C1 modeling with A-patches from rational trivariate functions

We approximate a manifold triangulation in IR using smooth implicit algebraic surface patches, which we call A-patches. Here each A-patch is a real iso-contour of a trivariate rational function de ned within a tetrahedron. The rational trivariate function provides increased degrees of freedom so that the number of surface patches needed for free-form shape modeling is signi cantly reduced compared to earlier similar approaches. Furthermore, the surface patches have quadratic precision, that is they exactly recover quadratic surfaces. We give conditions under which a C smooth and single sheeted surface patch is isolated from the multiple sheets.