Circle Packings of Maps - the Euclidean Case
نویسنده
چکیده
In an earlier work, the author extended the AndreevKoebe-Thurston circle packing theorem. Additionally, a polynomial time algorithm for constructing primal-dual circle packings of arbitrary (essentially) 3-connected maps was found. In this note, additional details concerning surfaces of constant curvature 0 (with special emphasis on planar graphs where a slightly different treatment is necessary) are presented.
منابع مشابه
Apollonian Circle Packings of the Half-plane
We consider Apollonian circle packings of a half Euclidean plane. We give necessary and sufficient conditions for two such packings to be related by a Euclidean similarity (that is, by translations, reflections, rotations and dilations) and describe explicitly the group of self-similarities of a given packing. We observe that packings with a non-trivial self-similarity correspond to positive re...
متن کاملMa-schlenker C -octahedra in the 2-sphere
We present constructions inspired by the Ma-Schlenker example of [9] that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in [9] of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary constructions use only the inversive geometry of the 2-sphere.
متن کاملCortical Surface Flattening: a Quasi-conformal Approach Using Circle Packings
Comparing the location and size of functional brain activity across subjects is difficult due to individual differences in folding patterns and functional foci are often buried within cortical sulci. Cortical flat mapping is a tool which can address these problems by taking advantage of the two-dimensional sheet topology of the cortical surface. Flat mappings of the cortex assist in simplifying...
متن کاملOn Tightest Packings in the Minkowski Plane
is satisfied for any two distinct points P, Q of L. Since the work of Thue on circle packings in the plane, many people have noted that the mesh of a lattice is the inverse of the density of its points and have asked whether there are arbitrary pointsets of maximal density satisfying the packing condition. C. A. Rogers [8] showed in 1951, for example, that for the Euclidean plane no packing is ...
متن کامل0 Conformally symmetric circle packings . A generalization of Doyle spirals
Circle packings (and more generally patterns) as discrete analogs of conformal mappings is a fast developing field of research on the border of analysis and geometry. Recent progress was initiated by Thurston’s idea [T] about the approximation of the Riemann mapping by circle packings. The corresponding convergence was proven by Rodin and Sullivan [RS]; many additional connections with analytic...
متن کامل