Function s2::predicates::robust_sign

pub fn robust_sign(a: &Point, b: &Point, c: &Point) -> Direction

robust_sign returns a Direction representing the ordering of the points. CounterClockwise is returned if the points are in counter-clockwise order, Clockwise for clockwise, and Indeterminate if any two points are the same (collinear), or the sign could not completely be determined.

This function has additional logic to make sure that the above properties hold even when the three points are coplanar, and to deal with the limitations of floating-point arithmetic.

RobustSign satisfies the following conditions:

(1) RobustSign(a,b,c) == Indeterminate if and only if a == b, b == c, or c == a (2) RobustSign(b,c,a) == RobustSign(a,b,c) for all a,b,c (3) RobustSign(c,b,a) == -RobustSign(a,b,c) for all a,b,c

In other words:

(1) The result is Indeterminate if and only if two points are the same. (2) Rotating the order of the arguments does not affect the result. (3) Exchanging any two arguments inverts the result.

On the other hand, note that it is not true in general that RobustSign(-a,b,c) == -RobustSign(a,b,c), or any similar identities involving antipodal points.