void barycentric ( const GsPnt2& p1, const GsPnt2& p2, const GsPnt2& p3, const GsPnt2& p,
float& u, float& v, float& w )
{
# define DET3(a,b,c,d,e,f,g,h,i) a*e*i +b*f*g +d*h*c -c*e*g -b*d*i -a*f*h
float A = DET3 ( p1.x, p2.x, p3.x, p1.y, p2.y, p3.y, 1, 1, 1 );
float A1 = DET3 ( p.x, p2.x, p3.x, p.y, p2.y, p3.y, 1, 1, 1 );
float A2 = DET3 ( p1.x, p.x, p3.x, p1.y, p.y, p3.y, 1, 1, 1 );
//float A3 = DET3 ( p1.x, p2.x, p.x, p1.y, p2.y, p.y, 1, 1, 1 );
# undef DET3
u = A1/A;
v = A2/A;
w = 1.0f-u-v; // == A3/A;
}
mat4 inverse( const mat4& m0 )
{
SLMATH_VEC_ASSERT( check(m0) );
const float* const mp = &m0[0][0];
const float a = mp[0]; const float b = mp[1]; const float c = mp[2]; const float d = mp[3];
const float e = mp[4]; const float f = mp[5]; const float g = mp[6]; const float h = mp[7];
const float i = mp[8]; const float j = mp[9]; const float k = mp[10]; const float l = mp[11];
const float m = mp[12]; const float n = mp[13]; const float o = mp[14]; const float p = mp[15];
const float min_a = DET3(f,g,h,j,k,l,n,o,p);
const float min_b = DET3(e,g,h,i,k,l,m,o,p);
const float min_c = DET3(e,f,h,i,j,l,m,n,p);
const float min_d = DET3(e,f,g,i,j,k,m,n,o);
const float det_m = a*min_a - b*min_b + c*min_c - d*min_d;
SLMATH_VEC_ASSERT( det_m > FLT_MIN || det_m < -FLT_MIN ); // invertible?
mat4 res;
res[0][0] = min_a;
res[1][0] = -min_b;
res[2][0] = min_c;
res[3][0] = -min_d;
res[0][1] = -DET3(b,c,d,j,k,l,n,o,p);
res[1][1] = DET3(a,c,d,i,k,l,m,o,p);
res[2][1] = -DET3(a,b,d,i,j,l,m,n,p);
res[3][1] = DET3(a,b,c,i,j,k,m,n,o);
res[0][2] = DET3(b,c,d,f,g,h,n,o,p);
res[1][2] = -DET3(a,c,d,e,g,h,m,o,p);
res[2][2] = DET3(a,b,d,e,f,h,m,n,p);
res[3][2] = -DET3(a,b,c,e,f,g,m,n,o);
res[0][3] = -DET3(b,c,d,f,g,h,j,k,l);
res[1][3] = DET3(a,c,d,e,g,h,i,k,l);
res[2][3] = -DET3(a,b,d,e,f,h,i,j,l);
res[3][3] = DET3(a,b,c,e,f,g,i,j,k);
return res * (1.f/det_m);
/*
res *= (1.f/det_m);
mat4 res2;
res2[0][0] = m0[1][2]*m0[2][3]*m0[3][1] - m0[1][3]*m0[2][2]*m0[3][1] + m0[1][3]*m0[2][1]*m0[3][2] - m0[1][1]*m0[2][3]*m0[3][2] - m0[1][2]*m0[2][1]*m0[3][3] + m0[1][1]*m0[2][2]*m0[3][3];
res2[0][1] = m0[0][3]*m0[2][2]*m0[3][1] - m0[0][2]*m0[2][3]*m0[3][1] - m0[0][3]*m0[2][1]*m0[3][2] + m0[0][1]*m0[2][3]*m0[3][2] + m0[0][2]*m0[2][1]*m0[3][3] - m0[0][1]*m0[2][2]*m0[3][3];
res2[0][2] = m0[0][2]*m0[1][3]*m0[3][1] - m0[0][3]*m0[1][2]*m0[3][1] + m0[0][3]*m0[1][1]*m0[3][2] - m0[0][1]*m0[1][3]*m0[3][2] - m0[0][2]*m0[1][1]*m0[3][3] + m0[0][1]*m0[1][2]*m0[3][3];
res2[0][3] = m0[0][3]*m0[1][2]*m0[2][1] - m0[0][2]*m0[1][3]*m0[2][1] - m0[0][3]*m0[1][1]*m0[2][2] + m0[0][1]*m0[1][3]*m0[2][2] + m0[0][2]*m0[1][1]*m0[2][3] - m0[0][1]*m0[1][2]*m0[2][3];
res2[1][0] = m0[1][3]*m0[2][2]*m0[3][0] - m0[1][2]*m0[2][3]*m0[3][0] - m0[1][3]*m0[2][0]*m0[3][2] + m0[1][0]*m0[2][3]*m0[3][2] + m0[1][2]*m0[2][0]*m0[3][3] - m0[1][0]*m0[2][2]*m0[3][3];
res2[1][1] = m0[0][2]*m0[2][3]*m0[3][0] - m0[0][3]*m0[2][2]*m0[3][0] + m0[0][3]*m0[2][0]*m0[3][2] - m0[0][0]*m0[2][3]*m0[3][2] - m0[0][2]*m0[2][0]*m0[3][3] + m0[0][0]*m0[2][2]*m0[3][3];
res2[1][2] = m0[0][3]*m0[1][2]*m0[3][0] - m0[0][2]*m0[1][3]*m0[3][0] - m0[0][3]*m0[1][0]*m0[3][2] + m0[0][0]*m0[1][3]*m0[3][2] + m0[0][2]*m0[1][0]*m0[3][3] - m0[0][0]*m0[1][2]*m0[3][3];
res2[1][3] = m0[0][2]*m0[1][3]*m0[2][0] - m0[0][3]*m0[1][2]*m0[2][0] + m0[0][3]*m0[1][0]*m0[2][2] - m0[0][0]*m0[1][3]*m0[2][2] - m0[0][2]*m0[1][0]*m0[2][3] + m0[0][0]*m0[1][2]*m0[2][3];
res2[2][0] = m0[1][1]*m0[2][3]*m0[3][0] - m0[1][3]*m0[2][1]*m0[3][0] + m0[1][3]*m0[2][0]*m0[3][1] - m0[1][0]*m0[2][3]*m0[3][1] - m0[1][1]*m0[2][0]*m0[3][3] + m0[1][0]*m0[2][1]*m0[3][3];
res2[2][1] = m0[0][3]*m0[2][1]*m0[3][0] - m0[0][1]*m0[2][3]*m0[3][0] - m0[0][3]*m0[2][0]*m0[3][1] + m0[0][0]*m0[2][3]*m0[3][1] + m0[0][1]*m0[2][0]*m0[3][3] - m0[0][0]*m0[2][1]*m0[3][3];
res2[2][2] = m0[0][1]*m0[1][3]*m0[3][0] - m0[0][3]*m0[1][1]*m0[3][0] + m0[0][3]*m0[1][0]*m0[3][1] - m0[0][0]*m0[1][3]*m0[3][1] - m0[0][1]*m0[1][0]*m0[3][3] + m0[0][0]*m0[1][1]*m0[3][3];
res2[2][3] = m0[0][3]*m0[1][1]*m0[2][0] - m0[0][1]*m0[1][3]*m0[2][0] - m0[0][3]*m0[1][0]*m0[2][1] + m0[0][0]*m0[1][3]*m0[2][1] + m0[0][1]*m0[1][0]*m0[2][3] - m0[0][0]*m0[1][1]*m0[2][3];
res2[3][0] = m0[1][2]*m0[2][1]*m0[3][0] - m0[1][1]*m0[2][2]*m0[3][0] - m0[1][2]*m0[2][0]*m0[3][1] + m0[1][0]*m0[2][2]*m0[3][1] + m0[1][1]*m0[2][0]*m0[3][2] - m0[1][0]*m0[2][1]*m0[3][2];
res2[3][1] = m0[0][1]*m0[2][2]*m0[3][0] - m0[0][2]*m0[2][1]*m0[3][0] + m0[0][2]*m0[2][0]*m0[3][1] - m0[0][0]*m0[2][2]*m0[3][1] - m0[0][1]*m0[2][0]*m0[3][2] + m0[0][0]*m0[2][1]*m0[3][2];
res2[3][2] = m0[0][2]*m0[1][1]*m0[3][0] - m0[0][1]*m0[1][2]*m0[3][0] - m0[0][2]*m0[1][0]*m0[3][1] + m0[0][0]*m0[1][2]*m0[3][1] + m0[0][1]*m0[1][0]*m0[3][2] - m0[0][0]*m0[1][1]*m0[3][2];
res2[3][3] = m0[0][1]*m0[1][2]*m0[2][0] - m0[0][2]*m0[1][1]*m0[2][0] + m0[0][2]*m0[1][0]*m0[2][1] - m0[0][0]*m0[1][2]*m0[2][1] - m0[0][1]*m0[1][0]*m0[2][2] + m0[0][0]*m0[1][1]*m0[2][2];
res2 *= 1.f/det_m;
mat4 dres = res2-res;
float diff = length(dres[0])+length(dres[1])+length(dres[2])+length(dres[3]);
SLMATH_VEC_ASSERT( diff < 1e-6f );
return res;
*/
}
