Algorithms for Complex Shapes with Certified Numerics and Topology Envelope Surfaces
نویسندگان
چکیده
We construct a class of envelope surfaces in R, more precisely envelopes of balls. An envelopesurface is a closed C (tangent continuous) manifold wrapping tightly around the union of aset of balls. Such a manifold is useful in modeling since the union of a finite set of balls canapproximate any closed smooth manifold arbitrarily close.The theory of envelope surfaces generalizes the theoretical framework of skin surfaces [5]developed by Edelsbrunner for molecular modeling. However, envelope surfaces are more flexible:where a skin surface is controlled by a single parameter, envelope surfaces can be adapted locally.We show that a special subset of envelope surfaces is piecewise quadratic and derive condi-tions under which the envelope surface is C. These conditions can be verified automatically.We give examples of envelope surfaces to demonstrate their flexibility in surface design.
منابع مشابه
ACS Algorithms for Complex Shapes with Certified Numerics and Topology Application of algebraic tools to CSG operations on curves and surfaces
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