X-Git-Url: https://harrygodden.com/git/?a=blobdiff_plain;f=vg%2Fvg_m.h;fp=vg%2Fvg_m.h;h=577138fb12e575698d1c941e15958f05a898beeb;hb=6836e834f8db725e08015a98401f2be97e5b9849;hp=0000000000000000000000000000000000000000;hpb=b5740880fe3ffe59546bb80173ad3a6e1312648e;p=vg.git

diff --git a/vg/vg_m.h b/vg/vg_m.h
new file mode 100644
index 0000000..577138f
--- /dev/null
+++ b/vg/vg_m.h
@@ -0,0 +1,733 @@
+// Copyright (C) 2021 Harry Godden (hgn) - All Rights Reserved
+
+// Util
+// ==================================================================================================================
+
+#define VG_PIf  3.14159265358979323846264338327950288f
+#define VG_TAUf 6.28318530717958647692528676655900576f
+
+// Simple min/max replacements
+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 ) );
+}
+
+#define VG_MIN( A, B ) ((A)<(B)?(A):(B))
+#define VG_MAX( A, B ) ((A)>(B)?(A):(B))
+
+// Hopefully deprecate this!!
+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;
+}
+
+// Convert degrees to radians
+static inline float vg_rad( float deg )
+{
+	return deg * VG_PIf / 180.0f;
+}
+
+// Vector 2
+// ==================================================================================================================
+
+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_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]);
+}
+
+// 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 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;
+}
+
+// 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;
+}
+
+// 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_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 );
+}
+
+// Warning: These functions are unoptimized..
+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] } );
+}
+
+// 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])
+	;
+}