C-1 modeling with A-patches from rational trivariate functions

We approximate a manifold triangulation in R-3 using smooth implicit algebr aic surface patches. which we call A-patches. Here each A-patch is a real i so-contour of a trivariate rational function defined within a tetrahedron. The rational trivariate function provides increased degrees of freedom so t hat the number of surface patches needed for free-form shape modeling is si gnificantly reduced compared to earlier similar approaches. Furthermore, th e surface patches have quadratic precision. that is they exactly recover qu adratic surfaces. We give conditions under which a C-1 smooth and single sh eeted surface patch is isolated from the multiple sheets. (C) 2001 Elsevier Science B.V. All rights reserved.