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  A Circle Packing Algorithm (2003) [14 citations — 2 self]

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by Charles R. Collins, Kenneth Stephenson
Computational Geometry: Theory and Applications
http://www.math.utk.edu/~kens/ACPA/ACPA.ps.gz
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Abstract:

Abstract. A circle packing is a configuration P of circles realizing a specified pattern of tangencies. We describe an efficient algorithm for computing the radii of packings in euclidean and hyperbolic geometry, discuss its performance, and illustrate some recent applications.

Citations

74 The geometry and topology of 3-manifolds – Thurston - 1979
53 The Convergence of Circle Packings to the Riemann Mapping – Rodin, Sullivan - 1987
40 Separators in two and three dimensions – Miller, Thurston - 1990
34 On Thurston's uniformization theorem for three-dimensional manifolds – Morgan - 1984
30 The Uniformization Theorem for Circle Packings – Beardon, Stephenson - 1990
28 D.Rottenberg. Quasi-conformally flat mapping the human cerebellum – Hurdal, Bowers, et al.
19 The grothendieck theory of dessins d’enfants – Schneps - 1994
18 Harmonic functions on planar and almost planar graphs and manifolds, via circle packings, Invent – Benjamini, Schramm - 1996
17 A polynomial time circle packing algorithm – Mohar - 1993
16 A characterization of compact convex polyhedra in hyperbolic 3-space – Rivin, Hodgson - 1993
10 Circle Packing: Experiments in Discrete Analytic Function Theory – Dubejko, Stephenson - 1995
10 Uniformizing Dessins and Belyĭ Maps Via Circle Packing – Bowers, Stephenson - 2004
10 The branched Schwarz lemma: a classical result via circle packing – Dubejko, Stephenson - 1995
9 Branched circle packings and discrete Blaschke products – Dubejko - 1995
9 Convergence of circle packings of finite valence to Riemann mappings – He, Rodin - 1993
8 Circle Packings and Co-compact Extensions of Kleinian Groups – Brooks - 1986
8 The C ∞ -convergence of hexagonal disk packings to the Riemann map – He, Schramm - 1998
8 The Approximation of Conformal Structures Via Circle Packing.” Computational Methods and Function Theory 1997 – Stephenson - 1999
7 Schwarz's lemma for circle packings – Rodin - 1987
6 The upper Perron method for labelled complexes with applications to circle packings – Bowers - 1993
6 The Schwarz-Pick lemma for circle packings – Beardon, Stephenson - 1991
6 A branched Andreev-Thurston theorem for circle packings of the sphere – Bowers, Stephenson - 1996
6 A probabilistic proof of Thurston's conjecture on circle packings, Rendiconti del Seminario Mate. e Fisico di – Stephenson - 1996
5 The finite Riemann mapping theorem – Thurston - 1985
4 Circle Packings in Surfaces of Finite Type: An In Situ Approach with Application to Modui Space.” Topology, Volume 32 – Bowers, Stephenson - 1993
4 Finite subdivision rules – Cannon, Floyd, et al. - 2001
4 Layered circle packings – Dennis, Brock - 2005
3 On the conformal invariance of tiling-systems, preprint – Cannon, Floyd, et al. - 1996
3 On the convergence of circle packings to the Riemann map – He, Schramm - 1996
2 Branched circle packings, discrete complex polynomials, and the approximation of analytic functions – Dubejko - 1993
2 Combinatorial excursions in moduli space – Barnard, Williams
2 A regular pentagonal tiling of the plane, Conformal Geometry and Dynamics – Bowers, Stephenson - 1997
2 Verdière, Un principe variationnel pour les empilements de cercles – de - 1991
2 Circle Packing and Discrete Analytic Function Theory.” Handbook of Complex Analysis, Volume 1: Geometric Function Theory – Stephenson
2 Eeuwen, The discrete Schwarz-Pick lemma for overlapping circles – van - 1994
2 Discrete conformal welding – Williams - 1999
1 Inverse Riemann mapping theorem for relative circle domains – He, Schramm - 1995