SGP05: Eurographics Symposium on Geometry Processing
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Browsing SGP05: Eurographics Symposium on Geometry Processing by Subject "Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling"
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Item Modeling with Simplicial Diffeomorphisms(The Eurographics Association, 2005) Velho, Luiz; Mathieu Desbrun and Helmut PottmannIn this paper we introduce a new framework for geometric modeling that combines implicit and parametric surface representations with volumetric warpings. The framework is based on dynamic, adaptive simplicial decompositions of the embedding space and conforming piecewise diffeomorphisms.Item Reconstruction of Solid Models from Oriented Point Sets(The Eurographics Association, 2005) Kazhdan, Michael; Mathieu Desbrun and Helmut PottmannIn this paper we present a novel approach to the surface reconstruction problem that takes as its input an oriented point set and returns a solid, water-tight model. The idea of our approach is to use Stokes' Theorem to compute the characteristic function of the solid model (the function that is equal to one inside the model and zero outside of it). Specifically, we provide an efficient method for computing the Fourier coefficients of the characteristic function using only the surface samples and normals, we compute the inverse Fourier transform to get back the characteristic function, and we use iso-surfacing techniques to extract the boundary of the solid model. The advantage of our approach is that it provides an automatic, simple, and efficient method for computing the solid model represented by a point set without requiring the establishment of adjacency relations between samples or iteratively solving large systems of linear equations. Furthermore, our approach can be directly applied to models with holes and cracks, providing a method for hole-filling and zippering of disconnected polygonal models.Item Swept Volumes of many Poses(The Eurographics Association, 2005) Wallner, Johannes; Yang, Qinmin; Mathieu Desbrun and Helmut PottmannWe consider the swept volume A(X) of a rigid body X which assumes a general set A of positions. A special case of this is a one-parameter motion of X, where the set of poses is curve-like. Here we consider a full-dimensional subset A of the motion group. Such a set of poses can be seen as the tolerance zone of an imprecisely defined pose. Alternatively, a set of poses may be obtained by by measurements or simulation. We analyze the geometric properties of such sets of poses and give algorithms for computing the boundary deltaA(X) in the case that A is a discrete pose cloud. The dimension of the problem, which equals six a priori, is reduced to two.