A Uni ed Approach for Hierarchical Adaptive Tesselation of Surfaces

The polygonization, or tesselation, of surfaces is a classical problem that has many practical applications in computer graphics and geometric modeling. The problem consists in computing a piecewise linear approximation for a smooth surface described either by parametric or implicit functions. A polygonal mesh is the one of the simplest forms of surface description and therefore is the representation of choice in the implementation of a large number of algorithms. Moreover, existing graphics systems (e.g., OpenGL) have special support for polygonal primitives, specially for triangular meshes. Thus, despite the existence of more sophisticated forms for surface description (e.g., B ezier, B-splines, NURBS, etc.), there is always a need to represent surfaces in polygonal form.