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Feature-Aligned Poly-Square Mapping of Large-Scale 2D Geometries for Semi-Structured Quad Mesh Generation

Celong Liu, Kelin Hu, Qin Chen, Xin Li
2020 Zenodo  
The second is a feature-preserved poly-square parameterization.  ...  The Morse-Smale Complex has been used [30, 31] to design quadrilateral patches.  ...  We solve this problem using the Hybrid L-BFGS (Limited Memory Broyden-Fletcher-Goldfarb-Shanno Method) optimization framework [44] .  ... 
doi:10.5281/zenodo.3653396 fatcat:xbczqhxl7jh3dfmn7urlstjhty

Cool Patches: A Geometric Approach to Ray/Bilinear Patch Intersections [chapter]

Alexander Reshetov
2019 Ray Tracing Gems  
ACKNOWLEDGMENTS We used the Blender rendering package [4] and instant field-aligned meshes system [12] for mesh quadrangulation.  ...  [12] . 3. the Quadrangulation through Morse-parameterization hybridization system as proposed by Fang et al. [9] . Only the last system creates a fully quadrangulated mesh.  ...  Neither of the used quadrangulation systems know that we will be rendering nonplanar primitives.  ... 
doi:10.1007/978-1-4842-4427-2_8 fatcat:g3o3fcoed5cvjkfjmnsrdjz6fm

Mode Surfaces of Symmetric Tensor Fields: Topological Analysis and Seamless Extraction [article]

Botong Qu, Lawrence Roy, Yue Zhang, Eugene Zhang
2020 arXiv   pre-print
In this paper, we provide novel analysis on the topological structures of mode surfaces, including a common parameterization of all mode surfaces of a tensor field using 2D asymmetric tensors.  ...  This parameterization leads to a perfect quadrangulation of the medium eigenvector manifold (Figure 7 (b) : the quad grid) with the only irregular vertices in the quadrangulation being the singularities  ...  On average, our neutral surface extraction method is about 1.8 times faster than the hybrid method introduced by Roy et al.  ... 
arXiv:2009.04601v1 fatcat:yki6if6ifjecrf7ypwjdktmvb4

Volumetric parameterization and trivariate B-spline fitting using harmonic functions

T. Martin, E. Cohen, R.M. Kirby
2009 Computer Aided Geometric Design  
The trivariate B-spline geometric and attribute representations are generated from the resulting parameterization, creating trivariate B-spline material property representations over the same parameterization  ...  We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate B-spline to data so that simulation attributes  ...  This means that a quadrangulation in this area is of poorer quality. Note, that ν min and ν max were chosen in areas which are not important in the proposed simulation.  ... 
doi:10.1016/j.cagd.2008.09.008 fatcat:zsjtw4wc7nhddk5j5ao5jpqh5y

Volumetric parameterization and trivariate b-spline fitting using harmonic functions

Tobias Martin, Elaine Cohen, Mike Kirby
2008 Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08  
The trivariate B-spline geometric and attribute representations are generated from the resulting parameterization, creating trivariate B-spline material property representations over the same parameterization  ...  We present a methodology based on discrete volumetric harmonic functions to parameterize a volumetric model in a way that it can be used to fit a single trivariate B-spline to data so that simulation attributes  ...  This means that a quadrangulation in this area is of poorer quality. Note, that ν min and ν max were chosen in areas which are not important in the proposed simulation.  ... 
doi:10.1145/1364901.1364938 dblp:conf/sma/MartinCK08 fatcat:c7nab2lwlja3tj3nvxuijyntte

Geometric Modeling Based on Polygonal Meshes [article]

Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Levy
2008 Eurographics State of the Art Reports  
A Morse-Smale complex is extracted from one Laplacian eigenvector, and refined using a globally smooth parameterization technique.  ...  Figure 8 . 8 Figure 8.21: Spectral Surface Quadrangulation first computes a Laplace eigenfunction (A), then extracts its Morse complex (B), smooths it (C) and uses it to partition the mesh into quads,  ...  His research interests include various topics commonly referred to as geometry processing: Surface reconstruction, mesh generation, surface remeshing, mesh parameterization, mesh compression.  ... 
doi:10.2312/egt.20081055 fatcat:yypmklz4lvexpox3z6iinvwun4

Geometric modeling based on polygonal meshes

Mario Botsch, Mark Pauly, Leif Kobbelt, Pierre Alliez, Bruno Lévy, Stephan Bischoff, Christian Rössl
2007 ACM SIGGRAPH 2007 courses on - SIGGRAPH '07  
He has published several papers in the area of geometry compression, mesh approximation, surface remeshing, mesh generation and surface parameterization.  ...  Figure 10 . 14 : 1014 Spectral surface quadrangulation. Figure taken from [DBG + 06]. Figure 10 . 15 : 1015 Quadrangle surface tiling through contouring.  ...  A Morse-Smale complex is extracted from one Laplacian eigenvector, and refined using a globally smooth parameterization technique.  ... 
doi:10.1145/1281500.1281640 dblp:conf/siggraph/BotschPKALBR07 fatcat:khwj3g4lu5eurovnvvt7hzenye

Quadrilateral mesh simplification

Joel Daniels, Cláudio T. Silva, Jason Shepherd, Elaine Cohen
2008 ACM Transactions on Graphics  
Morse-Smale complexes automatically segment a surface into regions homeomorphic to a disc [Ni et al. 2004] , and parameterization methods can guide the quadrilateral-based remesh [Dong et al. 2006; Tong  ...  For instance, it is not possible to create a quadrangulation of a planar surface region bounded by a polyline with an odd number of vertices.  ... 
doi:10.1145/1409060.1409101 fatcat:t7q3eyqmbbfazewxnljviguu2u

Quadrilateral mesh simplification

Joel Daniels, Cláudio T. Silva, Jason Shepherd, Elaine Cohen
2008 ACM SIGGRAPH Asia 2008 papers on - SIGGRAPH Asia '08  
Morse-Smale complexes automatically segment a surface into regions homeomorphic to a disc [Ni et al. 2004] , and parameterization methods can guide the quadrilateral-based remesh [Dong et al. 2006; Tong  ...  For instance, it is not possible to create a quadrangulation of a planar surface region bounded by a polyline with an odd number of vertices.  ... 
doi:10.1145/1457515.1409101 fatcat:55hai3dxvra67fosdeg4vf5ftu

Ginzburg-Landau energy and placement of singularities in generated cross fields [article]

Alexis Macq, Maxence Reberol, François Henrotte, Pierre-Alexandre Beaufort, Alexandre Chemin, Jean-François Remacle, Jean Van Schaftingen
2020 arXiv   pre-print
The third approach uses Morse parameterization hybridization (see [28] ). Materials and methods We will begin by presenting our method for placing singularities in a domain.  ...  The paper of Myles and Zorin [12] does not consider additional integer constraints needed for quadrangulation.  ... 
arXiv:2010.16381v1 fatcat:rs4mqgpmsngvtdcveesfs664ba

Analysis-aware higher order smooth three-dimensional representations: creation, simulation and visualization

Tobias Martin
2012
r s i t y o f U t a h G r a d u a t e S c h o o l STATEMENT OF DISSERTATION APPROVAL The dissertation of has been approved by the following supervisory committee members: , Chair ABSTRACT Volumetric parameterization  ...  At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions  ...  Note that g l (ω) is parameterized through the harmonic field w(x, y, z).  ... 
doi:10.26053/0h-hs1m-7n00 fatcat:4xsm7lwhjfhrlcfcqvun2t2z2u

Flow-complex-based shape reconstruction from 3D curves

Bardia Sadri, Karan Singh
2014 ACM Transactions on Graphics  
Recently [Bessmeltsev et al. 2012 ] surface complex curve loops by quadrangulating them into multiple 4-sided patches.  ...  A hybrid approach that geometrically improves the flow complex based reconstruction using Delaunay elements, is subject to future work.  ... 
doi:10.1145/2560328 fatcat:khdm4l7clrhk7pha4cvuqmoer4

2-D blind deconvolution by partitioning into coupled 1-D problems using discrete Radon transforms

H. Ahn, A.E. Yagle
Proceedings., International Conference on Image Processing  
hybrid linear modeling.  ...  After the surface is parameterized, we can analyze and solve problems defined on the surface on the simpler domain. Conformal parameterization is often used.  ...  The question of maintaining a diffeomorphism through the process motivates the proposed work.  ... 
doi:10.1109/icip.1995.537409 dblp:conf/icip/AhnY95 fatcat:ecos74jfmfgonkuk5gsq2essp4