Computational Methods and Function Theory 3 (2003), No. 1, 325--347
Copyright Heldermann Verlag 2003
Charles R. Collins
ccollins@math.utk.edu , Mathematics, University of Tennessee, Knoxville, TN 37996-1300, U.S.A.
Tobin A. Driscoll
driscoll@math.udel.edu , Mathematical Sciences, University of Delaware, Newark DE 19716, U.S.A.
Kenneth Stephenson
kens@math.utk.edu , Mathematics, University of Tennessee, Knoxville, TN 37996-1300, U.S.A.
We use a simple example to introduce a notion of curvature flow in the conformal mapping of polyhedral surfaces. The inquiry was motivated by experiments with discrete conformal maps in the sense of circle packing. We describe the classical theory behind these flows and demonstrate how to modify the Schwarz-Christoffel method to obtain classical numerical confirmation. We close with some additional examples.
Keywords: Circle packing, conformal mapping, curvature, Schwarz-Christoffel.
MSC 2000: Primary: 52C26, 30C30, 53A30; Secondary: 65D15, 37E35, 53A05.
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