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NUMERICAL ANALYSIS OF QUASICONFORMAL MAPPINGS BY CIRCLE PACKINGS 被引量:3
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作者 蓝师义 戴道清 《Acta Mathematica Scientia》 SCIE CSCD 2006年第1期94-98,共5页
Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximatin... Thurston proposed that conformal mappings can be approximated by circle packing isomorphisms and the approach can be implemented efficiently. Based on the circle packing methods the rate of convergence of approximating solutions for quasiconformal mappings in the plane is discussed. 展开更多
关键词 circle packing quasiconformal mapping Beltrami equation numerical solution
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ON THE CONVERGENCE OF CIRCLE PACKINGS TO THE QUASICONFORMAL MAP
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作者 黄小军 沈良 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1173-1181,共9页
Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. ... Rodin and Sullivan (1987) proved Thurston's conjecture that a scheme based on the Circle Packing Theorem converges to the Riemann mapping, thereby proved a refreshing geometric view of the Riemann Mapping Theorem. Naturally, we consider to use the ellipses to pack the bounded simply connected domain and obtain similarly a sequence simplicial homeomorphism between the ellipse packing and the circle packing. In this paper, we prove that these simplicial homeomorphism approximate a quasiconformal mapping from the bounded simply connected domain onto the unit disk with the modulus of their complex dilatations tending to 1 almost everywhere in the domain when the ratio of the longer axis and shorter axis of the ellipse tending to ∞. 展开更多
关键词 circle packing quasiconformal map complex dilation
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The character of Thurston's circle packings
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作者 Huabin Ge Aijin Lin 《Science China Mathematics》 SCIE CSCD 2024年第7期1623-1640,共18页
We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if ... We introduce the character of Thurston's circle packings in the hyperbolic background geometry.Consequently, some quite simple criteria are obtained for the existence of hyperbolic circle packings. For example,if a closed surface X admits a circle packing with all the vertex degrees d_(i)≥7, then it admits a unique complete hyperbolic metric so that the triangulation graph of the circle packing is isotopic to a geometric decomposition of X. This criterion is sharp due to the fact that any closed hyperbolic surface admits no triangulations with all d_(i)≤6. As a corollary, we obtain a new proof of the uniformization theorem for closed surfaces with genus g≥2;moreover, any hyperbolic closed surface has a geometric decomposition. To obtain our results, we use Chow-Luo's combinatorial Ricci flow as a fundamental tool. 展开更多
关键词 CHARACTER circle packings combinatorial Ricci flow
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A note on circle packing
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作者 Young Joon AHN Christoph M. HOFFMANN Paul ROSEN 《Journal of Zhejiang University-Science C(Computers and Electronics)》 SCIE EI 2012年第8期559-564,共6页
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 parMlelized ... 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 parMlelized 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 commodity hardware. The speedups so achieved are discussed based on a number of experiments. 展开更多
关键词 circle packing Algorithm performance Parallel computation Graphics processing unit (GPU)
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Concrete Physics Method for Solving NP hard Problem
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作者 Huang Wen\|qi College of Computer Science, Huazhong University of Science and Technology, Wuhan 430074,China Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China 《Wuhan University Journal of Natural Sciences》 CAS 2001年第Z1期140-146,共7页
With a NP hard problem given, we may find a equivalent physical world. The rule of the changing of the physical states is simply the algorithm for solving the original NP hard problem .It is the most natural algorithm... With a NP hard problem given, we may find a equivalent physical world. The rule of the changing of the physical states is simply the algorithm for solving the original NP hard problem .It is the most natural algorithm for solving NP hard problems. In this paper we deal with a famous example , the well known NP hard problem——Circles Packing. It shows that our algorithm is dramatically very efficient. We are inspired that, the concrete physics algorithm will always be very efficient for NP hard problem. 展开更多
关键词 concrete physics algorithm NP hard problem circles packing the rule of the changing of the physical states
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Engineering the Divide-and-Conquer Closest Pair Algorithm 被引量:2
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作者 江铭辉 古熙悠 《Journal of Computer Science & Technology》 SCIE EI CSCD 2007年第4期532-540,共9页
We improve the famous divide-and-conquer algorithm by Bentley and Shamos for the planar closest-pair problem. For n points on the plane, our algorithm keeps the optimal O(n log n) time complexity and, using a circle... We improve the famous divide-and-conquer algorithm by Bentley and Shamos for the planar closest-pair problem. For n points on the plane, our algorithm keeps the optimal O(n log n) time complexity and, using a circle-packing property, computes at most 7n/2 Euclidean distances, which improves Ge et al.'s bound of (3n log n)/2 Euclidean distances. We present experimental results of our comparative studies on four different versions of the divide-and-conquer closest pair algorithm and propose two effective heuristics. 展开更多
关键词 algorithmic engineering analysis of algorithms circle packing closest pair computational geometry
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Zero asymptotic Lipschitz distance and finite Gromov-Hausdorff distance
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作者 Luo-fei LIU College of Mathematics and Computer Science, Jishou University, Jishou 416000, China 《Science China Mathematics》 SCIE 2007年第3期345-350,共6页
We give an example which shows that the Burago’s bounded distance theorem does not hold in a non-intrinsic metric case. The argument is based on the classical answer to the densest circle packing problem in ?2.
关键词 asymptotic Lipschitz distance Gromov-Hausdorff distance densest circle packing 51K05 05B40
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A Note on the Uniqueness of Koebe–Andreev–Thurston Theorem
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作者 Xiao Jun HUANG Zi Peng WANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第7期1469-1474,共6页
In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theore... In this paper, we present a new proof of the uniqueness of Koebe-Andreev-Thurston theorem. Our method is based on the argument principle in complex analysis and reviews the connection between the circle packing theorem and complex analysis. 展开更多
关键词 circle packing argument principle MSbius transformation
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