C-1 modeling with A-patches from rational trivariate functions
We approximate a manifold triangulation in R-3 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 defined 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 significantly 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-1 smooth and single sheeted surface patch is isolated from the multiple sheets. (C) 2001 Elsevier Science B.V. All rights reserved.
triangulation algebraic surface rational a-patch surface fit