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Spherical Parameterization of Genus-Zero Meshes Using the Lagrange-Newton Method

Ying Li, Zhouwang Yang, Jiansong Deng
2007 2007 10th IEEE International Conference on Computer-Aided Design and Computer Graphics  
In this paper, an improved algorithm is constructed for parameterization of genus-zero meshes and aim to obtain high-quality surfaces fitting with PHT-splines.  ...  Several examples show that parametric surfaces of PHT-splines can be constructed adaptively and efficiently to fit given meshes associated with the parameterization results.  ...  Possibly a parameterization result behaves better for texture mapping, but worse for surface fitting. For a genus-zero mesh, there have existed some methods to parameterize it onto a sphere.  ... 
doi:10.1109/cadcg.2007.4407846 dblp:conf/cadgraphics/LiYD07 fatcat:6ghh7r2kwzhchnsw5dzltnwpre

Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy

Ying Li, Zhou-wang Yang, Jian-song Deng
2006 Journal of Zhejiang University: Science A  
In this paper, we will propose a method to parameterize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result.  ...  And for a certain application, some parametrization results might behave better than others.  ...  Possibly a parametrization result behaves better for texture mapping, but worse for surface fitting. For a genus-zero mesh, there are some methods to parametrize it onto a sphere.  ... 
doi:10.1631/jzus.2006.a1589 fatcat:djo2ybd3pfhrvatabfoypvneni

A Two Stage CVT / Eikonal Convection Mesh Deformation Approach for Large Nodal Deformations [article]

Stephan Schmidt
2014 arXiv   pre-print
A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is considered.  ...  The paper concludes with applications in 2D and 3D fluid dynamics and automatic code generation and manages to solve these problems without any remeshing.  ...  The resulting mesh is shown in Figure 3 .4 and is very well behaved.  ... 
arXiv:1411.7663v1 fatcat:z3mfxhlp5fb7lmdpyd5eok42ne

A Re-Parameterization Approach for the Construction of Domes with Planar Facets

Romain Mesnil
2018 Journal of the International Association for Shell and Spatial Structures  
The method can be used in various contexts and allows designers to design with two superimposed parameterizations, which allows for a potential decoupling between structure and envelope.  ...  The derivation of the analytical solution allows to link the method with the creation of meshes with planar hexagonal facets and of circle packing on spheres.  ...  Moulding surfaces are regularly used for the geometric generation of stadia. PQ-meshes and developable strips The pattern showed in Figure 12 is dual to lines of curvatures.  ... 
doi:10.20898/j.iass.2018.198.016 fatcat:qdz4lwp5jfd3nmkt7gi36mfzxq

Free-form shape design using triangulated surfaces

William Welch, Andrew Witkin
1994 Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94  
Automatic refinement, mesh smoothing, and re-triangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around  ...  This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying  ...  Thanks also to Hans Pedersen and Zoran Popović for their help with the figures.  ... 
doi:10.1145/192161.192216 dblp:conf/siggraph/WelchW94 fatcat:ur54s4w7ojgp5g6ucwgoitvliq

Hexagonal Global Parameterization of Arbitrary Surfaces

M. Nieser, J. Palacios, K. Polthier, E. Zhang
2012 IEEE Transactions on Visualization and Computer Graphics  
Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing.  ...  We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal  ...  ACKNOWLEDGMENTS The authors wish to thank Felix Kälberer and Ulrich Reitebuch for fruitful discussions on parameterization and help on remeshing. Craig Anderson helped with the video production.  ... 
doi:10.1109/tvcg.2011.118 pmid:21690644 fatcat:fsvd4dak2nerjc6cagxnp42lqm

Hexagonal global parameterization of arbitrary surfaces

Matthias Nieser, Jonathan Palacios, Konrad Polthier, Eugene Zhang
2010 ACM SIGGRAPH ASIA 2010 Sketches on - SA '10  
Such parameterizations enable the tiling of surfaces with nearly regular hexagonal or triangular patterns, and can be used for triangular remeshing.  ...  We demonstrate the usefulness of our geometry-aware global parameterization with applications such as surface tiling with nearly regular textures and geometry patterns, as well as triangular and hexagonal  ...  ACKNOWLEDGMENTS The authors wish to thank Felix Kälberer and Ulrich Reitebuch for fruitful discussions on parameterization and help on remeshing. Craig Anderson helped with the video production.  ... 
doi:10.1145/1899950.1899955 dblp:conf/siggrapha/NieserPPZ10 fatcat:gxlvuxxy5bfqhhw5ke6l5kj43i

ESTIMATING CURVATURE ON TRIANGULAR MESHES

TIMOTHY D. GATZKE, CINDY M. GRIMM
2006 International journal of shape modeling  
This paper takes a systematic look at methods for estimating the curvature of surfaces represented by triangular meshes.  ...  These tests are applied to existing discrete curvature approximation techniques and common surface fitting methods. We also look at alternatives to the standard parameterization techniques.  ...  They choose a uniformly weighted Gaussian so that the derivatives at the data points are well-behaved.  ... 
doi:10.1142/s0218654306000810 fatcat:iuwipc4uorci5pqov3jpyamp6q

Dynamic remeshing and applications

J. Vorsatz, Ch. Rössl, H.-P. Seidel
2003 Proceedings of the eighth ACM symposium on Solid modeling and applications - SM '03  
Triangle meshes are a flexible and generally accepted boundary representation for complex geometric shapes.  ...  A dynamic skeleton ensures that our approach is able to preserve surface features, which are particularly important for the visual quality of the mesh.  ...  Even for the tooth model at highest resolution (77K∆), the response times never exceeded 4-5 seconds.  ... 
doi:10.1145/781606.781633 dblp:conf/sma/VorsatzRS03 fatcat:yzao6zexmzfm3ew4xmsuu6athi

Dynamic remeshing and applications

J. Vorsatz, Ch. Rössl, H.-P. Seidel
2003 Proceedings of the eighth ACM symposium on Solid modeling and applications - SM '03  
Triangle meshes are a flexible and generally accepted boundary representation for complex geometric shapes.  ...  A dynamic skeleton ensures that our approach is able to preserve surface features, which are particularly important for the visual quality of the mesh.  ...  Even for the tooth model at highest resolution (77K∆), the response times never exceeded 4-5 seconds.  ... 
doi:10.1145/781632.781633 fatcat:fyu2cxhp2bfxbnhw36fxyid24q

Interactive geometry remeshing

Pierre Alliez, Mark Meyer, Mathieu Desbrun
2002 ACM Transactions on Graphics  
Filtering Transfer function Filtering Curvature Output 3D Meshes Remeshing Pipeline 2D Mesh Figure 1: A brief overview of our remeshing process: The input surface patch (top left) is first parameterized  ...  As a result, our remeshing technique is extremely versatile and general, being able to produce arbitrarily complex meshes with a variety of properties including: uniformity, regularity, semiregularity,  ...  We thus strongly advocate for the conformal parameterization as defined in [32, 11] since it behaves extremely well even on irregular triangulations [9] .  ... 
doi:10.1145/566570.566588 fatcat:qsgt7u7fgfeupd5wdhejllfwbe

Spectral Conformal Parameterization

Patrick Mullen, Yiying Tong, Pierre Alliez, Mathieu Desbrun
2008 Computer graphics forum (Print)  
We present a spectral approach to automatically and efficiently obtain discrete free-boundary conformal parameterizations of triangle mesh patches, without the common artifacts due to positional constraints  ...  High-quality parameterizations are computed through a constrained minimization of a discrete weighted conformal energy by finding the largest eigenvalue/eigenvector of a generalized eigenvalue problem  ...  Acknowledgements: We wish to express our thanks to the reviewers for providing meshes and advice, and to Lily Kharevych for providing the Circle Patterns examples used in this paper.  ... 
doi:10.1111/j.1467-8659.2008.01289.x fatcat:fk3276oyeje3vkpxkhvrc7zeba

Quad Layout Embedding via Aligned Parameterization

M. Campen, L. Kobbelt
2014 Computer graphics forum (Print)  
This process involves determining the layout's combinatorial structure as well as its geometric embedding in the surface.  ...  and meshing.  ...  Acknowledgements Thanks go to David Bommes and Henrik Zimmer for numerous helpful discussions and to Jan Möbius for support with the OpenFlipper framework.  ... 
doi:10.1111/cgf.12401 fatcat:czqntlvuejcanc3devd3ziuyy4

An analysis and comparison of parameterization-based computation of differential quantities for discrete surfaces

Duo Wang, Bryan Clark, Xiangmin Jiao
2009 Computer Aided Geometric Design  
Normals and curvatures are fundamental for geometric modeling and computer-aided design, but their accurate computations on discrete surfaces are challenging.  ...  Two types of methods, namely height-function based and parameterization based polynomial fittings, are well founded mathematically and can be proven to deliver convergent results under reasonable assumptions  ...  We also thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1016/j.cagd.2009.02.006 fatcat:lgzou2lppjd5nmc4codlwagqpa

Texturify: Generating Textures on 3D Shape Surfaces [article]

Yawar Siddiqui, Justus Thies, Fangchang Ma, Qi Shan, Matthias Nießner, Angela Dai
2022 arXiv   pre-print
Texturify operates directly on the surface of the 3D objects by introducing face convolutional operators on a hierarchical 4-RoSy parametrization to generate plausible object-specific textures.  ...  We thus propose Texturify, a GAN-based method that leverages a 3D shape dataset of an object class and learns to reproduce the distribution of appearances observed in real images by generating high-quality  ...  Further, we thank the authors of LTG [54] for assistance with their code and data.  ... 
arXiv:2204.02411v1 fatcat:m3z2xhadkzhy7meng3ef5i75qa
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