Multi-scale Geometric Modeling of Ambiguous Shapes with Toleranced Balls and Compoundly Weighted a-shapes

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dc.contributor.authorFrederic Cazalsen_US
dc.contributor.authorTom Dreyfusen_US
dc.date.accessioned2015-02-23T17:15:43Z
dc.date.available2015-02-23T17:15:43Z
dc.date.issued2010en_US
dc.description.abstractDealing with ambiguous data is a challenge in Science in general and geometry processing in particular. One route of choice to extract information from such data consists of replacing the ambiguous input by a continuum, typically a one-parameter family, so as to mine stable geometric and topological features within this family. This work follows this spirit and introduces a novel framework to handle 3D ambiguous geometric data which are naturally modeled by balls. First, we introduce toleranced balls to model ambiguous geometric objects. A toleranced ball consists of two concentric balls, and interpolating between their radii provides a way to explore a range of possible geometries. We propose to model an ambiguous shape by a collection of toleranced balls, and show that the aforementioned radius interpolation is tantamount to the growth process associated with an additively-multiplicatively weighted Voronoi diagram (also called compoundly weighted or CW). Second and third, we investigate properties of the CW diagram and the associated CW a-complex, which provides a filtration called the lambda-complex. Fourth, we sketch a naive algorithm to compute the CW VD. Finally, we use the lambdal-complex to assess the quality of models of large protein assemblies, as these models inherently feature ambiguities.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume29en_US
dc.identifier.doi10.1111/j.1467-8659.2010.01780.xen_US
dc.identifier.pages1713-1722en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1713-1722en_US
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/CGF.v29i5pp1713-1722
dc.titleMulti-scale Geometric Modeling of Ambiguous Shapes with Toleranced Balls and Compoundly Weighted a-shapesen_US
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29-Issue 5
SGP10: Eurographics Symposium on Geometry Processing