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convex hull theorem for multiply connected domains in the plane with an estimate of the quasiconformal constant

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Science China Mathematics 2009年第5期52卷 932-940页

作者： LIU Gang WU ShengJian LMAM School of Mathematical SciencesPeking UniversityBeijing 100871China

For any multiply connected domain Ω in ?2, let S be the boundary of the convex hull in H 3 of ?2Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on ?S = ?Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.

关键词： convex hull quasiconformal mapping multiply connected domain 30C62

convex hull of set in thick part of Teichmller space

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Science China Mathematics 2014年第9期57卷 1799-1810页

作者： LIU LiXin SHIGA Hiroshige SUN ZongLiang Department of Mathematics Sun Yat-sen University Department of Mathematics Tokyo Institute of Technology Department of Mathematics Shenzhen University

Let X be a non-elementary Riemann surface of type(g,n),where g is the number of genus and n is the number of punctures with 3g-3+n>*** T(X)be the Teichmller space of *** constructing a certain subset E of T(X),we show that the convex hull of E with respect to the Teichmller metric,the Carathodory metric and the Weil-Petersson metric is not in any thick part of the Teichmler space,*** implies that convex hulls of thick part of Teichmller space with respect to these metrics are not always in thick part of Teichmller space,as well as the facts that thick part of Teichmller space is not always convex with respect to these metrics.

关键词： Carathéodory metric Teichmuller metric Weil-Petersson metric convex hull Dehn twist

A new algorithm for computing the convex hull of a planar point set

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第8期8卷 1210-1217页

作者： LIU Guang-hui CHEN Chuan-bo College of Computer Science and Technology Huazhong University of Science and Technology Wuhan 430074 China

When the edges of a convex polygon are traversed along one direction,the interior of the convex polygon is always on the same side of the edges. Based on this characteristic of convex polygons,a new algorithm for computing the convex hull of a simple polygon is proposed in this paper,which is then extended to a new algorithm for computing the convex hull of a planar point set. First,the extreme points of the planar point set are found,and the subsets of point candidate for vertex of the convex hull between extreme points are obtained. Then,the ordered convex hull point sequences between extreme points are constructed separately and concatenated by removing redundant extreme points to get the convex hull. The time complexity of the new planar convex hull algorithm is O(nlogh) ,which is equal to the time complexity of the best output-sensitive planar convex hull algorithms. Compared with the algorithm having the same complexity,the new algorithm is much faster.

关键词： Computational geometry convex hull Extreme points Ordered convex hull point sequence

A Quick convex hull Building Algorithm Based on Grid and Binary Tree

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Chinese Journal of Electronics 2015年第2期24卷 317-320页

作者： GAO Yang CHENG Yuhu WANG Xuesong School of Information and Electrical Engineering China University of Mining and Technology

A quick convex hull building algorithm using grid and binary tree is proposed for the minimum convex buidling of planar point set. Grids are used to assess and eliminate those interior points wihtout any contribution to convex hull building and points are sought in the boundary grid only so as to enhance the efficiency of algorithm. The minimum convex bull is built by taking such advantages of binary tree as quick, convenient and applicable for various point sets with different distributions, so as to resolve the description problem of concave point. The time complexity of the algorithm is low because of grid pretreatment. As the results of comparative expriment of random point and actual picture show, the proposed algorithm can obtain the best profile of 2D planar picture with minimum time, which is applicable for describing the shape of irregular convex-concave objects.

关键词： convex hull Gird Binary tree Concave point Time complexity

A quantum search algorithm of two-dimensional convex hull

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Communications in Theoretical Physics 2021年第11期73卷 85-92页

作者： Cheng Wang Ri-Gui Zhou College of Information Engineering Shanghai Maritime UniversityShanghai201306China Research Center of Intelligent Information Processing and Quantum Intelligent Computing Shanghai201306China

Despite the rapid development of quantum research in recent years,there is very little research in computational *** this paper,to achieve the convex hull of a point set in a quantum system,a quantum convex hull algorithm based on the quantum maximum or minimum searching algorithm(QUSSMA)is ***,the novel enhanced quantum representation of digital images is employed to represent a group of point set,and then the QUSSMA algorithm and vector operation are used to search the convex hull of the point *** addition,the algorithm is simulated and compared with the classical *** is concluded that the quantum algorithm accelerates the classical algorithm when the Mpvalue of the convex hull point is under a certain condition.

关键词： quantum algorithm convex hull computational geometry quantum searching

Determination of the nucleotide or amino acid composition of genome or protein sequences by using natural vector method and convex hull principle

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Fundamental Research 2021年第5期1卷 559-564页

作者： Xiaopei Jiao Shaojun Pei Zeju Sun Jiayi Kang Stephen S-T.Yau Department of Mathematical Sciences Tsinghua UniversityBeijing100084China Yanqi Lake Beijing Institute of Mathematical Sciences and Applications Beijing101408China

Although with the continuous development of sequencing technology,the number of genome and protein sequences has grown rapidly,these sequences are only a small part of ***,it is still a challenging and important problem to detect and predict some new genome or protein sequences based on real sequence data,which motivates us to solve the problem *** first step to predict the new sequences is determining the nucleotide or amino acid composition of *** this paper,we apply natural vector method and convex hull principle to determine the nucleotide or amino acid composition of new genome or protein *** algorithm is based on optimization *** SARS-CoV-2 genome and protein datasets are used to verify the feasibility of our *** experiments show that our algorithm can detect and predict possible number of each nucleotide or amino acid of genome and protein sequence with respect to the second order natural vectors.

关键词： Natural vector convex hull New sequences Optimization

A NEW convex hull ALGORITHM FOR ANY POLYGON

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Computer Aided Drafting,Design and Manufacturing 1997年第1期7卷 61-64页

作者： Hu Zhanqi Li Yupeng Wang Jun Qiao Lei

A new algorithm for finding convex hull of a polygon is proposed. An example is given to show the effectiveness and the simplicity of the algorithm.

关键词： non-simple polygon convex hull algorithm

convex Decomposition Based Cluster Labeling Method for Support Vector Clustering

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Journal of Computer Science & Technology 2012年第2期27卷 428-442页

作者：平源田英杰周亚建杨义先 Information Security Center Beijing University of Posts and Telecommunications Department of Computer Science and Technology Xuchang University Graduate University of Chinese Academy of Sciences

Support vector clustering (SVC) is an important boundary-based clustering algorithm in multiple applications for its capability of handling arbitrary cluster ***,SVC’s popularity is degraded by its highly intensive time complexity and poor label *** overcome such problems,we present a novel efficient and robust convex decomposition based cluster labeling (CDCL) method based on the topological property of *** CDCL decomposes the implicit cluster into convex hulls and each one is comprised by a subset of support vectors (SVs).According to a robust algorithm applied in the nearest neighboring convex hulls,the adjacency matrix of convex hulls is built up for finding the connected components;and the remaining data points would be assigned the label of the nearest convex hull *** approach’s validation is guaranteed by geometric *** complexity analysis and comparative experiments suggest that CDCL improves both the efficiency and clustering quality significantly.

关键词： support vector clustering convex decomposition convex hull geometric

A Level Set Representation Method for N-Dimensional convex Shape and Applications

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Communications in Mathematical Research 2021年第2期37卷 180-208页

作者： Lingfeng Li Shousheng Luo Xue-Cheng Tai Jiang Yang Department of Mathematics of Hong Kong Baptist University Hong KongSARChina Department of Mathematics of Southern University of Science and Technology ShenzhenChina School of Mathematics and Statistics Henan Engineering Research Center for Artificial Intelligence Theory and AlgorithmsHenan UniversityKaifengChina

In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set *** the best of our knowledge,the proposed prior is the first one which can work for high dimensional *** prior is very useful for object completion in computer *** is a very challenging task to represent high dimensional convex *** this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance ***,the second order condition of convex functions is used to characterize the shape convexity *** apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three *** algorithm based on the alternating direction method of multipliers is presented for the optimization *** experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.

关键词： convex shape prior level-set method image segmentation convex hull ADMM