CCV Publication Abstract
C1 Modeling with A-patches from Rational Trivariate Functions
G. Xu, C. Bajaj, H. Huang
Computer Aided Geometric Design, 18:3(2001), 221-243
We approximate a manifold triangulation in IR3 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 the C1 smooth and single sheeted surface patch is isolated from the multiple sheets. (pdf)
Figure 1: Edge patches and face patches for a head. Figure 2: Rational A-patch construction for a head.
Figures 1 and 2 show a smooth A-patch construction model of a human head. In this example, the number 3 and 4 coefficients in the construction of the function are given by the default choice of section 4.2. In figure 1, edge patches and face patches are shown separately by different shading, to depict the topology of the input triangulation as well as its adaptivity. The higher curved regions have more triangles. If the input triangulation is relatively flat at an edge, then the edge patch is correspondingly degenerate.