predicate_incircle

float  predicate_incircle(vector2 a, vector2 b, vector2 c, vector2 d)

Given 3 points a, b, and c on the plane, return a positive value if d is inside the circumcircle of the triangle abc, a negative value if d is outside, and zero if d is exactly on the circumcircle.

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

[a_x a_y a^2 1; b_x b_y b^2 1; c_x c_y c^2 1; d_x d_y d^2 1]

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