Reconstructing surfaces and functions on surfaces from unorganized three-dimensional data

Algorithmica (New York)

Volumn 19, Issue 1, 1997, Pages 243-261

  Bajaj, C L ^a   Bernardini, F ^a,b   Xu, G ^a,c  

^a Purdue University   (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Algebraic surfaces; Delaunay triangulation; Implicit surfaces; Range data; Shape reconstruction; Shape

Indexed keywords

EID: 0001029519     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00014418     Document Type: Article

References (46)

1. Alfeld, P. A trivariate Clough-Tocher scheme for tetrahedral data. Computer Aided Geometric Design 1 (1984), 169-181.
2. Alfeld, P. Scattered data interpolation in three or more variables. In Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. Schumaker, Eds. Academic Press, New York, 1989, pp. 1-34.
3. Aurenhammer, F. Voronoi diagrams - a survey of a fundamental geometric data structure. ACM Computing Surveys 23 (1991), 345-406.
4. Bajaj, C. The emergence of algebraic curves and surfaces in geometric design. In Directions in Geometric Computing, R. Martin, Ed. Information Geometers Press, 1993, pp. 1-29.
5. Bajaj, C., Bernardini, F., and Xu, G. Automatic reconstruction of surfaces and scalar fields from 3D scans. Proceedings of SIGGRAPH 95, pp. 109-118.
6. Bajaj, C., Chen, J., and Xu, G. Modeling with cubic A-patches. ACM Transactions on Graphics 14(2) (1995), 103-133.
7. 2 scattered function data on curved surfaces. In Fundamentals of Computer Graphics, J. Chen, N. Thalmann, Z. Tang, and D. Thalmann, Eds., World Scientific, Beijing, 1994, pp. 19-29.
8. Barnhill, R. Surfaces in computer aided geometric design: a survey with new results. Computer Aided Geometric Design 2 (1985), 1-17.
9. Barnhill, R., and Foley, T. Methods for constructing surfaces on surfaces. In Geometric Modeling: Methods and Their Applications, G. Farin, Ed. Springer-Verlag, Berlin, 1991, pp. 1-15.
10. Barnhill, R., Opitz, K., and Pottmann, H. Fat surfaces: a trivariate approach to triangle-based interpolation on surfaces. Computer Aided Geometric Design 9 (1992), 365-378.
11. Barnhill, R., Piper B., and Rescorla, K. Interpolation to arbitrary data on a surface. In Geometric Modeling, G. Farin, Ed. SIAM, Philadelphia, PA, 1987, pp. 281-289.
12. Bernardini, F., and Bajaj, C. Sampling and reconstructing manifolds using alpha-shapes. Tech. Rep. CSD-TR-97-013, Department of Computer Sciences, Purdue University, 1997. Submitted for publication.
13. Bernardini, F., Bajaj, C., Chen, J., and Schikore, D. Automatic reconstruction of 3D CAD models from digital scans. Tech. Rep. CSD-TR-97-012, Department of Computer Sciences, Purdue University 1997. Submitted for publication.
14. Boissonnat, J.-D. Geometric structures for three-dimensional shape representation. ACM Transactions in Graphics 3(4) (1984), 266-286.
15. Choi, B. K., Shin, H. Y., Yoon, Y. I., and Lee, J. W. Triangulation of scattered data in 3D space. Computer Aided Design 20(5) (1988), 239-248.
16. Clarkson, K. L. A randomized algorithm for closest-point queries. SIAM Journal on Computing 17 (1988), 830-847.
17. Curless, B., and Levoy, M. A volumetric method for building complex models from range images. Proceedings of SIGGRAPH 96, pp. 303-312.
18. Dahmen, W. Smooth piecewise quadratic surfaces. In Mathematical Methods in Computer Aided Geometric Design, T. Lyche and L. Schumaker, Eds. Academic Press, Boston, 1989, pp. 181-193.
19. Dahmen, W., and Thamm-Schaar, T.-M. Cubicoids: modeling and visualization. Computer Aided Geometric Design 10 (1993), 93-108.
20. Dey, T., Bajaj, C., and Sugihara, K. On good triangulations in three dimensions. International Journal of Computer Geometry and Applications 2(1) (1992), 75-95.
21. Eck, M., and Hoppe, H. Automatic reconstruction of B-splines surfaces of arbitrary topological type. Proceedings of SIGGRAPH 96, pp. 325-334.
22. Edelsbrunner, H. Algorithms in Combinatorial Geometry. Springer-Verlag, New York, 1987.
23. Edelsbrunner, H. Weighted alpha shapes. Tech. Rep. UIUCDCS-R-92-1760, Department of Computer Science, University of Illinois, Urbana-Champaign, IL, 1992.
24. Edelsbrunner, H., and Mücke, E. P. Three-dimensional alpha shapes. ACM Transactions on Graphics 13(1) (Jan. 1994), 43-72.
25. Edlesbrunner, H., and Shah, N. R. Incremental topological flipping works for regular triangulations. Algorithmica 15 (1966), 223-241.
26. Farin, G. Triangular Bernstein-Bézier patches. Computer Aided Geometric Design 3 (1986), 83-127.
27. Franke, R. Recent advances in the approximation of surfaces from scattered data. In Multivariate Approximation, C. K. Chui, L. L. Schumarker, and F. I. Utreras, Eds. Academic Press, New York, 1987, pp. 275-335.
28. Guo, B. Surface generation using implicit cubics. In Scientific Visualization of Physical Phenomena, N. Patnkalakis, Ed. Springer-Verlag, Tokyo, 1991, pp. 485-530.
29. Guo, B. Non-splitting macro patches for implicit cubic spline surfaces. Computer Graphics Forum 12(3) (1993), 434-445.
30. Hoppe, H., DeRose, T., Duchamp, T., Halstead, M., Jin, H., McDonald, J., Schwitzer, J., and Stuelzle, W. Piecewise smooth surface reconstruction. Proceedings of SIGGRAPH 94, pp. 295-302.
31. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., and Stuetzle, W. Surface reconstruction from unorganized points. (Proceedings of SIGGRAPH 92.) Computer Graphics 26(2) (1992), 71-78.
32. Krishnamurty, V., and Levoy, M. Fitting smooth surfaces to dense polygonal meshes. Proceedings of SIGGRAPH 96, pp. 313-324.
33. Moore, D., and Warren, J. Approximation of dense scattered data using algebraic surfaces. In Proceedings of the 24th Hawaii International Conference on System Sciences (Kauai, HI, 1991), pp. 681-690.
34. Nielson, G. Modeling and visualizing volumetric and surface-on-surface data. In Focus on Scientific Visualization, H. Hagen, H. Muller, and G. Nielson, Eds. Springer-Verlag, Berlin, 1992, pp. 219-274.
35. Nielson, G. Scattered data modeling. IEEE Computer Graphics and Applications 13 (1993), 60-70.
36. Nielson, G., Foley, T., Hamann, B., and Lane, D. Visualizing and modeling scattered multivariate data. IEEE Computer Graphics and Applications 11 (1991), 47-55.
37. Nielson, G., Foley, T., Lane, D., Franke, R., and Hagen, H. Interpolation of scattered data on closed surfaces. Computer Aided Geometric Design 7(4) (1990), 303-312.
38. Nielson, G., and Franke, R. Scattered data interpolation and applications: a tutorial and survey. In Geometric Modeling: Methods and Their Applications, H. Hagen and D. Roller, Eds. Springer-Verlag, Berlin, 1990, pp. 131-160.
39. O'Rourke, J. Polyhedra of minimal area as 3D object models. In Proceedings of the International Joint Conference on Artificial Intelligence (1981), pp. 664-666.
40. Pottmann, H. Interpolation on surfaces using minimum norm networks. Computer Aided Geometric Design 9 (1992), 51-67.
41. Preparata, F., and Shamos, M. Computational Geometry, An Introduction. Springer-Verlag, New York, 1985.
42. 1 trivariate polynomial interpolation. Computer Aided Geometric Design 4 (1987), 237-244.
43. Sederberg, T. W. Piecewise algebraic surface patches. Computer Aided Geometric Design 2 (1985), 53-59.
44. Turk, G., and Levoy, M. Zippered polygonal meshes from range images. Proceedings of SIGGRAPH 94, pp. 311-318.
45. Veltkamp, R. 3D computational morphology. Computer Graphics Forum 12(3) (1993), 115-127.
46. Worsey, A. J., and Farin, G. An n-dimensional Clough-Tocher interpolant. Constructive Approximation 3 (1987), 99-110.