Approximating Triangular Meshes by Implicit, Multi-Sided Surfaces

The I-patch is a multi-sided surface representation, defined as combination of implicit ribbon and bounding surfaces, whose pairwise intersections determine the natural boundaries patch. Our goal to show how collection smoothly connected I-patches can be used approximate triangular meshes. We start from coarse, user-defined vertex graph which specifies an initial subdivision surface. Based on this, we create ribbons that tightly fit mesh along its edges in both positional tangential sense, then optimize free parameters patch better interior. If surfaces are not sufficiently accurate, network needs refined; here exploit construction naturally supports T-nodes. also describe normalization method nicely approximates Euclidean distance field, efficiently evaluated. capabilities limitations approach analyzed through several examples.