Interactive deformable modeling with A-patches
Abstract
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 $C\sp1$ and quintic for $C\sp2$. We call such iso-splines A-patches, where "A" stands for algebraic. We have designed different algorithms to construct smooth A-patch surfaces that interpolate or approximate scattered 3D point data or simple polyhedra of arbitrary topology. 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.
Degree
Ph.D.
Advisors
Bajaj, Purdue University.
Subject Area
Computer science|Mechanical engineering|Mathematics
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