As-Killing-As-Possible Vector Fields for Planar Deformation

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dc.contributor.authorSolomon, Justinen_US
dc.contributor.authorBen-Chen, Mirelaen_US
dc.contributor.authorButscher, Adrianen_US
dc.contributor.authorGuibas, Leonidasen_US
dc.contributor.editorMario Botsch and Scott Schaeferen_US
dc.date.accessioned2015-02-27T15:03:23Z
dc.date.available2015-02-27T15:03:23Z
dc.date.issued2011en_US
dc.description.abstractCartoon animation, image warping, and several other tasks in two-dimensional computer graphics reduce to the formulation of a reasonable model for planar deformation. A deformation is a map from a given shape to a new one, and its quality is determined by the type of distortion it introduces. In many applications, a desirable map is as isometric as possible. Finding such deformations, however, is a nonlinear problem, and most of the existing solutions approach it by minimizing a nonlinear energy. Such methods are not guaranteed to converge to a global optimum and often suffer from robustness issues. We propose a new approach based on approximate Killing vector fields (AKVFs), first introduced in shape processing. AKVFs generate near-isometric deformations, which can be motivated as direction fields minimizing an as-rigid-as-possible (ARAP) energy to first order. We first solve for an AKVF on the domain given user constraints via a linear optimization problem and then use this AKVF as the initial velocity field of the deformation. In this way, we transfer the inherent nonlinearity of the deformation problem to finding trajectories for each point of the domain having the given initial velocities. We show that a specific class of trajectories - the set of logarithmic spirals - is especially suited for this task both in practice and through its relationship to linear holomorphic vector fields. We demonstrate the effectiveness of our method for planar deformation by comparing it with existing state-of-the-art deformation methods.en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.identifier.issn1467-8659en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2011.02028.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.subjectThreeen_US
dc.subjectdimensional graphics and realism [I.3.7]en_US
dc.subjectAnimationen_US
dc.titleAs-Killing-As-Possible Vector Fields for Planar Deformationen_US
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