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Optimal Interpolatory Wavelets Transform for Multiresolution Triangular Meshes

Chong Zhao, Hanqiu Sun
2011 Applied Mathematics  
The matrix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and 3 subdivision.  ...  The new wavelets transform not only inherits the advantages of subdivision, but also offers more resolutions of complex models.  ...  By selecting the function vector as: Jiang et al. [20] extended the matrix-valued loop subdivision scheme to the interpolatory loop subdivision scheme.  ... 
doi:10.4236/am.2011.23044 fatcat:bir6w6rk5ncjhh4ylgxzyk5cia

Recent advances in multiresolution analysis of 3D meshes and their applications

Michaël Roy, Sebti Foufou, Frédéric Truchetet, Frédéric Truchetet, Olivier Laligant
2010 Wavelet Applications in Industrial Processing VII  
The concept of multiresolution analysis proposes an efficient and versatile tool for digital geometric processing allowing for numerous applications.  ...  When representing complex shapes in raw data format, meshes consume a large amount of space.  ...  The authors use the progressive mesh algorithm 32 to build the coarse resolution mesh, and a smoothing operator to estimate the high resolution mesh.  ... 
doi:10.1117/12.845595 fatcat:6zxujtivmvfvzgdk6ymexdcuuy

Isogeometric Analysis for Surface PDEs with Extended Loop Subdivision [article]

Qing Pan, Timon Rabczuk, Gang Xu, Chong Chen
2019 arXiv   pre-print
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach.  ...  of the extended Loop subdivision for different initial control meshes.  ...  The other reason is the computation around the boundary patches is more complex for our IGA-Loop than FEM-Linear because the extended Loop subdivision scheme embodies the angle information different of  ... 
arXiv:1905.02977v1 fatcat:ed7ycpupm5ghpdlwa4kea6acfy

Smooth reverse Loop and Catmull–Clark subdivision

Javad Sadeghi, Faramarz F. Samavati
2011 Graphical Models  
This approach is then used to find smooth reverse of the Loop and Catmull-Clark subdivisions. We discuss the advantages of using this technique in various surface editing and synthesis applications.  ...  We first introduce a general reverse subdivision approach that starts from a trial set of biorthogonal multiresolution filters and refines the resulting coarse points using local masks.  ...  (b) Detail visualization using reverse Catmull-Clark scheme of Olsen and Samavati. (c) Detail visualization using smooth reverse Catmull-Clark subdivision.  ... 
doi:10.1016/j.gmod.2011.03.004 fatcat:kv3l4m736bbzdi4pmonpqzjpcy

Slow Growing Subdivision (SGS) in Any Dimension: Towards Removing the Curse of Dimensionality

V. Pascucci
2002 Computer graphics forum (Print)  
In recent years subdivision methods have been one of the most successful techniques applied to the multi-resolution representation and visualization of surface meshes.  ...  In this paper we mainly tackle the first part of the problem introducing a subdivision scheme that generalizes to 3D and higher dimensional meshes without the excessive vertex proliferation typical of  ...  We have experimented with a very simple averaging rule that has been proven visually smooth for the 2D case and extends naturally to the volumetric and higher dimensional cases.  ... 
doi:10.1111/1467-8659.t01-1-00605 fatcat:3p2ykc2ivfdzpflxhs73fm57kq

Slow Growing Subdivision (SGS) in Any Dimension: Towards Removing the Curse of Dimensionality

Valerio Pascucci
2002 Computer graphics forum (Print)  
In recent years subdivision methods have been one of the most successful techniques applied to the multi-resolution representation and visualization of surface meshes.  ...  In this paper we mainly tackle the first part of the problem introducing a subdivision scheme that generalizes to 3D and higher dimensional meshes without the excessive vertex proliferation typical of  ...  We have experimented with a very simple averaging rule that has been proven visually smooth for the 2D case and extends naturally to the volumetric and higher dimensional cases.  ... 
doi:10.1111/1467-8659.00605 fatcat:wunuomyshnh5bcrffcntht2cty

SUBDIVISION ON ARBITRARY MESHES: ALGORITHMS AND THEORY [chapter]

Denis Zorin
2007 Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore  
This survey is an introduction to subdivision algorithms for arbitrary meshes and related mathematical theory; we review the most important subdivision schemes the theory of smoothness of subidivision  ...  surfaces, and known facts about approximation properties of subdivision bases.  ...  Loop and Catmull-Clark subdivision produce surfaces of higher visual quality, as these schemes reduce to C 2 splines on a regular mesh.  ... 
doi:10.1142/9789812709066_0001 fatcat:2zsbmji6ifdjjj3rtkia77iymi

Beyond Catmull-Clark? A Survey of Advances in Subdivision Surface Methods

Thomas J. Cashman
2011 Computer graphics forum (Print)  
This survey summarizes research on subdivision surfaces over the last fifteen years in three major strands: analysis, integration into existing systems, and the development of new schemes.  ...  We also examine the reason for the low adoption of new schemes with theoretical advantages, explain why Catmull-Clark surfaces have become a de facto standard in geometric modelling, and conclude by identifying  ...  Section 5.3; • a unified analysis for these non-linear schemes, extending the work in Section 3.5; • schemes which fully realize the promise of arbitrarytopology NURBS (Section 5.5) with at least bounded  ... 
doi:10.1111/j.1467-8659.2011.02083.x fatcat:zmlwwk4l2zfwdmhyum3z7zhqoe

Non-linear subdivision using local spherical coordinates

Nicolas Aspert, Touradj Ebrahimi, Pierre Vandergheynst
2003 Computer Aided Geometric Design  
Numerical criteria are proposed to verify basic properties, such as convergence of the scheme and the regularity of the limit function.  ...  In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable.  ...  Surface subdivision results The proposed surface subdivision scheme is compared with two well known schemes : the Butterfly scheme (extended as proposed in [27] ) and the Loop scheme.  ... 
doi:10.1016/s0167-8396(03)00028-1 fatcat:riadvxndz5azxpnabu55jwz3n4

Efficient view-dependent refinement of 3D meshes using sqrt{3}-subdivision

Pierre Alliez, Nathalie Laurent, Henri Sanson, Francis Schmitt
2003 The Visual Computer  
We demonstrate that the √ 3 subdivision operator recently introduced by Kobbelt offers many benefits, including view-dependent refinement, removal of polygonal aspect and highly tunable level of detail  ...  Our main goal is the design of fast and robust smooth surface reconstruction from coarse meshes.  ...  This work is part of the 3D project V2NET, backed by a grant from the RNRT (National Telecommunications Research Network), and has been partially supported by the Integrated Media Systems Center, a NSF  ... 
doi:10.1007/s00371-002-0165-z fatcat:iofcfh7cu5hxdekexsa63vaxuy

Taxonomy of interpolation constraints on recursive subdivision surfaces

Ahmad H. Nasri, Malcolm A. Sabin
2002 The Visual Computer  
This is the second of two papers which describe and classify situations which any complete study of interpolation constraints for a recursive subdivision surface needs to consider.  ...  It addresses surface interpolation constraints, building upon the concepts and categories introduced in the first paper, on interpolation constraints on recursive subdivision curves.  ...  Thanks are due to the American University of Beirut, the Lebanese National Council for Scientific Research, and the Royal Society of London for supporting this work.  ... 
doi:10.1007/s003710100155 fatcat:m5vbcowrdfgaflpw6df7ti5dhq

Real-Time Reconstruction of Wavelet-Encoded Meshes for View-Dependent Transmission and Visualization

P. Gioia, O. Aubault, C. Bouville
2004 IEEE transactions on circuits and systems for video technology (Print)  
It enables fast, homogeneous accommodation and suppression of wavelet coefficients at any level of subdivision, with time complexity independent of the size of the reconstructed mesh.  ...  Wavelet methods for geometry encoding is a recently emerged superset of multiresolution analysis which has proven to be very efficient in term of compression and adaptive transmission of 3D content.  ...  In the general case, better prediction is obtained using more elaborate, classical subdivisions schemes, in particular Loop and Butterfly [7] [8] .  ... 
doi:10.1109/tcsvt.2004.830672 fatcat:ktlllfrebrhonkfc3q3aur3o4y

Subdivision Surface Tesselation on the Fly using a versatile Mesh Data Structure

Kerstin Müller, Sven Havemann
2000 Computer graphics forum (Print)  
In this paper, we present a realization of tesselation-on-the-fly for Loop subdivision surfaces as part of a framework for interactive visualization.  ...  But with larger control meshes, efficient adaptive rendering techniques are indispensable for interactive visualization and shape modeling.  ...  However, focusing on the most popular subdivision schemes from Loop 5 and Catmull and Clark 1 , a fundamental requirement is that the mesh be locally 2-manifold everywhere, but may have boundaries.  ... 
doi:10.1111/1467-8659.00407 fatcat:xybxu44rrfe7lh4hgshafg4t6u

Multiresolution analysis for irregular meshes

Michael Roy, Sebti Foufou, Andreas Koschan, Frederic Truchetet, Mongi Abidi, Frederic Truchetet
2004 Wavelet Applications in Industrial Processing  
The concept of multiresolution analysis applied to irregular meshes has become more and more important.  ...  We show the efficiency of our framework through a number of applications including filtering, denoising and adaptive simplification.  ...  The authors used Loop subdivision for the estimation of the high resolution mesh from the coarse representation.  ... 
doi:10.1117/12.515974 fatcat:agbsyew5zbgyvkk5deckk44hxa

Subdivision surface fitting for efficient compression and coding of 3D models

Guillaume Lavoué, Florent Dupont, Atilla Baskurt
2005 Visual Communications and Image Processing 2005  
steps, the subdivision surfaces will visually represent the shape of the original meshes (of which original connectivity will not be kept).  ...  The found subdivision control polyhedron is much more compact than the original mesh and visually represents the same shape after several subdivision steps, without artifacts or cracks, like traditional  ...  ACKNOWLEDGEMENTS This work is supported by the French Research Ministry and the RNRT (Réseau National de Recherche en Télécommunications) within the framework of the Semantic-3D national project (http:  ... 
doi:10.1117/12.631641 fatcat:2qfa4ifuvfdctptf43hv64xnky
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