An inverse problem for circle packing and conformal mapping

Authors:
Ithiel Carter and Burt Rodin

Journal:
Trans. Amer. Math. Soc. **334** (1992), 861-875

MSC:
Primary 52C15; Secondary 30C20, 30C30, 51M15

DOI:
https://doi.org/10.1090/S0002-9947-1992-1081937-X

MathSciNet review:
1081937

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Abstract | References | Similar Articles | Additional Information

Abstract: Figure 1.1 illustrates the fact that if a region is almost packed with circles of radius in the hexagonal pattern and if the unit disk is packed in an isomorphic pattern with circles of varying radii then, after suitable normalization, the correspondence of circles converges to the Riemann mapping function as (see [15]). In the present paper an inverse of this result is obtained as illustrated by Figure 1.2; namely, if the unit disk is almost packed with -circles there is an isomorphic circle packing almost filling the region such that, after suitable normalization, the circle correspondence converges to the conformal map of the disk onto the region as . Note that this set up yields an approximate triangulation of the region by joining the centers of triples of mutually tangent circles. Since this triangulation is intimately related to the Riemann mapping it may be useful for grid generation [18].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1081937-X

Keywords:
Discrete conformal geometry,
circle packing,
numerical conformal mapping,
grid generation

Article copyright:
© Copyright 1992
American Mathematical Society