Homotopic Morphing of Planar Curves

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dc.contributor.authorDym, Nadaven_US
dc.contributor.authorShtengel, Annaen_US
dc.contributor.authorLipman, Yaronen_US
dc.contributor.editorMirela Ben-Chen and Ligang Liuen_US
dc.date.accessioned2015-07-06T05:01:17Z
dc.date.available2015-07-06T05:01:17Z
dc.date.issued2015en_US
dc.description.abstractThis paper presents an algorithm for morphing between closed, planar piecewise-C1 curves. The morph is guaranteed to be a regular homotopy, meaning that pinching will not occur in the intermediate curves. The algorithm is based on a novel convex characterization of the space of regular closed curves and a suitable symmetric length-deviation energy. The intermediate curves constructed by the morphing algorithm are guaranteed to be regular due to the convexity and feasibility of the problem. We show that our method compares favorably with standard curve morphing techniques, and that these methods sometimes fail to produce a regular homotopy, and as a result produce an undesirable morph. We explore several applications and extensions of our approach, including morphing networks of curves with simple connectivity, morphing of curves with different turning numbers with minimal pinching, convex combination of several curves, and homotopic morphing of b-spline curves via their control polygon.en_US
dc.description.number5en_US
dc.description.sectionheadersCurves and Graphsen_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume34en_US
dc.identifier.doi10.1111/cgf.12712en_US
dc.identifier.pages239-251en_US
dc.identifier.urihttps://doi.org/10.1111/cgf.12712en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleHomotopic Morphing of Planar Curvesen_US
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34-Issue 5
SGP15: Eurographics Symposium on Geometry Processing (CGF 34-5)