Survey of Surface Reconstruction Algorithms

Amin Alqudah

Computer Engineering Department, Hijjawi Faculty for Engineering Technology, Yarmouk University, Irbid, Jordan.

DOI: 10.4236/jsip.2014.53009                

Abstract

Surface reconstruction is a problem in the field of computational geometry that is concerned with recreating a surface from scattered data points sampled from an unknown surface. To date, the primary application of surface reconstruction algorithms has been in computer graphics, where physical models are digitized in three dimensions with laser range scanners or mechanical digitizing probes (Bernardini et al., 1999 [1]). Surface reconstruction algorithms are used to convert the set of digitized points into a wire frame mesh model, which can be colored, textured, shaded, and placed into a 3D scene (in a movie or television commercial, for example). In this paper, we discuss some computational geometry preliminaries, and then move on to a summary of some different techniques used to address the surface reconstruction problem. The coming sections describe two algorithms: that of Hoppe, et al. (1992 [2]) and Amenta, et al. (1998 [3]). Finally, we present other applications of surface reconstruction and a brief comparison for some algorithms in this filed emphasizing on their advantages and disadvantages.

Keywords

Surface Reconstruction, Convex Hull, Delaunay Triangulation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Bernardini, F., Bajaj, C., Chen, J. and Schikore, D. (1999,) Automatic Reconstruction of 3D CAD Models from Digital Scans. International Journal of Computational Geometry Applications, 9, 327-370.
[2]	Hoppe, H., DeRose, T. and Duchamp, T. (1992) Surface Reconstruction from Unorganized Points. Proceedings of ACM SIGGRAPH’92, 27-31 July 1992, Chicago, 71-78.
[3]	Amenta, N., Bern, M. and Kamvysselis, M. (1998) A New Voronoi-Based Surface Reconstruction Algrorithm. Proceedings of ACM SIGGRAPH’98, 19-24 July 1998, Orlando, 415-422.
[4]	O’Rourke, J. (1998) Computational Geometry in C. 2nd Edition, Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511804120
[5]	de Berg, M., van Kreveld, M., Overmars, M. and Schwarzkopf, O. (1997) Computational Geometry: Algorithms and Applications. Springer-Verlag, Berlin. http://dx.doi.org/10.1007/978-3-662-03427-9
[6]	Crossno, P.J. and Angel, E.S. (1999) Spiraling Edge: Fast Surface Reconstruction from Partially Organized Sample Points. IEEE Visualization’99, 24-29 October 1999, San Francisco, 317-324. http://dx.doi.org/10.1109/VISUAL.1999.809903
[7]	Boissonnat, J.-D. (1984) Geometric Structures for Three-Dimensional Shape Representation. ACM Transactions on Graphics, 3, 266-286. http://dx.doi.org/10.1145/357346.357349
[8]	Bentley, J.L. and Friedman, J.H. (1979) Data Structures for Range Searching. Computing Surveys, 111, 398-409.
[9]	Lorensen, W.E. and Cline, H. E. (1987) Marching Cubes: A High Resolution 3D Surface Construction Algorithm. Computer Graphics, 21, 163-169. http://dx.doi.org/10.1145/37402.37422
[10]	Boissonnat, J.-D. and Cazals, F. (2000) Smooth Shape Reconstruction via Natural Neighbor Interpolation of Distance Functions. ACM Symposium on Computational Geometry, 12-14 June 2000, Hong Kong, 223-232.
[11]	Carr, J.C., Beatson, R.K., Cherrie, J.B., Mitchell, T.J., Fright, W.R., McCallum, B.C. and Evans, T.R. (2001) Reconstruction and Representation of 3D Objects with Radial Basis Functions. Proceedings of ACM SIGGRAPH’01, 12-17 August 2001, Los Angeles, 67-76.