Optimization Techniques for Approximation with Subdivision Surfaces

dc.contributor.authorMarinov, M.en_US
dc.contributor.authorKobbelt, L.en_US
dc.contributor.editorGershon Elber and Nicholas Patrikalakis and Pere Bruneten_US
dc.date.accessioned2016-02-17T18:02:45Z
dc.date.available2016-02-17T18:02:45Z
dc.date.issued2004en_US
dc.description.abstractWe present a method for scattered data approximation with subdivision surfaces which actually uses the true representation of the limit surface as a linear combination of smooth basis functions associated with the control vertices. This is unlike previous techniques which used only piecewise linear approximations of the limit surface. By this we can assign arbitrary parameterizations to the given sample points, including those generated by parameter correction. We present a robust and fast algorithm for exact closest point search on Loop surfaces by combining Newton iteration and non-linear minimization. Based on this we perform unconditionally convergent parameter correction to optimize the approximation with respect to the L2 metric and thus we make a well-established scattered data tting technique which has been available before only for B-spline surfaces, applicable to subdivision surfaces. Further we exploit the fact that the control mesh of a subdivision surface can have arbitrary connectivity to reduce the L1 error up to a certain user-de ned tolerance by adaptively restructuring the control mesh. By employing iterative least squares solvers, we achieve acceptable running times even for large amounts of data and we obtain high quality approximations by surfaces with relatively low control mesh complexity compared to the number of sample points. Since we are using plain subdivision surfaces, there is no need for multiresolution detail coef cients and we do not have to deal with the additional overhead in data and computational complexity associated with them.en_US
dc.description.sectionheadersSubdivision Schemesen_US
dc.description.seriesinformationSolid Modelingen_US
dc.identifier.doi10.2312/sm.20041382en_US
dc.identifier.isbn3-905673-55-Xen_US
dc.identifier.issn1811-7783en_US
dc.identifier.pages113-122en_US
dc.identifier.urihttps://doi.org/10.2312/sm.20041382en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectI.3.5 [Computer Graphics]en_US
dc.subjectCurveen_US
dc.subjectsurfaceen_US
dc.subjectsoliden_US
dc.subjectand object representationsen_US
dc.titleOptimization Techniques for Approximation with Subdivision Surfacesen_US
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