This Article 
 Bibliographic References 
 Add to: 
An Evaluation of Implicit Surface Tilers
November/December 1993 (vol. 13 no. 6)
pp. 33-41

The authors review the principal algorithms for the polygonization of implicit surfaces and provide a framework for identifying their conceptual similarities and practical differences. The algorithms' merits are evaluated according to topological disambiguation, implementation complexity, and triangle count. Special attention is devoted to the ambiguity problem, and proposed solutions are analyzed in the context of consistency and correctness. It is argued that consistency suffices for many purposes and is achievable with single-entry tetrahedral or cubical tables.

1. A.D. Kalvin, "A Survey of Algorithms for Constructing Surfaces from 3D Volume Data," IBM Research Report RC 17600 (#77606). IBM, Jan. 1992.
2. J. Bloomenthal, "Polygonization of Implicit Surfaces,"Computer-Aided Geometric Design, Vol. 5, 1988, pp. 341-355.
3. M. Hall and J. Warren, "Adaptive Polygonalization of Implicitly Defined Surfaces,"IEEE CG&A, Vol. 10, No. 6, Nov. 1990, pp. 33- 42.
4. P. Ning and L. Hesselink, "Octree Pruning for Variable-Resolution Isosurfaces,"Proc. Computer Graphics Int'l, Springer-Verlag, Tokyo, June 1992, pp. 349-363.
5. H. Muller and M. Stark, "Adaptive Generation of Surfaces in Volume Data,"The Visual Computer, Vol. 9, No. 4, Jan. 1993, pp. 182- 199.
6. J. Wilhelms and A. Van Gelder, "Octrees for Faster Isosurface Generation,"ACM Trans. Graphics, Vol. 11, No. 3, July 1992, pp. 201-227.
7. E. Allgower and K. Georg,Numerical Continuation Methods: An Introduction, Springer-Verlag, Berlin, 1990.
8. G. Wyvill, C. McPheeters, and B. Wyvill, "Data Structures for Soft Objects,"The Visual Computer, Vol. 2, No. 4. Aug. 1986, pp. 227- 234.
9. W.E. Lorensen and H.E. Cline, "Marching Cubes: A High-Resolution 3D Surface Construction Algorithm,"Computer Graphics(Proc. Siggraph 87), ACM Press, New York, Vol. 21, No. 4, 1987, pp. 163-169.
10. H.H. Baker, "Building Surfaces of Evolution: The Weaving Wall,"Int'l J. Computer Vision, Vol. 3, No. 1, May 1989, pp. 51-71.
11. A. Wallin, "Constructing Isosurfaces from CT Data,"IEEE CG&A, Vol. 11, No. 6, Nov. 1991, pp. 28-33.
12. M.J. Duurst, "Additional Reference to Marching Cubes,"Computer Graphics, Vol. 22, No. 2, Apr. 1988, pp. 72-73.
13. B.A. Payne and A.W. Toga, "Surface Mapping Brain Function on 3D Models,"IEEE CG&A, Vol. 10, No. 5, Sept. 1990, pp. 33-41.
14. G.M. Nielson et al., "Visualizing and Modeling Scattered Multivariate Data,"IEEE CG&A, Vol. 11, No. 3, May 1991, pp. 47-55.
15. J. Wilhelms and A. Van Gelder, "Topological Considerations in Isosurface Generation,"Computer Graphics, Vol. 24, No. 5, Nov. 1990, pp. 79-86.
16. B. Wyvill and D. Jevans, "Table Driven Polygonization," Siggraph Course Notes:Modeling and Animating withImplicit Surfaces, ACM Press, New York, 1990, pp. 7.1-7.6.
17. P. Ning and L. Hesselink, "Adaptive Isosurface Generation in a Distortion-Rate Framework,"Proc. SPIE, Vol. 1459, SPIE, Bellingham, Wash., Feb. 1991, pp. 11-21.
18. B.K. Natarajan, "On Generating Topologically Correct Isosurfaces from Uniform Samples," Hewlett-Packard Laboratories Technical Report HPL-91-76, Hewlett-Packard, Palo Alto, Calif., June 1991.
19. G.M. Nielson and B. Hamann, "The Asymptotic Decider : Resolving the Ambiguity in Marching Cubes,"Proc. IEEE Visualization 91, IEEE Computer Society Press, Los Alamitos, Calif., Oct. 1991, pp. 83-91.

Paul Ning, Jules Bloomenthal, "An Evaluation of Implicit Surface Tilers," IEEE Computer Graphics and Applications, vol. 13, no. 6, pp. 33-41, Nov.-Dec. 1993, doi:10.1109/38.252552
Usage of this product signifies your acceptance of the Terms of Use.