Filling method

A filling method is a way of defining the interior of a finite non-skew polytope that generally self-intersects. Filling methods are important for the visualization of polytopes.

Filling methods are defined inductively, as the interior of an n-polytope requires defining the interiors of its elements. For the sake of filling methods, the interior of a point is defined to be its location.

Several filling methods have been defined:


 * Binary filling: draw a ray starting at a point P. If, not including P, the ray intersects with the interiors of n elements, P is in the interior iff n is even.
 * Solid filling: P is in the interior iff there does not exist a ray starting at P that, not including P, does not intersect with the interiors of any elements.