B-morphs between b-compatible curves

1 We define b-compatibility for planar curves and propose three 2 ball morphing techniques (b-morphs) between pairs of b3 compatible curves. B-morphs use the automatic ball-map 4 correspondence, proposed by Chazel et al. [11], from which 5 they derive vertex trajectories (Linear, Circular, Parabolic). 6 All are symmetric, meeting both curves with the same an7 gle, which is a right angle for the Circular and Parabolic. 8 We provide simple constructions for these b-morphs using 9 the maximal disks in the finite region bounded by the two 10 curves. We compare the b-morphs to each other and to other 11 simple morphs (Linear Interpolation (LI ), Closest Projec12 tion (CP), Curvature Interpolation (CI ), Laplace Blend13 ing (LB), Heat Propagation (HP)) using seven measures of 14 quality deficiency (travel distance, distortion, stretch, local 15 acceleration, surface area, average curvature, maximal cur16 vature). We conclude that the ratios of these measures de17 pends heavily on the test case, especially for LI, CI, and 18 LB which compute correspondence from a uniform geodesic 19 parameterization. Nevertheless, we found that the Linear b20 morph has consistently the shortest travel distance and that 21 the Circular b-morph has the least amount of distortion. 22