Graceful planes and thin tunnel-free meshes

Abstract

In this paper we present art approach to describe polyhedra by meshes of discrete triangles. The study is based on the theory of arithmetic geometry [10]. We introduce a new class of discrete planes (respectively lines) which we call graceful planes (respectively graceful lines). We use naive planes and graceful lines to obtain as thin as possible triangular mesh discretization admitting an analytical description. The interiors of the triangles are portions of naive planes. while the sides are graceful lines.