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Four-triangles adaptive algorithms for RTIN terrain meshes

Authors:

A. PlazaAuthors Info & Claims

Mathematical and Computer Modelling: An International Journal, Volume 49, Issue 5-6

Pages 1012 - 1020

https://doi.org/10.1016/j.mcm.2008.02.012

Published: 01 March 2009 Publication History

Abstract

We present a refinement and coarsening algorithm for the adaptive representation of Right-Triangulated Irregular Network (RTIN) meshes. The refinement algorithm is very simple and proceeds uniformly or locally in triangle meshes. The coarsening algorithm decreases mesh complexity by reducing unnecessary data points in the mesh after a given error criterion is applied. We describe the most important features of the algorithms and give a brief numerical study on the propagation associated with the adaptive scheme used for the refinement algorithm. We also present a comparison with a commercial tool for mesh simplification, Rational Reducer, showing that our coarsening algorithm offers better results in terms of accuracy of the generated meshes.

References

[1]

Cignoni, P., Montani, C. and Varshney, A., A comparison of mesh simplification algorithms. Comput. Graph. v22 i1. 37-54.

[2]

Cignoni, P., Rocchini, C. and Scopigno, R., Metro: measuring error on simplified surfaces. Comput. Graph. Forum. v17 i2. 167-174.

[3]

Bellenger, E. and Coorevits, P., Adaptive mesh refinement for the control of cost and quality in finite element analysis. Finite Elem. Anal. Des. v41 i15. 1413-1440.

Digital Library

[4]

Evans, W., Kirkpatrick, D. and Townsend, G., Right-triangulated irregular networks. Algorithmica. v30 i2. 264-286.

[5]

Li, M.H., Cheng, H.P. and Yeh, G.T., An adaptive multigrid approach for the simulation of contaminant transport in the 3d subsurface. Comput. Geosci. v31 i8. 1028-1041.

Digital Library

[6]

P. Lindstrom, D. Koller, W. Ribarsky, L. Hodeges, N. Faust, G. Turner, Real-time, continuous level of detail rendering of height fields, in: ACM Computer Graphics, Conf. Proc. Annual Conference Series, SIGGRAPH'96, 1996

Digital Library

[7]

System in motion. Rational reducer. http://www.rational-reducer.com

[8]

R. Pajarola, Large scale terrain visualization using the restricted quadtree triangulation, in: Proceedings IEEE Visualization, 1998, pp. 19-26

Digital Library

[9]

R. Pajarola, M. Antonijuan, R. Lario, Quadtin: Quadtree based triangulated irregular networks, in: Proceedings IEEE Visualization, 2002, pp. 395-402

Digital Library

[10]

Plaza, A., Suárez, J.P., Padrón, M.A., Falcón, S. and Amieiro, D., Mesh quality improvement and other properties in the four-triangles longest-edge partition. Comput. Aided Geome. Design. v21 i4. 353-369.

Digital Library

[11]

Rivara, M.C. and Iribarren, G., The 4-triangles longest-side partition of triangles and linear refinement algorithms. Math. Comp. v65 i216. 1485-1502.

Digital Library

[12]

Rossignac, J. and Borrel, P., Multiresolution 3D approximation for rendering complex scenes. In: Geometric Modeling in Computer Graphics, Springer Verlag. pp. 455-465.

[13]

Suárez, J.P. and Plaza, A., Refinement and hierarchical coarsening schemes for triangulated surfaces. Journal of WSCG. v11.

[14]

Suárez, J.P., Plaza, A. and Carey, G.F., Graph based data structures for skeleton based refinement algorithms. Commun. Numer. Methods Eng. v17 i12. 903-910.

[15]

Suárez, J.P., Plaza, A. and Carey, G.F., Propagation of longest-edge mesh pattern in local adaptive refinement. Commun. Numer. Methods Eng.

[16]

J.P. Suárez, A. Plaza, M.A. Padrón, Mesh graph structure for longest-edge refinement algorithms, 7th International Meshing Roundtable, Michigan, USA. SAND 98-2250, Sandia National Laboratories, 1998

[17]

Velho, L. and Zorin, D., 4-8 subdivision. Computer-Aided Geometric Design. v18 i5. 397-427.

Digital Library

[18]

Wang, Y., Renaud, J.-P., Anderson, M.G. and Allen, C.B., A boundary and soil interface conforming unstructured local mesh refinement for geological structures. Finite Elem. Anal. Des. v40. 1429-1443.

Digital Library

[19]

A surface modeling algorithm designed for speed and ease of use with all petroleum industry data. Comput. Geosci. v29. 1175-1182.

Cited By

Marks DElmore PBlain CBourgeois BPetry FFerrini V(2017)A variable resolution right TIN approach for gridded oceanographic dataComputers & Geosciences10.1016/j.cageo.2017.07.008109:C(59-66)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.cageo.2017.07.008
Korotov SPlaza ÁSuárez J(2016)Longest-edge n -section algorithmsJournal of Computational and Applied Mathematics10.1016/j.cam.2015.03.046293:C(139-146)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1016/j.cam.2015.03.046
Tian YZheng YZheng C(2016)Development of a visualization tool for integrated surface water-groundwater modelingComputers & Geosciences10.1016/j.cageo.2015.09.01986:C(1-14)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cageo.2015.09.019
Show More Cited By

Four-triangles adaptive algorithms for RTIN terrain meshes
1. Computing methodologies
  1. Computer graphics
2. Theory of computation

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Information

Published In

cover image Mathematical and Computer Modelling: An International Journal

Mathematical and Computer Modelling: An International Journal Volume 49, Issue 5-6

March, 2009

443 pages

ISSN:0895-7177

Issue’s Table of Contents

Copyright © Elsevier Ltd © 2008.

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 March 2009

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Cited By

Marks DElmore PBlain CBourgeois BPetry FFerrini V(2017)A variable resolution right TIN approach for gridded oceanographic dataComputers & Geosciences10.1016/j.cageo.2017.07.008109:C(59-66)Online publication date: 1-Dec-2017
https://dl.acm.org/doi/10.1016/j.cageo.2017.07.008
Korotov SPlaza ÁSuárez J(2016)Longest-edge n -section algorithmsJournal of Computational and Applied Mathematics10.1016/j.cam.2015.03.046293:C(139-146)Online publication date: 1-Feb-2016
https://dl.acm.org/doi/10.1016/j.cam.2015.03.046
Tian YZheng YZheng C(2016)Development of a visualization tool for integrated surface water-groundwater modelingComputers & Geosciences10.1016/j.cageo.2015.09.01986:C(1-14)Online publication date: 1-Jan-2016
https://dl.acm.org/doi/10.1016/j.cageo.2015.09.019
Liu ZPeng MDi K(2014)A continuative variable resolution digital elevation model for ground-based photogrammetryComputers & Geosciences10.5555/2745549.274565662:C(71-79)Online publication date: 1-Jan-2014
https://dl.acm.org/doi/10.5555/2745549.2745656
Perdomo FPlaza Á(2013)Proving the non-degeneracy of the longest-edge trisection by a space of triangular shapes with hyperbolic metricApplied Mathematics and Computation10.5555/2745046.2745153221:C(424-432)Online publication date: 15-Sep-2013
https://dl.acm.org/doi/10.5555/2745046.2745153

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