Shape-Up: Shaping Discrete Geometry with Projections

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dc.contributor.authorBouaziz, Sofienen_US
dc.contributor.authorDeuss, Marioen_US
dc.contributor.authorSchwartzburg, Yuliyen_US
dc.contributor.authorWeise, Thibauten_US
dc.contributor.authorPauly, Marken_US
dc.contributor.editorEitan Grinspun and Niloy Mitraen_US
dc.date.accessioned2015-02-28T07:44:10Z
dc.date.available2015-02-28T07:44:10Z
dc.date.issued2012en_US
dc.description.abstractWe introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one-ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least-squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape-preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state-of-the-art methods.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume31
dc.identifier.doi10.1111/j.1467-8659.2012.03171.x
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2012.03171.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectComputational Geometry and Object Modelingen_US
dc.subjectGeometric algorithmsen_US
dc.subjectlanguagesen_US
dc.subjectand systemsen_US
dc.titleShape-Up: Shaping Discrete Geometry with Projectionsen_US
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31-Issue 5
SGP12: Eurographics Symposium on Geometry Processing