Abstract
Edelsbrunner et al. defined a framework of shape deformations with shapes bounded by skin manifold. We prove that the infinitely many synthesized shapes in the deformation sequence share finitely many common Voronoi complexes. Therefore, we propose a new algorithm to compute the common Voronoi complexes efficiently for the deformations, and use these common complexes to compute the synthesized shapes in real time. This makes generating, visualizing, and customizing shape deformations feasible.
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References
Chazelle, B.: An optimal convex hull algorithm in any fixed dimension. Discrete Comput. Geom. 10, 377–409 (1993)
Cheng, H., Edelsbrunner, H., Fu, P.: Shape Space from Deformation. In: Proc. 6th Pacific Conf. Comput. Graphics Appl., pp. 104–113 (1998)
Clarkson, K.L., Shor, P.W.: Applications of random sampling in computational geometry, II. In: Discrete and Computational Geometry, vol. 4(1), pp. 387–421 (1989)
Edelsbrunner, H.: Deformable Smooth Surface Design. Discrete Comput. Geom. 21, 87–115 (1999)
Seidel, R.: Linear programming and convex hulls made easy. In: Proc. 6th Annu ACM Sympos. Coput. Geom., pp. 211–215 (1990)
Seidel, R.: Small-dimensional linear programming and convex hulls made easy. In: Discrete Comput. Geom., pp. 423–434 (1991)
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© 2004 Springer-Verlag Berlin Heidelberg
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Chen, C., Cheng, HL. (2004). Superimposing Voronoi Complexes for Shape Deformation. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_30
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DOI: https://doi.org/10.1007/978-3-540-30551-4_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24131-7
Online ISBN: 978-3-540-30551-4
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