A circle packing algorithm
نویسندگان
چکیده
A circle packing is a configuration P of circles realizing a specified pattern of tangencies. Radii of packings in the euclidean and hyperbolic planes may be computed using an iterative process suggested by William Thurston. We describe an efficient implementation, discuss its performance, and illustrate recent applications. A central role is played by new and subtle monotonicity results for “flowers” of circles. 2003 Elsevier Science B.V. All rights reserved.
منابع مشابه
Combinatorial Ricci Flows on Surfaces
We show that the analogue of Hamilton’s Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston’s circle packing on surfaces. As a consequence, a new proof of Thurston’s existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.
متن کاملPrimal-dual Circle packing of Planar Maps
This work is based on Mohar [1]’s recent algorithm for circle packing for the Euclean case. We implement his polynomial time algorithm for constructing primal-dual circle packings of almost 3-connected planar maps. We have improved Mohar’s algorithm and have been able to get near an order of magnitude speed up for large graphs. We describe our implementation in C/C++ style pseudo-code.
متن کاملA Two-Level Search Strategy for Packing Unequal Circles into a Circle Container
We propose a two-level search strategy to solve a two dimensional circle packing problem. At the first level, a good enough packing algorithm called A1.0 uses a simple heuristic to select the next circle to be packed. This algorithm is itself used at the second level to select the next circle to be packed. The resulted packing procedure called A1.5 considerably improves the performance of the a...
متن کاملOptimal Substructures in Optimal and Approximate Circle Packings
This paper deals with the densest packing of equal circles in a square problem. Sharp bounds for the density of optimal circle packings have given. Several known optimal and approximate circle packings contain optimal substructures. Based on this observation it is sometimes easy to determine the minimal polynomials of the arrangements.
متن کاملCircle Packings of Maps - the Euclidean Case
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 necessar...
متن کاملNote : Anote on circle packing ∗
The problem of packing circles into a domain of prescribed topology is considered. The circles need not have equal radii. The Collins-Stephenson algorithm computes such a circle packing. This algorithm is parallelized in two different ways and its performance is reported for a triangular, planar domain test case. The implementation uses the highly parallel graphics processing unit (GPU) on comm...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Comput. Geom.
دوره 25 شماره
صفحات -
تاریخ انتشار 2003