| The main impediments to the widespread use of implicit surfaces for geometric modeling are multiple sheets, self-intersections and several other undesirable singularities. Our A-patch technique provides simple ways to guarantee that the constructed implicit surface is single-sheeted and free of undesirable singularities. The technique uses the zero contouring surfaces of trivariate Bernstein-Bezier polynomials to construct a piecewise smooth surface, cubic for ;An A-patch is easy to modify by manipulating the coefficients. The constraints imposed on an A-patch also make it easy to be polygonized quickly. We discuss schemes to edit A-patch models interactively as well as schemes to polygonize an A-patch surface quickly into a triangulated mesh.;The A-patch technique, combined with the physically-based modeling technique, is also suitable for free-form surface design. Most of the existing surface representations fail to support interactive design efficiently and intuitively. Among a few exceptions is the physically-based modeling technique, in which a geometric shape is modeled as an elastic object so that a user can modify it by applying virtual forces. We have developed an elastic model built on top of the A-patch representation. The optimization of the energy of an A-patch is no more complicated than a quadratic programming problem, which dramatically reduces the computational overhead in general physically based methods. |
