void v2_add( v2f a, v2f b, v2f d )
@@ -157,6 +186,24 @@ static inline void v2_lerp( v2f a, v2f b, float t, v2f d )
 	d[1] = a[1] + t*(b[1]-a[1]);
 }
 
+static inline void v2_normalize( v2f a )
+{
+	v2_muls( a, 1.0f / v2_length( a ), a );
+}
+
+static void v2_normalize_clamp( v2f a )
+{
+   float l2 = v2_length2( a );
+   if( l2 > 1.0f )
+      v2_muls( a, 1.0f/sqrtf(l2), a );
+}
+
+static inline void v2_floor( v2f a, v2f b )
+{
+   b[0] = floorf( a[0] );
+   b[1] = floorf( a[1] );
+}
+
 /*
  * Vector 3
  */
@@ -205,16 +252,25 @@ 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 )
+static inline void v3_cross( v3f a, v3f b, v3f dest )
 {
-  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];
+   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];
+   v3_copy( d, dest );
 }
 
 static inline float v3_length2( v3f a )
@@ -249,6 +305,19 @@ static inline float vg_lerpf( float a, float b, float t )
 	return a + t*(b-a);
 }
 
+static inline double vg_lerp( double a, double b, double t )
+{
+	return a + t*(b-a);
+}
+
+/* correctly lerp around circular period -pi -> pi */
+static float vg_alerpf( float a, float b, float t )
+{
+   float d = fmodf( b-a, VG_TAUf ),
+         s = fmodf( 2.0f*d, VG_TAUf ) - d;
+   return a + s*t;
+}
+
 static inline void v3_lerp( v3f a, v3f b, float t, v3f d )
 {
 	d[0] = a[0] + t*(b[0]-a[0]);
@@ -294,6 +363,13 @@ static inline void v3_floor( v3f a, v3f b )
    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];
@@ -301,6 +377,24 @@ static inline void v3_negate( v3f a, v3f b )
    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
  */
@@ -314,7 +408,15 @@ 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 )
+static inline void v4_muls( v4f a, float s, v4f d )
+{
+	d[0] = a[0]*s; 
+   d[1] = a[1]*s;
+   d[2] = a[2]*s;
+   d[3] = a[3]*s;
+}
+
+static inline void v4_muladds( v4f a, v4f b, float s, v4f d )
 {
 	d[0] = a[0]+b[0]*s; 
    d[1] = a[1]+b[1]*s;
@@ -322,6 +424,24 @@ static inline void v4_muladds( v3f a, v3f b, float s, v3f d )
    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
  */
@@ -528,6 +648,52 @@ static inline void m4x3_to_3x3( m4x3f a, m3x3f b )
 	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 void m4x3_invert_full( m4x3f src, m4x3f dst )
+{
+  float t2, t4, t5,
+        det,
+        a = src[0][0], b = src[0][1], c = src[0][2],
+        e = src[1][0], f = src[1][1], g = src[1][2],
+        i = src[2][0], j = src[2][1], k = src[2][2],
+        m = src[3][0], n = src[3][1], o = src[3][2];
+
+   t2 = j*o - n*k;
+   t4 = i*o - m*k;
+   t5 = i*n - m*j;
+   
+   dst[0][0] =  f*k - g*j;
+   dst[1][0] =-(e*k - g*i);
+   dst[2][0] =  e*j - f*i;
+   dst[3][0] =-(e*t2 - f*t4 + g*t5);
+   
+   dst[0][1] =-(b*k - c*j);
+   dst[1][1] =  a*k - c*i;
+   dst[2][1] =-(a*j - b*i);
+   dst[3][1] =  a*t2 - b*t4 + c*t5;
+   
+   t2 = f*o - n*g;
+   t4 = e*o - m*g; 
+   t5 = e*n - m*f;
+   
+   dst[0][2] =  b*g - c*f ;
+   dst[1][2] =-(a*g - c*e );
+   dst[2][2] =  a*f - b*e ;
+   dst[3][2] =-(a*t2 - b*t4 + c * t5);
+
+   det = 1.0f / (a * dst[0][0] + b * dst[1][0] + c * dst[2][0]);
+   v3_muls( dst[0], det, dst[0] );
+   v3_muls( dst[1], det, dst[1] );
+   v3_muls( dst[2], det, dst[2] );
+   v3_muls( dst[3], det, dst[3] );
+}
+
 static inline void m4x3_copy( m4x3f a, m4x3f b )
 {
 	v3_copy( a[0], b[0] );
@@ -579,6 +745,20 @@ static inline void m4x3_mulv( m4x3f m, v3f v, v3f d )
 	v3_copy( res, d );
 }
 
+/* 
+ * Transform plane ( xyz, distance )
+ */
+static inline void m4x3_mulp( m4x3f m, v4f p, v4f d )
+{
+   v3f o;
+
+   v3_muls( p, p[3], o );
+   m4x3_mulv( m, o, o );
+   m3x3_mulv( m, p, d );
+   
+   d[3] = v3_dot( o, d );
+}
+
 /*
  * Affine transforms
  */
@@ -597,6 +777,13 @@ static inline void m4x3_scale( m4x3f m, float s )
 	v3_muls( m[2], s, m[2] );
 }
 
+static inline void m4x3_scalev( m4x3f m, v3f v )
+{
+   v3_muls(m[0], v[0], m[0]);
+   v3_muls(m[1], v[1], m[1]);
+   v3_muls(m[2], v[2], m[2]);
+}
+
 static inline void m4x3_rotate_x( m4x3f m, float angle )
 {
 	m4x3f t = M4X3_IDENTITY;
@@ -666,6 +853,12 @@ static inline void m4x3_expand_aabb_point( m4x3f m, boxf box, v3f point )
 	v3_maxv( box[1], v, box[1] );
 }
 
+static inline void box_addpt( boxf a, v3f pt )
+{
+	v3_minv( a[0], pt, a[0] );
+	v3_maxv( a[1], pt, a[1] );
+}
+
 static inline void box_concat( boxf a, boxf b )
 {
 	v3_minv( a[0], b[0], a[0] );
@@ -678,6 +871,21 @@ static inline void box_copy( boxf a, boxf b )
 	v3_copy( a[1], b[1] );
 }
 
+static inline int box_overlap( boxf a, boxf b )
+{
+   return
+	( a[0][0] <= b[1][0] && a[1][0] >= b[0][0] ) &&
+	( a[0][1] <= b[1][1] && a[1][1] >= b[0][1] ) &&
+	( a[0][2] <= b[1][2] && a[1][2] >= b[0][2] )
+	;
+}
+
+static inline void box_init_inf( boxf box )
+{
+	v3_fill( box[0],  INFINITY );
+	v3_fill( box[1], -INFINITY );
+}
+
 static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 {
 	v3f a; v3f b;
@@ -687,14 +895,50 @@ static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 	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], a[1], a[2] } );
 	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){ b[0], a[1], a[2] } );
+
+	m4x3_expand_aabb_point( m, box, (v3f){ a[0], a[1], b[2] } );
 	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] } );
+	m4x3_expand_aabb_point( m, box, (v3f){ b[0], a[1], b[2] } );
+}
+
+int ray_aabb( boxf box, v3f co, v3f dir, float dist )
+{
+   v3f v0, v1;
+   float tmin, tmax;
+
+   v3_sub( box[0], co, v0 );
+   v3_sub( box[1], co, v1 );
+   v3_div( v0, dir, v0 );
+   v3_div( v1, dir, v1 );
+   
+   tmin = vg_minf( v0[0], v1[0] );
+   tmax = vg_maxf( v0[0], v1[0] );
+   tmin = vg_maxf( tmin, vg_minf( v0[1], v1[1] ));
+   tmax = vg_minf( tmax, vg_maxf( v0[1], v1[1] ));
+   tmin = vg_maxf( tmin, vg_minf( v0[2], v1[2] ));
+   tmax = vg_minf( tmax, vg_maxf( v0[2], v1[2] ));
+
+   return tmax >= tmin && tmin < dist && tmax > 0;
+}
+
+static inline void m4x3_lookat( m4x3f m, v3f pos, v3f target, v3f up )
+{
+   v3f dir;
+   v3_sub( target, pos, dir );
+   v3_normalize( dir );
+
+   v3_copy( 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] );
 }
 
 /*
@@ -705,31 +949,35 @@ static inline void m4x3_transform_aabb( m4x3f m, boxf box )
 								{ 0.0f, 1.0f, 0.0f, 0.0f },\
 								{ 0.0f, 0.0f, 1.0f, 0.0f },\
 								{ 0.0f, 0.0f, 0.0f, 1.0f }}
+#define M4X4_ZERO			{{0.0f, 0.0f, 0.0f, 0.0f },\
+								{ 0.0f, 0.0f, 0.0f, 0.0f },\
+								{ 0.0f, 0.0f, 0.0f, 0.0f },\
+								{ 0.0f, 0.0f, 0.0f, 0.0f }}
 
 static void m4x4_projection( m4x4f m, float angle,
-      float ratio, float near, float far )
+      float ratio, float fnear, float ffar )
 {
-   float scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * near,
+   float scale = tanf( angle * 0.5f * VG_PIf / 180.0f ) * fnear,
          r = ratio * scale,
          l = -r,
          t = scale,
          b = -t;
 
-   m[0][0] =  2.0f * near / (r - l); 
+   m[0][0] =  2.0f * fnear / (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][1] =  2.0f * fnear / (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][2] = -(ffar + fnear) / (ffar - fnear); 
    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][2] = -2.0f * ffar * fnear / (ffar - fnear); 
    m[3][3] =  0.0f;
 } 
 
@@ -754,6 +1002,12 @@ static inline void m4x4_identity( m4x4f a )
 	m4x4_copy( id, a );
 }
 
+static inline void m4x4_zero( m4x4f a )
+{
+	m4x4f zero = M4X4_ZERO;
+	m4x4_copy( zero, 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],
@@ -784,6 +1038,75 @@ static inline void m4x4_mul( m4x4f a, m4x4f b, m4x4f d )
   d[3][3] = a03*b30 + a13*b31 + a23*b32 + a33*b33;
 }
 
+static inline void m4x4_mulv( m4x4f m, v4f v, v4f d ) 
+{
+	v4f res;
+  
+	res[0] = m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]*v[3];
+	res[1] = m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]*v[3];
+	res[2] = m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]*v[3];
+	res[3] = m[0][3]*v[0] + m[1][3]*v[1] + m[2][3]*v[2] + m[3][3]*v[3];
+
+	v4_copy( res, d );
+}
+
+static inline void m4x4_inv( m4x4f a, 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],
+         det,
+         t[6];
+
+   t[0] = a22*a33 - a32*a23;
+   t[1] = a21*a33 - a31*a23;
+   t[2] = a21*a32 - a31*a22;
+   t[3] = a20*a33 - a30*a23;
+   t[4] = a20*a32 - a30*a22;
+   t[5] = a20*a31 - a30*a21;
+
+   d[0][0] =  a11*t[0] - a12*t[1] + a13*t[2];
+   d[1][0] =-(a10*t[0] - a12*t[3] + a13*t[4]);
+   d[2][0] =  a10*t[1] - a11*t[3] + a13*t[5];
+   d[3][0] =-(a10*t[2] - a11*t[4] + a12*t[5]);
+
+   d[0][1] =-(a01*t[0] - a02*t[1] + a03*t[2]);
+   d[1][1] =  a00*t[0] - a02*t[3] + a03*t[4];
+   d[2][1] =-(a00*t[1] - a01*t[3] + a03*t[5]);
+   d[3][1] =  a00*t[2] - a01*t[4] + a02*t[5];
+
+   t[0] = a12*a33 - a32*a13;
+   t[1] = a11*a33 - a31*a13;
+   t[2] = a11*a32 - a31*a12;
+   t[3] = a10*a33 - a30*a13;
+   t[4] = a10*a32 - a30*a12;
+   t[5] = a10*a31 - a30*a11;
+
+   d[0][2] =  a01*t[0] - a02*t[1] + a03*t[2];
+   d[1][2] =-(a00*t[0] - a02*t[3] + a03*t[4]);
+   d[2][2] =  a00*t[1] - a01*t[3] + a03*t[5];
+   d[3][2] =-(a00*t[2] - a01*t[4] + a02*t[5]);
+
+   t[0] = a12*a23 - a22*a13;
+   t[1] = a11*a23 - a21*a13;
+   t[2] = a11*a22 - a21*a12;
+   t[3] = a10*a23 - a20*a13;
+   t[4] = a10*a22 - a20*a12;
+   t[5] = a10*a21 - a20*a11;
+
+   d[0][3] =-(a01*t[0] - a02*t[1] + a03*t[2]);
+   d[1][3] =  a00*t[0] - a02*t[3] + a03*t[4];
+   d[2][3] =-(a00*t[1] - a01*t[3] + a03*t[5]);
+   d[3][3] =  a00*t[2] - a01*t[4] + a02*t[5];
+   
+   det = 1.0f / (a00*d[0][0] + a01*d[1][0] + a02*d[2][0] + a03*d[3][0]);
+   v4_muls( d[0], det, d[0] );
+   v4_muls( d[1], det, d[1] );
+   v4_muls( d[2], det, d[2] );
+   v4_muls( d[3], det, d[3] );
+}
+
 /*
  * Planes (double precision)
  */
@@ -856,3 +1179,213 @@ static inline double plane_polarity( double p[4], double a[3] )
 	-(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_nlerp( v4f a, v4f b, float t, v4f d )
+{
+   if( v4_dot(a,b) < 0.0f )
+   {
+      v4_muls( b, -1.0f, d );
+      v4_lerp( a, d, t, d );
+   }
+   else
+      v4_lerp( a, b, t, d );
+
+   q_normalize( d );
+}
+
+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;
+}
+
+static void m3x3_q( m3x3f m, v4f q )
+{
+   float diag, r, rinv;
+
+   diag = m[0][0] + m[1][1] + m[2][2];
+   if( diag >= 0.0f )
+   {
+      r    = sqrtf( 1.0f + diag );
+      rinv = 0.5f / r;
+      q[0] = rinv * (m[1][2] - m[2][1]);
+      q[1] = rinv * (m[2][0] - m[0][2]);
+      q[2] = rinv * (m[0][1] - m[1][0]);
+      q[3] = r    * 0.5f;
+   } 
+   else if( m[0][0] >= m[1][1] && m[0][0] >= m[2][2] )
+   {
+      r    = sqrtf( 1.0f - m[1][1] - m[2][2] + m[0][0] );
+      rinv = 0.5f / r;
+      q[0] = r    * 0.5f;
+      q[1] = rinv * (m[0][1] + m[1][0]);
+      q[2] = rinv * (m[0][2] + m[2][0]);
+      q[3] = rinv * (m[1][2] - m[2][1]);
+   } 
+   else if( m[1][1] >= m[2][2] )
+   {
+      r    = sqrtf( 1.0f - m[0][0] - m[2][2] + m[1][1] );
+      rinv = 0.5f / r;
+      q[0] = rinv * (m[0][1] + m[1][0]);
+      q[1] = r    * 0.5f;
+      q[2] = rinv * (m[1][2] + m[2][1]);
+      q[3] = rinv * (m[2][0] - m[0][2]);
+   } 
+   else 
+   {
+      r    = sqrtf( 1.0f - m[0][0] - m[1][1] + m[2][2] );
+      rinv = 0.5f / r;
+      q[0] = rinv * (m[0][2] + m[2][0]);
+      q[1] = rinv * (m[1][2] + m[2][1]);
+      q[2] = r    * 0.5f;
+      q[3] = rinv * (m[0][1] - m[1][0]);
+   }
+}
+
+static int ray_tri( v3f tri[3], v3f co, v3f dir, float *dist )
+{
+   float const kEpsilon = 0.00001f;
+
+   v3f v0, v1, h, s, q, n;
+   float a,f,u,v,t;
+
+   float *pa = tri[0],
+         *pb = tri[1],
+         *pc = tri[2];
+
+   v3_sub( pb, pa, v0 );
+   v3_sub( pc, pa, v1 );
+   v3_cross( dir, v1, h );
+   v3_cross( v0, v1, n );
+
+   if( v3_dot( n, dir ) > 0.0f ) /* Backface culling */
+      return 0;
+   
+   /* Parralel */
+   a = v3_dot( v0, h );
+   if( a > -kEpsilon && a < kEpsilon )
+      return 0;
+
+   f = 1.0f/a;
+   v3_sub( co, pa, s );
+
+   u = f * v3_dot(s, h);
+   if( u < 0.0f || u > 1.0f )
+      return 0;
+   
+   v3_cross( s, v0, q );
+   v = f * v3_dot( dir, q );
+   if( v < 0.0f || u+v > 1.0f )
+      return 0;
+
+   t = f * v3_dot(v1, q);
+   if( t > kEpsilon )
+   {
+      *dist = t;
+      return 1;
+   }
+   else return 0;
+}
+
+static inline float vg_randf(void)
+{
+   return (float)rand()/(float)(RAND_MAX);
+}
+
+static inline void vg_rand_dir(v3f dir)
+{
+   dir[0] = vg_randf();
+   dir[1] = vg_randf();
+   dir[2] = vg_randf();
+
+   v3_muls( dir, 2.0f, dir );
+   v3_sub( dir, (v3f){1.0f,1.0f,1.0f}, dir );
+
+   v3_normalize( dir );
+}
+
+static inline void vg_rand_sphere( v3f co )
+{
+   vg_rand_dir(co);
+   v3_muls( co, cbrtf( vg_randf() ), co );
+}
+
+static inline int vg_randint(int max)
+{
+   return rand()%max;
+}
+
+static void eval_bezier_time( v3f p0, v3f p1, v3f h0, v3f h1, float t, v3f p )
+{
+   float tt = t*t,
+         ttt = tt*t;
+
+   v3_muls( p1, ttt, p );
+   v3_muladds( p, h1, 3.0f*tt  -3.0f*ttt, p );
+   v3_muladds( p, h0, 3.0f*ttt -6.0f*tt  +3.0f*t, p );
+   v3_muladds( p, p0, 3.0f*tt  -ttt -3.0f*t +1.0f, p );
+}
+
+#endif /* VG_M_H */