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Designing Quadrangulations with Discrete Harmonic Forms [article]

Y. Tong, P. Alliez, D. Cohen-Steiner, M. Desbrun
2006 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
Based on discrete differential forms, our method hinges on extending the discrete Laplacian operator (used extensively in modeling and animation) to allow for line singularities and singularities with  ...  a pure quadrangle tiling, with no T-junctions.  ...  Designing a Tiling Designing the final quadrangulation amounts to deciding on an assignment of (u, v) values at each corner of every metaface.  ... 
doi:10.2312/sgp/sgp06/201-210 fatcat:u2ziy2v3zffttaxjwe4dzqlsm4

Anisotropic quadrangulation

Denis Kovacs, Ashish Myles, Denis Zorin
2011 Computer Aided Geometric Design  
Quadrangulation methods aim to approximate surfaces by semi-regular meshes with as few extraordinary vertices as possible.  ...  Both types of techniques create near-isotropic quads; featurealigned quadrangulation algorithms reduce the remeshing error by aligning isotropic quads with principal curvature directions.  ...  As Figure 11 demonstrates, anisotropic harmonic quadrangulation can handle models with sharp features robustly, even with no feature alignment.  ... 
doi:10.1016/j.cagd.2011.06.003 fatcat:uvh7fuzejvd2lcmhzcojpkegia

Controlled field generation for quad-remeshing

Oliver Schall, Rhaleb Zayer, Hans-Peter Seidel
2008 Proceedings of the 2008 ACM symposium on Solid and physical modeling - SPM '08  
Treating the surface as an inhomogeneous domain we can endow specific surface regions with field attraction/repulsion properties.  ...  While the construction of such fields is by now a standard technique in geometry processing, enforcing design constraints is still not fully investigated.  ...  Based on a modified discrete Laplacian operator, two scalar fields whose iso-contours form the quadrangular mesh are computed.  ... 
doi:10.1145/1364901.1364942 dblp:conf/sma/SchallZS08 fatcat:56hh3ddojvcw7dfsl364pjfi5q

Boundary aligned smooth 3D cross-frame field

Jin Huang, Yiying Tong, Hongyu Wei, Hujun Bao
2011 ACM Transactions on Graphics  
To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2.  ...  With such a representation, we can formulate an efficient smoothness measure of the cross-frame field.  ...  As with the numerous applications of symmetric vector fields on surfaces, this new methodology may open a valuable line of research into ways to control the cross-frame field with constraints designed  ... 
doi:10.1145/2070781.2024177 fatcat:4qb6i2lkirbenp7cp7fr6nvlvq

Boundary aligned smooth 3D cross-frame field

Jin Huang, Yiying Tong, Hongyu Wei, Hujun Bao
2011 Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11  
To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2.  ...  With such a representation, we can formulate an efficient smoothness measure of the cross-frame field.  ...  As with the numerous applications of symmetric vector fields on surfaces, this new methodology may open a valuable line of research into ways to control the cross-frame field with constraints designed  ... 
doi:10.1145/2070752.2024177 fatcat:jjxtadjnozazzoinoh5li2rnse

Boundary aligned smooth 3D cross-frame field

Jin Huang, Yiying Tong, Hongyu Wei, Hujun Bao
2011 Proceedings of the 2011 SIGGRAPH Asia Conference on - SA '11  
To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2.  ...  With such a representation, we can formulate an efficient smoothness measure of the cross-frame field.  ...  As with the numerous applications of symmetric vector fields on surfaces, this new methodology may open a valuable line of research into ways to control the cross-frame field with constraints designed  ... 
doi:10.1145/2024156.2024177 fatcat:k42v6ihbfrdd5hljuxlebwoeva

Spectral surface quadrangulation

Shen Dong, Peer-Timo Bremer, Michael Garland, Valerio Pascucci, John C. Hart
2006 ACM Transactions on Graphics  
We describe a fundamentally new approach to the quadrangulation of manifold polygon meshes using Laplacian eigenfunctions, the natural harmonics of the surface.  ...  From this, we can construct a well-shaped quadrilateral mesh with very few extraordinary vertices.  ...  Simple surfaces (sphere, torus) work well with lower harmonics whereas higher genus surfaces require higher harmonics.  ... 
doi:10.1145/1141911.1141993 fatcat:64nok2zdlffnlm57rmrdwua65u

Spectral surface quadrangulation

Shen Dong, Peer-Timo Bremer, Michael Garland, Valerio Pascucci, John C. Hart
2006 ACM SIGGRAPH 2006 Papers on - SIGGRAPH '06  
We describe a fundamentally new approach to the quadrangulation of manifold polygon meshes using Laplacian eigenfunctions, the natural harmonics of the surface.  ...  From this, we can construct a well-shaped quadrilateral mesh with very few extraordinary vertices.  ...  Simple surfaces (sphere, torus) work well with lower harmonics whereas higher genus surfaces require higher harmonics.  ... 
doi:10.1145/1179352.1141993 fatcat:dqbhgaks6jbqrcpfhrqfm2agra

Eigenmodes of Surface Energies for Shape Analysis [chapter]

Klaus Hildebrandt, Christian Schulz, Christoph von Tycowicz, Konrad Polthier
2010 Lecture Notes in Computer Science  
In addition, we discuss a spectral quadrangulation scheme for surfaces.  ...  In this work, we study the spectra and eigenmodes of the Hessian of various discrete surface energies and discuss applications to shape analysis.  ...  As an example of such an energy we consider a discrete energy that is designed for thin shell simulation. Discrete shells.  ... 
doi:10.1007/978-3-642-13411-1_20 fatcat:4fx6ay3wenebvcace6fd4nd2ea

A Comparison of GPU Tessellation Strategies for Multisided Patches [article]

Gerben Jan Hettinga, Pieter J. Barendrecht, Jiri Kosinka
2018 Eurographics State of the Art Reports  
We propose an augmentation of the traditional tessellation pipeline with several different strategies that efficiently render multisided patches using generalised barycentric coordinates.  ...  There exist various forms of generalised barycentric coordinates [Flo15] such as Wachspress coordinates [Wac75] and harmonic coordinates [JMD * 07].  ...  Designing such models requires awareness of the abilities of multisided patches.  ... 
doi:10.2312/egs.20181041 fatcat:m4vdexawczbuxkvuhpp3bu26vy

Mixed-integer quadrangulation

David Bommes, Henrik Zimmer, Leif Kobbelt
2009 ACM Transactions on Graphics  
Abstract We present a novel method for quadrangulating a given triangle mesh.  ...  a) (b) (c) (d) Figure 1: Quadrangulation example: (a) A sparse set of conservatively estimated orientation and/or alignment constraints is selected on the input mesh by some simple heuristic or by the  ...  We would like to thank Felix Kälberer and Matthias Nieser for their helpful support, Tamal Dey, Muyang Zhang, AIM@SHAPE and Carlos Hernández (www.tsi.enst.fr/3dmodels) for providing us with datasets, Jan  ... 
doi:10.1145/1531326.1531383 fatcat:okemceaazrbbdolbnxwa6r33mm

Mixed-integer quadrangulation

David Bommes, Henrik Zimmer, Leif Kobbelt
2009 ACM SIGGRAPH 2009 papers on - SIGGRAPH '09  
Abstract We present a novel method for quadrangulating a given triangle mesh.  ...  a) (b) (c) (d) Figure 1: Quadrangulation example: (a) A sparse set of conservatively estimated orientation and/or alignment constraints is selected on the input mesh by some simple heuristic or by the  ...  We would like to thank Felix Kälberer and Matthias Nieser for their helpful support, Tamal Dey, Muyang Zhang, AIM@SHAPE and Carlos Hernández (www.tsi.enst.fr/3dmodels) for providing us with datasets, Jan  ... 
doi:10.1145/1576246.1531383 fatcat:rx5cnkdydjckjo46epkqwdaz7a

Quadrangular Parameterization for Reverse Engineering [chapter]

David Bommes, Tobias Vossemer, Leif Kobbelt
2010 Lecture Notes in Computer Science  
The shape of each chart is optimized non-linearly for isometry of the underlying parameterization to produce meshes with low edge-length distortion.  ...  Starting with a coarse, user-prescribed layout this is achieved by using affine functions for the transition between non-orthogonal quadrangular charts of a global parameterization.  ...  A discrete harmonic parameterization of a surface with disc topology mapping to a single chart is a well studied topic where typically the boundary of the surface is mapped to the boundary of a disc and  ... 
doi:10.1007/978-3-642-11620-9_5 fatcat:aig2v25m35gijgeibnnuvbb2bm

Interactive Quadrangulation with Reeb Atlases and Connectivity Textures

Julien Tierny, Joel Daniels II, Luis Gustavo Nonato, Valerio Pascucci, Claudio T. Silva
2012 IEEE Transactions on Visualization and Computer Graphics  
Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with  ...  Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design.  ...  We design a user-centric approach that offers exhaustive capabilities and comprehensive control during quadrangulation design.  ... 
doi:10.1109/tvcg.2011.270 pmid:22025751 fatcat:muwl2xcywndaxlp34jitw4khj4

Meshless quadrangulation by global parameterization

Er Li, Bruno Lévy, Xiaopeng Zhang, Wujun Che, Weiming Dong, Jean-Claude Paul
2011 Computers & graphics  
Point cloud is a basic description of discrete shape information. Parameterization of unorganized points is important for shape analysis and shape reconstruction of natural objects.  ...  The resultant parameterization can be used to triangulate and quadrangulate the point cloud simultaneously in a fully automatic manner, where the shape of the data is of any genus.  ...  [8] use a singularity graph to control the alignment and design the quadrangulation with discrete harmonic forms to create quads. Based on their work of [7] , Huang et al.  ... 
doi:10.1016/j.cag.2011.05.003 fatcat:xjv4p77jbvbphfazjhpfbmvi54
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