predicate_orient3d

float  predicate_orient3d(vector a, vector b, vector c, vector d)

Given 3 points a, b and c in space, return a negative value if d is behind the plane defined by the triangle abc (with right hand rule winding order), a positive value if its in front of the plane, and zero if points a, b, c and d are coplanar.

More precisely, this function computes the determinant of the matrix:

[a_x a_y a_z 1; b_x b_y b_z 1; c_x c_y c_z 1; d_x d_y d_z 1]

…with a guaranteed correct sign.