Interactive Shape Control and Rapid Display of A- patches
Chandrajit Bajaj, Jindon Chen, Guoliang Xu · 1994
A-patches are implicit surfaces in Bernstein-B'ezier(BB) form that are smooth and singlesheeted. In this paper, we present algorithms to utilize the extra degrees of freedom of each A-patch for local shape control. A ray shooting scheme is also given to rapidly generate polygonal approximations of A-patches for graphic display. A distributed implementation of this scheme gives nice "real time" performance on rendering the A-patches to support interactive shape control. Keywords: algebraic surface, free form surface, interactive techniques, smoothing, spline and piecewise surface, rendering, polygonization, computer-aided geometric design, solid modeling. 1 Introduction The A-patch is a smooth and single-sheeted zero-contour patch of a trivariate polynomial in Bernstein-B'ezier(BB) form defined within a tetrahedron[BCX94a], where the "A" stands for algebraic. Solutions to the problem of constructing a C 1 mesh of implicit algebraic patches based on polyhedron P have been given by [...