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Polycube splines
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DOI：10.1016/j.cad.2008.01.012.png)
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Abstract
En 中文
This paper proposes a new concept of polycube splines and develops novel modeling techniques for using file polycube splines in solid Modeling and Shape computing. Polycube splines are essentially a novel variant of manifold splines which are built Upon the polycube map. serving as its parametric domain. Our rationale for defining spline surfaces over polycubes is that polycubes have rectangular structures everywhere over their domains, except a very small number of corner points. The boundary of polycubes can he naturally decomposed into a set of regular structures, Which facilitate tensor-product surface definition, GPU-centric geometric computing, and image-based geometric processing. We develop algorithms to construct polycube maps, and show that the introduced polycube map naturally induces the affine structure with a finite number of extraordinary points. Besides its intrinsic rectangular structure, the polycube map may approximate any original scanned data-set with a very low geometric distortion, so our method for building polycube splines is both natural and necessary, as its parametric domain call mimic the geometry of modeled objects in a topologically correct and geometrically meaningful manner. We design a new data structure that facilitates the intuitive and rapid construction of polycube splines in this paper. We demonstrate the polycube splines, with applications ill surface reconstruction and shape computing. (C) 2008 Elsevier Ltd. All rights reserved.
Keywords:
manifold splines
T-splines
affine structure
conformal structure
holomorphic 1-form
harmonic map
discrete Ricci flow
polycube map
Journal
C
IF:
3.1
Papers:
3.1K
Citations:
6.4K