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Automatic Generation of Riemann Surface Meshes [chapter]

Matthias Nieser, Konstantin Poelke, Konrad Polthier
2010 Lecture Notes in Computer Science  
By applying domain coloring to the automatically constructed Riemann surface models, we generalize this approach to deal with functions which cannot be entirely visualized in the complex plane.  ...  We present an algorithm for constructing Riemann surfaces as meshes in R 3 from explicitly given branch points with corresponding branch indices.  ...  To the best of our knowledge it is the only work that automatically generates visualizations of Riemann surfaces -most available images of Riemann surfaces usually show explicitly parametrized surfaces  ... 
doi:10.1007/978-3-642-13411-1_11 fatcat:ha74uycsh5elhho54g6oe7i5x4

The Return of the Riemann Surface

Michael Trott
2008 The Mathematica Journal  
My favorite subject~Riemann surfaces~is revisited through the eyes (functions) of Mathematica 6.  ...  RiemannSurfacePlot3D RiemannSurfacePlot3D@w == f@zD, reim@w@zDD, 8z, w<D plots a Riemann surface of w as the real or imaginary part reim of w over the complex z-plane.  ...  the Riemann Surface 629 Using a transparent surface makes it easier to see the inner parts of more compli- cated Riemann surfaces.  ... 
doi:10.3888/tmj.10.4-1 fatcat:5gel6ueo6jdobiob7og3y57pbe

Quadrilateral Mesh Generation III: Optimizing Singularity Configuration Based on Abel-Jacobi Theory [article]

Xiaopeng Zheng, Yiming Zhu, Na Lei, Zhongxuan Luo, Xianfeng Gu
2020 arXiv   pre-print
This work proposes a rigorous and practical algorithm for generating meromorphic quartic differentials for the purpose of quad-mesh generation.  ...  the resulting T-Mesh.  ...  We will also design algorithms for adjusting the conformal structure of the surface to ensure the finiteness of the trajectories of meromorphic differentials and automatic quad-mesh generation.  ... 
arXiv:2007.07334v1 fatcat:raoc2fxgrfgnxhrh7lj7lq2fsi

A New Lagrangian Method for Three-Dimensional Steady Supersonic Flows

Ching-Yuen Loh, Meng-Sing Liou
1994 Journal of Computational Physics  
Test problems show that the extended Lagrangian method retains all the advantages of the two-dimensional method (e.g., crisp resolution of a slip-surface (contact discontinuity) and automatic grid generation  ...  The derivation of the conservation form and the solution of the local Riemann solver using the Godunov and the high-resolution TVD (total variation diminished) schemes is presented.  ...  Figure 9 (f) displays the shape of a slip-surface and several typical meshes. Note that the meshes are automatically deformed, expanded, or condensed according to the flow.  ... 
doi:10.1006/jcph.1994.1132 fatcat:627oywdcmbhtdlkn2jxeclv3r4

Brain Surface Conformal Parameterization Using Riemann Surface Structure

Yalin Wang, Lok Ming Lui, Xianfeng Gu, Kiralee M. Hayashi, Tony F. Chan, Arthur W. Toga, Paul M. Thompson, Shing-Tung Yau
2007 IEEE Transactions on Medical Imaging  
Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each  ...  Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces.  ...  As an application of our automatic landmark tracking algorithm, we use the automatically labelled landmark curves to generate an optimized conformal mapping on the surface.  ... 
doi:10.1109/tmi.2007.895464 pmid:17679336 pmcid:PMC3197830 fatcat:qe6uqvdavfcatnkv6acmkvjkky

Conformal virtual colon flattening

Wei Hong, Xianfeng Gu, Feng Qiu, Miao Jin, Arie Kaufman
2006 Proceedings of the 2006 ACM symposium on Solid and physical modeling - SPM '06  
., minute handle) is located and removed automatically. The holomorphic 1-form, a pair of orthogonal vector fields, is then computed on the 3D colon surface mesh using the conjugate gradient method.  ...  Moreover, our algorithm is general which can handle high genus surfaces. First, the colon wall is segmented and extracted from the CT dataset.  ...  The CT colon datasets are courtesy of Stony Brook University Hospital. AK discloses that he owns a fraction of Viatronix shares.  ... 
doi:10.1145/1128888.1128901 dblp:conf/sma/HongGQJK06 fatcat:zreemvf3qjardgzci3p5incucu

Conformal Spherical Parametrization for High Genus Surfaces

Xianfeng Gu, Xin Li, Shing-Tung Yau, Wei Zeng
2007 Communications in Information and Systems  
Our method is based on Riemann surface theory.  ...  This setup allows us to transfer the existing applications based on general spherical parameterization to the field of high genus surfaces, such as remeshing, consistent parameterization, shape analysis  ...  In this work, we aims at automatic generalizing conformal spherical parameterizations for high genus surfaces.  ... 
doi:10.4310/cis.2007.v7.n3.a4 fatcat:pxj2xusib5b2jpte4ppffqbd3m

Conformal Surface Morphing with Applications on Facial Expressions [article]

Mei-Heng Yueh, Xianfeng David Gu, Wen-Wei Lin, Chin-Tien Wu, Shing-Tung Yau
2015 arXiv   pre-print
Furthermore, by composition of the M\"obius transformation and the 3D deformation field, the morphing sequence can be generated from the mean curvatures and the conformal factors on a unified mesh structure  ...  The dilation and relative orientations of the 3D surfaces can be linked through the M\"obius transformation due to the conformal characteristic of the Riemann mapping.  ...  [4] proposed a method of generating smooth-looking transformations between pairs of surfaces that may differ in topology by specifying a sparse control mesh on each surface and by associating each face  ... 
arXiv:1504.00097v1 fatcat:unscmai3gvfhndwylvooyutufe

A Godunov-like point-centered essentially Lagrangian hydrodynamic approach

Nathaniel R. Morgan, Jacob I. Waltz, Donald E. Burton, Marc R. Charest, Thomas R. Canfield, John G. Wohlbier
2015 Journal of Computational Physics  
Notable advantages include reduced complexity in generating conformal meshes, reduced complexity in mesh reconnection, and preserving tetrahedron cells with automatic mesh refinement.  ...  In addition, an approximate 1D Riemann problem is solved on each face of the nodal control volume to advect mass, momentum, and total energy.  ...  Dean Risinger for developing data structures for unstructured tetrahedron meshes.  ... 
doi:10.1016/j.jcp.2014.10.048 fatcat:5wbqhxmhebbgheqt5n2aq6u67a

Page 2720 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
Summary: “In this paper, a general approach to automatic gener- ation of quadrilaterals on three-dimensional surfaces is presented.  ...  (KR-GYSG-ME; Chinju) General approach to automatic generation of quadrilaterals on three-dimensional surfaces. (English summary) Comm. Numer. Methods Engrg. 14 (1998), no. 7, 609-620.  ... 

Riemann solvers and pressure gradients in Godunov-type schemes for variable density incompressible flows [article]

Shannon Leakey, Vassilis Glenis, Caspar J. M. Hewett
2021 arXiv   pre-print
at the free surface.  ...  Based on a rearrangement of the momentum equation and an exploitation of the other gradients and source terms, the new pressure gradient calculation automatically captures the pressure gradient discontinuity  ...  surface automatically.  ... 
arXiv:2108.08769v1 fatcat:pizzp5tgrrfefpqtlknwor5ow4

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

P. Glaister
1994 Computers and Mathematics with Applications  
The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section.  ...  This is in contrast to usual 'square root' averages found in this type of Riemann solver, where the computational expense can be prohibitive.  ...  ., values of +i/& > 7.2, 100 mesh points are generally needed to obtain a good approximation to the exact solution.  ... 
doi:10.1016/0898-1221(94)90008-6 fatcat:6bngzwrpz5eyffvgvzvqvuunny

Brain Morphometry Analysis with Surface Foliation Theory [article]

Chengfeng Wen, Na Lei, Ming Ma, Xin Qi, Wen Zhang, Yalin Wang, David Xianfeng Gu
2018 arXiv   pre-print
Given brain cortical surfaces with automatically extracted landmark curves, we first construct finite foliations on surfaces.  ...  The proposed method is rigorous, geometric, and automatic.  ...  A colorable quad-mesh method was employed to generate the quadrilateral mesh based on Strebel differentials, which then leads to the structured hexahedral mesh of the enclosed volume for high genus surfaces  ... 
arXiv:1809.02870v1 fatcat:p3ddmywe6bexxn37edw64aedwq

Spacetime simulation of dynamic fracture with crack closure and frictional sliding

Reza Abedi, Robert B. Haber
2018 Advanced Modeling and Simulation in Engineering Sciences  
Powerful adaptive spacetime meshing tracks dynamic evolution of fracture-surface networks and captures moving solution features.  ...  planar path to fragmentation of rock by an explosively loaded wellbore with stochastic nucleation, free propagation, and coalescence of fracture surfaces. which permits unrestricted use, distribution,  ...  Availability of data and materials Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.  ... 
doi:10.1186/s40323-018-0116-5 fatcat:niqyhwxuzna67kikhu5eths2ty

Surface parameterization using Riemann surface structure

Yalin Wang, Xianfeng Gu, K.M. Hayashi, T.F. Chan, P.M. Thompson, Shing-Tung Yau
2005 Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1  
We propose a general method that parameterizes general surfaces with complex (possible branching) topology using Riemann surface structure.  ...  Our method provides a surface-based framework for statistical comparison of surfaces and for generating grids on surfaces for PDE-based signal processing.  ...  Here we present a new method to parameterize general surfaces based on their Riemann surface structure.  ... 
doi:10.1109/iccv.2005.233 dblp:conf/iccv/WangGHCTY05 fatcat:uah4oshunffdneftiqymfayj5a
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