Fast Planar Harmonic Deformations with Alternating Tangential Projections

dc.contributor.authorHefetz, Eden Fedidaen_US
dc.contributor.authorChien, Edwarden_US
dc.contributor.authorWeber, Ofiren_US
dc.contributor.editorBærentzen, Jakob Andreas and Hildebrandt, Klausen_US
dc.date.accessioned2017-07-02T17:37:55Z
dc.date.available2017-07-02T17:37:55Z
dc.date.issued2017
dc.description.abstractWe present a planar harmonic cage-based deformation method with local injectivity and bounded distortion guarantees, that is significantly faster than state-of-the-art methods with similar guarantees, and allows for real-time interaction. With a convex proxy for a near-convex characterization of the bounded distortion harmonic mapping space from [LW16], we utilize a modified alternating projection method (referred to as ATP) to project to this proxy. ATP draws inspiration from [KABL15] and restricts every other projection to lie in a tangential hyperplane. In contrast to [KABL15], our convex setting allows us to show that ATP is provably convergent (and is locally injective). Compared to the standard alternating projection method, it demonstrates superior convergence in fewer iterations, and it is also embarrassingly parallel, allowing for straightforward GPU implementation. Both of these factors combine to result in unprecedented speed. The convergence proof generalizes to arbitrary pairs of intersecting convex sets, suggesting potential use in other applications. Additional theoretical results sharpen the near-convex characterization that we use and demonstrate that it is homeomorphic to the bounded distortion harmonic mapping space (instead of merely being bijective).en_US
dc.description.number5
dc.description.sectionheadersShape Analysis and Variation
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume36
dc.identifier.doi10.1111/cgf.13255
dc.identifier.issn1467-8659
dc.identifier.pages175-188
dc.identifier.urihttps://doi.org/10.1111/cgf.13255
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13255
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectI.3.5 [Computer Graphics]
dc.subjectComputational Geometry and Object Modeling
dc.subjectGeometric algorithms
dc.subjectlanguages
dc.subjectand systems
dc.subjectHierarchy and geometric transformations
dc.subjectI.3.7 [Computer Graphics]
dc.subjectThree Dimensional Graphics and Realism
dc.subjectAnimation G.1.6 [Numerical Analysis]
dc.subjectOptimization
dc.subjectConvex programming
dc.titleFast Planar Harmonic Deformations with Alternating Tangential Projectionsen_US
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