Shape representation using trihedral mesh projections

Abstract

This paper explores the possibility of approximating a surface by a trihedral polygonal mesh plus some triangles at strategic places. The presented approximation has several attractive properties. It turns out that the Z-coordinates of the vertices are completely governed by the Z-coordinates assigned to four selected ones. This allows describing the spatial polygonal mesh with just its 2D projection plus the heights of four vertices. As a consequence, these projections essentially capture the “spatial meaning” of the given surface, in the sense that, whatever spatial interpretations are drawn from them, they all exhibit the same shape, up to some trivial ambiguities.