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This paper describes a new technique that combines numerical optimization methods with triangulation methods for generating mathematical representations of solids from 3D point data. The solid representation obtained takes the form of an algebraic function whose level surface closely approximates the surface described by the data, The algebraic function is… (More)

This paper presents a multilevel algorithm to accelerate the numerical solution of thin shell finite element problems de-scribed by subdivision surfaces. Subdivision surfaces have become a widely used geometric representation for general curved three dimensional boundary models and thin shells as they provide a compact and robust framework for mod-eling 3D… (More)

The skeleton is a lower-dimensional geometric abstraction that is useful for performing a number of important geometric operations on solid models. In this paper we develop skeleton-based algorithms that demonstrat,e the utility of the skeleton in addressing: (1) 1 evel-of-detail control, the generation of hierarchical representations that preserve overall… (More)

This paper explores the concept of using skeletons as the basis for constructing a solid-editing system. Skeletal data (i.e., the skeleton and the associated maximal sphere radii) offers a valid solid representation scheme, and we examine the capability of the skeletal representation to support shape editing operations. In addition to general discussion of… (More)

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