Tunnel-Free Supercover 3D Polygons and Polyhedra

Abstract

A new discrete 3D line and 3D polygon, called Supercover 3D line and Supercover 3D polygon, are introduced. Analytical definitions are provided. The Supercover 3D polygon is a tunnel free plane segment defined by vertices and edges. An edge is a Supercover 3D line segment. Two different polygons can share a common edge and if they do, the union of both polygons is tunnel free. This definition of discrete polygons has the "most" properties in common with the continuous polygons. It is particularly interesting for modeling of discrete scenes, especially using tunnel-free discrete polyhedra. Algorithms for computing Supercover 3D Lines and Polygons are given and illustrated.