Piecewise Linear Mapping Optimization Based on the Complex View

dc.contributor.authorGolla, Björnen_US
dc.contributor.authorSeidel, Hans-Peteren_US
dc.contributor.authorChen, Renjieen_US
dc.contributor.editorFu, Hongbo and Ghosh, Abhijeet and Kopf, Johannesen_US
dc.date.accessioned2018-10-07T14:59:19Z
dc.date.available2018-10-07T14:59:19Z
dc.date.issued2018
dc.description.abstractWe present an efficient modified Newton iteration for the optimization of nonlinear energies on triangle meshes. Noting that the linear mapping between any pair of triangles is a special case of harmonic mapping, we build upon the results of Chen and Weber [CW17]. Based on the complex view of the linear mapping, we show that the Hessian of the isometric energies has a simple and compact analytic expression. This allows us to analytically project the per-element Hessians to positive semidefinite matrices for efficient Newton iteration. We show that our method outperforms state-of-the-art methods on 2D deformation and parameterization. Further, we inspect the spectra of the per triangle energy Hessians and show that given an initial mapping, simple global scaling can shift the energy towards a more convex state. This allows Newton iteration to converge faster than starting from the given initial state. Additionally, our formulations support adding an energy smoothness term to the optimization with little additional effort, which improves the mapping results such that concentrated distortions are reduced.en_US
dc.description.number7
dc.description.sectionheadersParameterization and Surface Texture
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume37
dc.identifier.doi10.1111/cgf.13563
dc.identifier.issn1467-8659
dc.identifier.pages233-243
dc.identifier.urihttps://doi.org/10.1111/cgf.13563
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf13563
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectTheory of computation
dc.subjectNonconvex optimization
dc.subjectComputing methodologies
dc.subjectComputer graphics
dc.titlePiecewise Linear Mapping Optimization Based on the Complex Viewen_US
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