Scale-isometric polytopal graphs in hypercubes and cubic by Michel-Marie Deza, Viacheslav Grishukhin, Mikhail I Shtogrin

By Michel-Marie Deza, Viacheslav Grishukhin, Mikhail I Shtogrin

This monograph identifies polytopes which are "combinatorially R1-embeddable", inside fascinating lists of polytopal graphs, i.e. such that corresponding polytopes are both trendy mathematically (regular walls, root lattices, uniform polytopes and so on), or appropriate in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, offers purposes to chemical graphs and, within the first case, it provides new combinatorial standpoint to "R2-prominent" affine polytopal items.

The lists of polytopal graphs within the ebook come from extensive parts of geometry, crystallography and graph idea. The e-book concentrates on such concise and, up to attainable, self reliant definitions. The scale-isometric embeddability — the most unifying query, to which these lists are subjected — is gifted with the minimal of technicalities.

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Additional resources for Scale-isometric polytopal graphs in hypercubes and cubic lattices: Polytopes in hypercubes and Zn

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However, a more theoretical analysis is needed in understanding anisotropic CVTs, and it remains a challenge to efficiently generate them. Lévy and Bonneel [34] proposed a novel approach to compute CVT in higher dimensions. They used it to generate anisotropic curvature-adapted surface meshes. However, it does not preserve sharp features. Our method is inspired by the idea of Lévy and Bonneel in [34], and it can easily preserve sharp features. 3 Surface Embedding in R6 The re-meshing method proposed in this paper is inspired by the method of Lévy and Bonneel [34].

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194(48), 5068–5082 (2005) 23. : Geometric surface mesh optimization. Comput. Vis. Sci. 1(3), 113–121 (1998) 24. : Optimal triangulation and quadric-based surface simplification. Comput. Geol. 14(1), 49–65 (1999) 25. : Progressive meshes. In: Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques, pp. 99–108. ACM, New York (1996) 26. : Mesh optimization. In: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, pp. 19–26. ACM, New York (1993) 27.

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