基于最优传输的网格参数化序列簇生成方法

doi:10.19678/j.issn.1000-3428.0048705

摘要/Abstract

摘要：

利用Ricci曲率流将原曲面上的面元测度前推到目标参数域上形成初始面元测度,对初始面元测度或目标面元测度进行变换,以构造一系列连续变换的面元测度序列,然后计算面元测度间的最优传输映射并构建连续变换的参数化序列簇。通过莫比乌斯变换、曲率强化和重要性驱动3种方式对面元测度进行变换实验,结果表明,相比拟等积方法,该方法可以构造出多种不同的参数化序列簇,并能取得较好的特殊参数化效果。

关键词: 参数化序列簇, 最优传输映射, Ricci曲率流, 测度控制, 莫比乌斯变换

Abstract:

Using Ricci curvature flow,the original surface panel measure is pushed forward to the target parameter domain to form the initial panel measure.After transforming the initial panel measure or the target panel measure,a series of continuous transformation panel measure sequences are constructed.Then the parameterized sequence clusters of continuous transformation is constructed by calculating the optimal transmission mapping between the panel measures.The transformation experiments are carried out by using Moebius transformation,curvature reinforcement and importance drive,and results show that compared with the Quasi-area method,this method can construct a variety of different parameterized sequence clusters and achieve better special parameterized effect.

Key words: parameterized sequence clusters, optimal transmission mapping, Ricci curvature flow, measure control, Moebius transformation

中图分类号:

TP391

夏诗羽,苏科华,陈彩玲. 基于最优传输的网格参数化序列簇生成方法[J]. 计算机工程, 2019, 45(1): 264-269,277.

XIA Shiyu,SU Kehua,CHEN Cailing. Grid Parameterized Sequence Clusters Generation Method Based on Optimal Transmission[J]. Computer Engineering, 2019, 45(1): 264-269,277.

参考文献

［1］HORMANN K,POLTHIER K,SHEFFER A.Mesh para-meterization:theory and practice［C］//Proceedings of SIGGRAPH Asia’08.New York,USA:ACM Press,2008:60-87.
［2］FLOATER M S,HORMANN K.Surface parameterization:a tutorial and survey［M］//DODGSON N A,FLOATER M S,SABIN M A.Advances in multiresolution for geometric modelling.Berlin,Germany:Springer,2005.
［3］SU Z,WANG Y,SHI R,et al.Optimal mass transport for shape matching and comparison［J］.IEEE Transactions on Pattern Analysis and Machine Intelligence,2015,37(11):2246-2259.
［4］DESBRUN M,MEYER M,ALLIEZ P.Intrinsic para-meterizations of surface meshes［J］.Computer Graphics Forum,2010,21(3):209-218.
［5］GU X,YAU S T.Global conformal surface parameteri-zation［C］//Proceedings of 2003 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing.New York,USA:ACM Press,2003:127-137.
［6］FLOATER M S.Mean value coordinates［J］.Computer Aided Geometric Design,2003,20(1):19-27.
［7］LVY B,PETITJEAN S,RAY N,et al.Least squares conformal maps for automatic texture atlas generation［C］//Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques.New York,USA:ACM Press,2002:362-371.
［8］SHEFFER A,DE STURLER E.Surface parameterization for meshing by triangulation flattening［EB/OL］.［2017-09-15］.http://www.math.vt.edu/people/sturler/Publications/IMR9proc.pdf.
［9］HORMANN K,GREINER G.MIPS:an efficient global parametrization method［EB/OL］.［2017-09-15］.http:// www.inf.usi.ch/hormann/papers/Hormann.2000.MAE.pdf.
［10］ZOU G,HU J,GU X,et al.Authalic parameterization of general surfaces using Lie advection［J］.IEEE Transactions on Visualization and Computer Graphics,2011,17(12):2005-2014.
［11］YOSHIZAWA S,BELYAEV A,SEIDEL H P.A fast and simple stretch-minimizing mesh parameterization［C］//Proceedings of SMI’04.Washington D.C.,USA:IEEE Computer Society,2004:200-208.
［12］DOMINITZ A,TANNENBAUM A.Texture mapping via optimal mass transport［J］.IEEE Transactions on Visualization and Computer Graphics,2010,16(3):419-433.
［13］ZHAO X,SU Z,GU X D,et al.Area-preservation mapping using optimal mass transport［J］.IEEE Transactions on Visualization and Computer Graphics,2013,19(12):2838-2847.
［14］SU K,CUI L,QIAN K,et al.Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation［J］.Computer Aided Geometric Design,2016,46(C):76-91.
［15］LIU L,ZHANG L,XU Y,et al.A local/global approach to mesh parameterization［J］.Computer Graphics Forum,2008,27(5):1495-1504.
［16］BONNOTTE N.From Knothe’s rearrangement to Brenier’s optimal transport map［J］.SIAM Journal on Mathematical Analysis,2012,45(1):64-87.
［17］KANTOROVICH L V.On a problem of Monge［J］.Journal of Mathematical Sciences,2006,133(4):1383-1386.
［18］BRENIER Y.Polar factorization and monotone rearrangement of vector-valued functions［J］.Communications on Pure and Applied Mathematics,1991,44(4):375-417.
［19］ALEXANDROV A D.Convex polyhedra［M］.Berlin,Germany:Springer,2005.
［20］GU X,LUO F,SUN J,et al.Variational principles for Minkowski type problems,discrete optimal transport,and discrete Monge-ampere equations［EB/OL］.［2017-09-15］.http://www.oalib.com/paper/3870868#.W-JWK_mtgUw.
［21］WANG Y,SHI J,YIN X,et al.Brain surface conformal parameterization with the Ricci flow［J］.IEEE Tran-sactions on Medical Imaging,2012,31(2):251-264.
［22］DEBERG M,VANKREVELD M,OVERMARS M,et al.Computational geometry:algorithms and applications［J］.Mathematical Gazette,2008,19(3):333-334. ［23］彭群生,胡国飞.三角网格的参数化［J］.计算机辅助设计与图形学学报,2004,16(6):731-739. ［24］郭凤华,张彩明,焦文江.网格参数化研究进展［J］.软件学报,2016,27(1):112-135.

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