Trivariate Biharmonic B‐Splines

Simple item page
dc.contributor.authorHou, Feien_US
dc.contributor.authorQin, Hongen_US
dc.contributor.authorHao, Aiminen_US
dc.contributor.editorDeussen, Oliver and Zhang, Hao (Richard)en_US
dc.date.accessioned2015-10-12T13:32:45Z
dc.date.available2015-10-12T13:32:45Z
dc.date.issued2015en_US
dc.description.abstract.In this paper, we formulate a novel trivariate biharmonic B‐spline defined over bounded volumetric domain. The properties of bi‐Laplacian have been well investigated, but the straightforward generalization from bivariate case to trivariate one gives rise to unsatisfactory discretization, due to the dramatically uneven distribution of neighbouring knots in 3D. To ameliorate, our original idea is to extend the bivariate biharmonic B‐spline to the trivariate one with novel formulations based on quadratic programming, approximating the properties of localization and partition of unity. And we design a novel discrete biharmonic operator which is optimized more robustly for a specific set of functions for unevenly sampled knots compared with previous methods. Our experiments demonstrate that our 3D discrete biharmonic operators are robust for unevenly distributed knots and illustrate that our algorithm is superior to previous algorithms.en_US
dc.description.number6en_US
dc.description.sectionheadersArticlesen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume34en_US
dc.identifier.doi10.1111/cgf.12516en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12516en_US
dc.publisherCopyright © 2015 The Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectbiharmonic b‐splineen_US
dc.subjectgreen's functionen_US
dc.subjectquadratic programmingen_US
dc.subjectI.3.5 [Computer Graphics]: Computational Geometry and Object Modelling—Splinesen_US
dc.titleTrivariate Biharmonic B‐Splinesen_US
Files
Collections
34-Issue 6