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Ball-Morph: Definition, Implementation, and Comparative Evaluation
June 2011 (vol. 17 no. 6)
pp. 757-769
Brian Whited, Walt Disney Animation Studios, Burbank
Jaroslaw (Jarek) Rossignac, Georgia Institute of Technology, Atlanta
We define b-compatibility for planar curves and propose three ball morphing techniques between pairs of b-compatible curves. Ball-morphs use the automatic ball-map correspondence, proposed by Chazal et al. [1], from which we derive different vertex trajectories (linear, circular, and parabolic). All three morphs are symmetric, meeting both curves with the same angle, which is a right angle for the circular and parabolic. We provide simple constructions for these ball-morphs and compare them to each other and other simple morphs (linear-interpolation, closest-projection, curvature-interpolation, Laplace-blending, and heat-propagation) using six cost measures (travel-distance, distortion, stretch, local acceleration, average squared mean curvature, and maximum squared mean curvature). The results depend heavily on the input curves. Nevertheless, we found that the linear ball-morph has consistently the shortest travel-distance and the circular ball-morph has the least amount of distortion.

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Index Terms:
Morphing, curve interpolation, medial axis, curve averaging, surface reconstruction from slices, ball-map.
Brian Whited, Jaroslaw (Jarek) Rossignac, "Ball-Morph: Definition, Implementation, and Comparative Evaluation," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 6, pp. 757-769, June 2011, doi:10.1109/TVCG.2010.115
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