predicate_insphere

float  predicate_insphere(vector a, vector b, vector c, vector d, vector e)

Given 4 points a, b, c, and d in 3D space, return a positive value if e is inside the circumsphere of the tetrahedron abcd, a negative value if e is outside, and zero if e lies exactly on the circumsphere.

More precisely, this function computes the determinant of the matrix

[a_x a_y a_z a^2 1; b_x b_y b_z b^2 1; c_x c_y c_z c^2 1; d_x d_y d_z d^2 1; e_x
e_y e_z e^2 1]

…with a guaranteed correct sign, where a^2, b^2, c^2, d^2 and e^2 are the squared lengths of the corresponding input vectors.