Piecewise optimal triangulation for the approximation of scattered data in the plane

Computer Aided Geometric Design

Volumn 17, Issue 8, 2000, Pages 767-787

  Bertram, Martin ^a   Barnes, James C ^a   Hamann, Bernd ^a   Joy, Kenneth I ^a   Pottmann, Helmut ^b   Wushour, Dilinur ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; DATA STRUCTURES; GRAPH THEORY; HIERARCHICAL SYSTEMS; LEAST SQUARES APPROXIMATIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS;

DATA-DEPENDENT TRIANGULATION; QUADRATIC POLYNOMIALS;

COMPUTATIONAL GEOMETRY;

EID: 0034276341     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8396(00)00026-1     Document Type: Article

References (31)

1. Barnes, J.C., Hamann, B. and Joy, K.I. (t.a.), An edge-preserving, data-dependent triangulation scheme for hierarchical rendering, in: Hagen, H. Nielson, G. and Post, F. (Eds.), Scientific Visualization - Methods and Applications, IEEE Computer Society Press, Springer-Verlag, New York.
2. Boehm W. and Prautzsch, H. (1994), Geometric Concepts for Geometric Design, A.K. Peters, Wellesley, MA.
3. Brown, J.L. (1991), Vertex based data dependent triangulations, Computer Aided Geometric Design 8(3), 239-251.
4. Daubechies, I., Guskov, I., Schröder, P. and Sweldens W. (t.a.), Wavelets on irregular point sets, Phil. Trans. R. Soc. Lond. A.
5. d'Azevedo, E.F. (1991), Optimal triangular mesh generation by coordinate transforma-tion, SIAM J. Sci. Statist. Comput. 12 (4), 755-786.
6. De Floriani, L., Falcidieno, B. and Pienovi, C. (1983), A Delaunay-based method for surface approximation, in: Proc. Eurographics '83, Amsterdam, Netherlands, 333-350.
7. De Floriani, L., Falcidieno, B., Nagy, G. and Pienovi, C. (1984), A hierarchical structure for surface approximation, Computers & Graphics 8 (2), 183-193.
8. Duchaineau, M., Wolinsky, M., Sigeti, D.E., Miller, M.C., Aldrich, C. and Mineev-Weinstein, M.B. (1997), ROAMing terrain: real-time optimally adapting meshes, in: Proc. Visualization '97, IEEE Computer Society Press, 81-88.
9. Dyn, N., Levin, D. and Rippa, S. (1990), Algorithms for the construction of data dependent triangulations, Mason J.C. and Cox, M.G. (Eds.), Algorithms for Approximation II, Chapman and Hall, New York, 185-192.
10. Edelsbrunner, H. and Mücke, E.P. (1994), Three-dimensional alpha shapes, ACM Trans. on Graphics 13 (1), 43-72.
11. Gieng, T.S., Hamann, B., Joy, K.I., Schussman, G.L. and Trotts, I.J. (1998), Constructing hierarchies for triangle meshes, IEEE Transactions on Visualization and Computer Graphics 4 (2), 145-161.
12. Gross, M.H., Gatti, R. and Staadt, O. (1995), Fast multiresolution surface meshing, in: Proc. Visualization '95, IEEE Computer Society Press, 135-142, 446.
13. Guskov, I., Sweldens, W. and Schröder, P. (1999), Multiresolution signal processing for meshes, Computer Graphics, in: Proc. SIGGRAPH '99, ACM, 325-334.
14. Hamann B. and Jordan, B. (1998), Triangulations from repeated bisection, in: Daehlen, M., Lyche, T. and Schumaker, L.L. (Eds.), Mathematical Methods for Curves and Surfaces II, Vanderbilt University Press, Nashville, TN, 229-236.
15. Heckbert P.S. and Garland, M. (1994), Multiresolution modeling for fast rendering, in: Proc. Graphics Interface '94, Canadian Inf. Process. Soc, 43-50 .
16. Heckel, B., Uva, A. and Hamann, B. (1998), Clustering-based generation of hierarchical surface models, in: Late Breaking Hot Topics Proceedings, Visualization '98, IEEE Computer Society Press, 41-44.
17. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. and Stuetzle, W. (1992), Surface reconstruction from unorganized points, Computer Graphics, in: Proc. SIGGRAPH '92, ACM, 71-78.
18. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. and Stuetzle, W. (1993), Mesh optimization, Computer Graphics, in: Proc. SIGGRAPH '93, ACM, 19-26.
19. Hoppe, H. (1998), Smooth view-dependent level-of-detail control and its application to terrain rendering, in: Proc. Visualization '98, IEEE Computer Society Press, 35-42, 516.
20. Klein, R., Cohen-Or, D. and Huttner, T. (1998), Incremental view-dependent multiresolution triangulation of terrain, J. Visualization and Computer Animation 9 (3), 129-143.
21. Kreylos O. and Hamann, B. (1999), On simulated annealing and the construction of linear spline approximations for scattered data, in: Gröller, E., Löffelmann, H. and Ribarsky, W. (Eds.), Data Visualization '99, Proc. EUROGRAPHICS-IEEE TCCG Symposium on Visualization, Springer-Verlag, Vienna, Austria, 189-198, 328.
22. Mallat, S.G. (1989), A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Analysis and Machine Intelligence 11 (7), 674-693.
23. Margaliot M. and Gotsman, C. (1994), Piecewise-linear surface approximation from noisy scattered samples, in: Proc. Visualization '94, IEEE Computer Society Press, 61-68.
24. 2 approximation on triangles, in: Chui, C.K., Schumaker, L.L. and Ward, J.D. (Eds.), Approximation Theory V, Academic Press, 499-502 .
25. Nielson, G.M. and Foley, T.A. (1989), A survey of applications of an affine invariant norm, in: Lyche, T. and Schumaker, L.L. (Eds.), Mathematical Methods in Computer Aided Geometric Design, Academic Press, 445-467.
26. Pottmann, H., Krasauskas, R., Hamann, B., Joy, K.I. and Seibold, W. (1999), On piecewise linear approximation of quadratic functions, J. Geom. Graphics, to appear.
27. Quak, E. and Schumaker, L.L. (1991), Least squares fitting by linear splines on data dependent triangulations, in: Laurent, P.J., Le Méhauté, A. and Schumaker, L.L. (Eds.), Curves and Surfaces, Academic Press, 387-390.
28. Rippa, S. (1992), Long and thin triangles can be good for linear interpolation, SIAM J. Numer. Anal. 29 (1), 257-270.
29. Schroeder, W.J., Zarge, J.A. and Lorensen, W.E. (1992), Decimation of triangle meshes, Computer Graphics, in: Proc. SIGGRAPH '92, ACM, 65-70.
30. Schumaker, L.L. (1993), Computing optimal triangulations using simulated annealing, Computer Aided Geometric Design 10 (3-4), 329-345.
31. Xia, J.C. and Varshney, A. (1996), Dynamic view-dependent simplification for polygonal models, in: Proc. Visualization '96, IEEE Computer Society Press, 327-334, 498.