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Refinement operators for triangle meshes

Marc Alexa
2002 Computer Aided Geometric Design  
Refinement operators for triangular meshes as used in subdivision schemes or remeshing are discussed.  ...  A numbering scheme is presented, covering all refinement operators that (topologically) map vertices onto vertices.  ...  Acknowledgements: Thanks to Leif Kobbelt and Malcolm Sabin for very fruitful and encouraging discussions on the subject.  ... 
doi:10.1016/s0167-8396(02)00084-5 fatcat:pxyxpks6srhenpjgwy2yz7yp5a

Selectively Refinable Subdivision Meshes [article]

Enrico Puppo
2006 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
We introduce RGB triangulations, an extension of red-green triangulations that can support selective refinement over subdivision meshes generated through quadrisection of triangles.  ...  Our mechanism permits to take an adaptive mesh at intermediate level of subdivision and process it through both refinement and coarsening operations, by remaining consistent with an underlying Loop subdivision  ...  To this aim, refinement and coarsening operations must be based on local operators.  ... 
doi:10.2312/sgp/sgp06/153-162 fatcat:pysv4dr2vndtnidtlqwetgp27y

Interpolatory √3-Subdivision

U. Labsik, G. Greiner
2000 Computer graphics forum (Print)  
We present a new interpolatory subdivision scheme for triangle meshes.  ...  Using this refinement operator the number of triangles only triples in each step. New vertices are computed with a Butterfly like scheme.  ...  Acknowledgments We are grateful to Leif Kobbelt for directing our attention to √ 3-subdivision schemes and for several helpful hints.  ... 
doi:10.1111/1467-8659.00405 fatcat:zivcop2ouvfpplvv5skpq2hrmm

√3-subdivision

Leif Kobbelt
2000 Proceedings of the 27th annual conference on Computer graphics and interactive techniques - SIGGRAPH '00  
The size of the surrounding mesh area which is affected by selective refinement is smaller than for the dyadic split operation.  ...  The new splitting operation enables locally adaptive refinement under builtin preservation of the mesh consistency without temporary crackfixing between neighboring faces from different refinement levels  ...  Acknowledgements I would like to thank Stephan Bischoff and Ulf Labsik for implementing the ¢ 3-subdivision scheme and performing some of the experiments.  ... 
doi:10.1145/344779.344835 dblp:conf/siggraph/Kobbelt00 fatcat:k3tzdzwohnepnlyd3pwqp6lepa

Adaptive Mesh Booleans [article]

Ryan Schmidt, Tyson Brochu
2016 arXiv   pre-print
We present a new method for performing Boolean operations on volumes represented as triangle meshes.  ...  Rather than depending on computing precise face intersections, our approach refines the input meshes in the intersection regions, then discards intersecting triangles and fills the resulting holes with  ...  (We use different minimum and maximum values for other mesh refinement operations in our larger mesh modeling package.)  ... 
arXiv:1605.01760v1 fatcat:yq4zixh5bffzzijywiaisjo7du

A Multiresolution Approach to Render 3D Models

Francisco RAMOS, Miguel CHOVER, Oscar RIPOLLES
2013 Informatica  
In this paper, we introduce a new and simple framework for performing on-the-fly refinement and simplification of meshes completely on the GPU.  ...  The tessellation step performs uniform refinement or simplification operations by applying a fixed subdivision criterion.  ...  In this paper, we propose an approach for refinement and simplification of triangle meshes on the GPU.  ... 
doi:10.15388/informatica.2013.06 fatcat:hlfkx2cpobexrcrh77qhyp22o4

Progressive transmission of subdivision surfaces

U. Labsik, L. Kobbelt, R. Schneider, H.-P. Seidel
2000 Computational geometry  
Triangle meshes are a standard representation for surface geometry in computer graphics and virtual reality applications.  ...  meshes.  ...  A uniform subdivision operator S refines a given mesh M k to a new mesh M k+1 .  ... 
doi:10.1016/s0925-7721(99)00045-0 fatcat:czewtdfmknewhekxsseac744xq

Obtaining a Canonical Polygonal Schema from a Greedy Homotopy Basis with Minimal Mesh Refinement [article]

Marco Livesu
2020 arXiv   pre-print
Despite this operation is conceptually simple, known refinement strategies do not scale well for high genus shapes, triggering a mesh growth that may exceed the amount of memory available in modern computers  ...  In this paper we study various local refinement operators to detach cycles in a system of loops, and show that there are important differences between them, both in terms of mesh complexity and preservation  ...  Fig. 4 . 4 The three possible refinement operators for a triangle mesh.  ... 
arXiv:2001.03664v1 fatcat:supfjrw4nrelrhxnbzfjf725hy

Polygon Laplacian Made Simple

Astrid Bunge, Philipp Herholz, Misha Kazhdan, Mario Botsch
2020 Computer graphics forum (Print)  
The discrete Laplace-Beltrami operator for surface meshes is a fundamental building block for many (if not most) geometry processing algorithms.  ...  By virtually inserting a carefully placed point we implicitly refine each polygon into a triangle fan, but then hide the refinement within the matrix assembly.  ...  Acknowledgments We thank the anonymous reviewers for their valuable comments and suggestions, and Marc Alexa and Fabian Prada for helpful discussions on Laplacians and discrete exterior calculus.  ... 
doi:10.1111/cgf.13931 fatcat:i6b3wfcq5bcvrhnpyy2dydqqpi

Iterative Image Coding Using Hybrid Wavelet-Based Triangulation [chapter]

Phichet Trisiripisal, Sang-Mook Lee, A. Lynn Abbott
2006 Lecture Notes in Computer Science  
This paper presents a novel hierarchical subdivision scheme for generating triangular meshes to represent intensity images.  ...  The resulting representation is well suited to content-based management of images and videos, including storage and retrieval for multimedia applications.  ...  Wavelet coefficients are used directly in selecting mesh node locations, in selecting node interconnections, and for mesh refinement.  ... 
doi:10.1007/978-3-540-69423-6_31 fatcat:4bkmd2e72jbvvhww2zvmmtjnoa

Refinement and Hierarchical Coarsening Schemes for Triangulated Surfaces

José P. Suárez, Angel Plaza
2003 International Conference in Central Europe on Computer Graphics and Visualization  
We present a refinement and a coarsening (also simplification or decimation) algorithm for the adaptive representation of bivariate functions.  ...  The refinement algorithm is very simple and of linear complexity in the number of vertices, and proceeds uniformly or locally in triangular meshes.  ...  Meanwhile the refinement algorithm operates on the triangles of a given mesh τ, the coarsening algorithm operates on the vertices for each intermediate mesh τ i of an input sequence T.  ... 
dblp:conf/wscg/SuarezP03 fatcat:o5roroqdzzhyrf3y4qnm4vwxae

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

Pierre Alliez, Nathalie Laurent, Henri Sanson, Francis Schmitt
2003 The Visual Computer  
In this paper we introduce an efficient view dependent refinement technique well-suited to adaptive visualization of 3D triangle meshes on a graphic terminal.  ...  In particular, we propose a new data structure that requires neither edges nor hierarchies for efficient and reversible view-dependent refinement.  ...  Acknowledgements A very special thanks to Gaspard Breton for helping to implement the camera transform, to Alexandre Buisson for invaluable help in optimization tips, and to Mathieu Desbrun for writing  ... 
doi:10.1007/s00371-002-0165-z fatcat:iofcfh7cu5hxdekexsa63vaxuy

Progressive forest split compression

Gabriel Taubin, André Guéziec, William Horn, Francis Lazarus
1998 Proceedings of the 25th annual conference on Computer graphics and interactive techniques - SIGGRAPH '98  
As in the Progressive Mesh (PM) method of Hoppe, a triangular mesh is represented as a low resolution polygonal model followed by a sequence of refinement operations, each one specifying how to add triangles  ...  In this paper we introduce the Progressive Forest Split (PFS) representation, a new adaptive refinement scheme for storing and transmitting manifold triangular meshes in progressive and highly compressed  ...  Acknowledgments Our thanks to Rhythm & Hues Studios, Inc. and Greg Turk for the Horse model. Thanks to Marc Levoy for the Bunny model.  ... 
doi:10.1145/280814.280834 dblp:conf/siggraph/TaubinGHL98 fatcat:7up46bxox5hn3jnfbl7df7uznu

Computational results for parallel unstructured mesh computations

Mark T. Jones, Paul E. Plassmann
1994 Computing Systems in Engineering  
We present a set of algorithms that allow the entire unstructured mesh computation process to execute in parallel-including adaptive mesh refinement, equation reordering, mesh partitioning, and sparse  ...  These unstructured meshes are often very large and require significant computational resources; hence they are excellent candidates for massively parallel computation.  ...  A n example of the basic operation of the parallel unstructured mesh strategy. On the left is T, for a processor and its neighbors with triangles marked for refinement.  ... 
doi:10.1016/0956-0521(94)90013-2 fatcat:izk4gngmlvfafftuqc5sb3d7ia

Visualizer: a mesh visualization system using view-dependent refinement

Uğur Güdükbay, Okan Arıkan, Bülent Özgüç
2002 Computers & graphics  
Progressive mesh (PM) is a multiresolution representation that defines continuous level of detail approximations for arbitrary triangle meshes.  ...  Arbitrary triangle mesh is a collection of 3D triangles without any shape or boundary restrictions.  ...  We thank T . urker Yılmaz for his help in modifying the implementation to measure the performance. Special thanks to Varol Akman and U$ gur Do$ grus . oz for valuable comments.  ... 
doi:10.1016/s0097-8493(02)00091-2 fatcat:hn6cunwb3fgw3avmfprkacynie
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