This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Controlled Topology Simplification
June 1996 (vol. 2 no. 2)
pp. 171-184

Abstract—We present a simple, robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by converting an object into multi-resolution volume rasters using a controlled filtering and sampling technique. A multiresolution triangle-mesh hierarchy can then be generated by applying the Marching Cubes algorithm. We further propose an adaptive surface generation algorithm to reduce the number of triangles generated by the standard Marching Cubes. Our method simplifies the topology of objects in a controlled fashion. In addition, at each level of detail, multilayered meshes can be used for an efficient antialiased rendering.

[1] J. Amanatides, "Ray Tracing With Cones," Computer Graphics (SIGGRAPH '84 Proc.), vol. 18, no. 3, pp. 129-135, July 1984.
[2] J. Bloomenthal, “Polygonization of Implicit Surfaces,” Computer Aided Geometric Design, vol. 5, no. 4, pp. 341-355, 1988.
[3] H. Bronnimann and M. Goodrich, "Almost Optimal Set Covers in Finite VC-Dimension," Proc. 10th ACM Symp. Computational Geometry, pp. 293-302, 1994.
[4] I. Carlbom, "Optimal Filter Design for Volume Reconstruction and Visualization," IEEE Visualization '93 Proc., pp. 54-61,San Jose, Calif., Oct. 1993.
[5] L. Carpenter, “The A-Buffer, an Antialiased Hidden Surface Method,” Computer Graphics, Proc. SIGGRAPH '84, vol. 18, no. 3, pp. 103-108, July 1984.
[6] J. Clark, "Hierarchical Geometric Models for Visible Surface Algorithms," Comm. ACM, vol. 19, no. 10, pp. 547-554, 1976.
[7] K.L. Clarkson, "Algorithms for Polytope Covering and Approximation," Proc. Third Workshop Algorithms Data Structure, Lecture Notes in Computer Science, 1993.
[8] F.C. Crow, "A More Flexible Image Generation Environment," Computer Graphics (Proc. Siggraph '82), vol. 16, no. 3, pp. 9-18, 1982.)
[9] G. Das and D. Joseph, "The Complexity of Minimum Convex Nested Polyhedra," Proc. Second Canadian Conf. Comput. Geom., pp. 296-301, 1990.
[10] M. DeHaemer, Jr. and M.J. Zyda, "Simplification of Objects Rendered by Polygonal Approximations," Computers and Graphics, vol. 15, no. 2, pp. 175-184, 1991.
[11] M. Dürst, “Letters: Additional Reference to Marching Cubes,” Computer Graphics, vol. 22, no. 2, pp. 72-73, 1988.
[12] M. Ech, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, "Multiresolution Analysis of Arbitrary Meshes," Computer Graphics Proc. Ann. Conf. Series (Proc. Siggraph '95), pp. 173-182, 1995.
[13] R. Fowler and J. Little, "Automatic Extraction of Irregular Network Digital Terrain Models," Computer Graphics, vol. 13, no. 2, pp. 199-207, Aug. 1979.
[14] I. Fujishiro, Y. Maeda, and H. Sato, "Interval Volume: A Solid Fitting Technique for Volumetric Data Display and Analysis," IEEE Visualization '95 Proc., pp. 151-158,Atlanta, Ga., Oct. 1995.
[15] T. Funkhouser and C. Sequin, “Adaptive Display Algorithm for Interactive Frame Rates During Visualization of Complex Virtual Environments,” Proc. SIGGRAPH '93, pp. 247-254, 1993.
[16] B. Guo, "Interval Set: A Volume Rendering Technique Generalizing Isosurface Extraction," IEEE Visualization '95 Proc., pp. 3-10,Atlanta, Ga., Oct. 1995.
[17] T. He, L. Hong, A. Kaufman, A. Varshney, and S. Wang, "Voxel-Based Object Simplification," IEEE Visualization '95 Proc., pp. 296-303,Atlanta, Ga., Oct. 1995.
[18] P. Heckbert and M. Garland, "Fast Polygonal Approximation of Terrains and Height Fields," Technical Report CMU-CS-95-181, Sept. 1995.
[19] W. Heidrich, M. McCool, and J. Stevens, "Interactive Maximum Projection Volume Rendering," IEEE Visualization '95 Proc., pp. 11-18,Atlanta, Ga., Oct. 1995.
[20] P. Hinker and C. Hansen, Geometric Optimization Proc. Visualization '93, pp. 189-195, 1993.
[21] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Proc. SIGGRAPH '93, pp. 19-26, 1993.
[22] A.D. Kalvin and R.H. Taylor, "SuperFaces: Polyhedral Approximation With Bounded Error," IBM Research Division, T.J. Watson Research Center, Yorktown Heights, N.Y. 10958, Technical Report RC 19808, 1994.
[23] M. Levoy, “Display of Surfaces from Volume Data,” IEEE Computer Graphics and Applications, vol. 8, no. 3, pp. 29-37, 1988.
[24] M. Levoy and R. Whitaker, “Gaze-Directed Volume Rendering,” Computer Graphics, vol. 24, no. 2, pp. 217-223, Mar. 1990.
[25] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3D Surface Construction Algorithm,” Computer Graphics (SIGGRAPH '87 Proc.), vol. 21, pp. 163-169, 1987.
[26] M. Lounsbery, T.D. DeRose, and J. Warren, "Multiresolution Analysis for Surfaces of Arbitrary Topological Type," TR 93-10-05B, Univ. of Washington at Seattle, Jan. 1994.
[27] R. Machiraju and R. Yagel, "Accuracy Control of Reconstruction Errors in Volume Slicing," Biomedical Visualization Proc. '95, pp. 50-57,Atlanta, Ga., Oct. 1995.
[28] J. Mitchell and S. Suri, "Separation and Approximation of Polyhedral Surfaces," Proc. Third ACM-SIAM Symp. Discrete Algorithms, pp. 296-306, 1992.
[29] C. Montani, R. Scateni, and R. Scopigno, "Discretized Marching Cubes," IEEE Visualization '94 Proc., pp. 281-287,Washington, D.C., 1994.
[30] H. Muller and M. Stark, "Adaptive Generation of Surfaces in Volume Data," The Visual Computer, vol. 9, no. 4, 1993, pp. 182-199.
[31] B. Payne and A. Toga, "Surface Mapping Brain Functions on 3D models," IEEE Computer Graphics and Applications, vol. 10, no. 2, pp. 41-53, July 1992.
[32] J. Rossignac and P. Borrel, "Multi-Resolution 3D Approximations for Rendering Complex Scenes," E B. Falcidieno and T.L. Kunni, eds., Modeling in Computer Graphics.New York: Springer-Verlag, pp. 455-465, 1993.
[33] G. Sakas and J. Hartig, "Interactive Visualization of Large Scalar Voxel Fields," A. Kaufman and E.G. Nielson, eds., IEEE Visualization '92 Proc., pp. 29-36,Boston, Mass., Oct. 1992.
[34] F.J. Schmitt, B.A. Barsky, and W. Du, "An Adaptive Subdivision Method for Surface-Fitting From Sample Data," Computer Graphics (SIGGRAPH '86 Proc.), vol. 20, no. 4, pp. 179-188, 1986.
[35] W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, pp. 65-70, 1992.
[36] W. Schroeder, K. Martin, and W. Lorensen, The Visualization Toolkit.Englewood, Cliffs, N.J.: Prentice Hall, 1996.
[37] G. Turk, "Retiling Polygonal Surfaces," Computer Graphics(Proc. Siggraph 92), vol. 26, no. 2, 1992, pp. 55-64.
[38] A. Varshney, "Hierarchical Geometric Approximations," Doctoral Dissertation, TR-050-1994, Dept. of Computer Science, Univ. of North Carolina, Chapel Hill, 1994.
[39] S. Wang and A. Kaufman, "Volume-Sampled 3D Modeling," IEEE Computer Graphics and Applications, Vol. 14, No. 5, 1994, pp. 26-32.
[40] L. Westover,“Footprint evaluation for volume rendering,” Proc. SIGGRAPH’90 (Dallas, Texas, Aug. 6-10, 1990). In Computer Graphics, vol. 24, no. 4, pp. 367-376, 1990.
[41] J. Wilhelms and A. Van Gelder, "Topological Consideration in Isosurface Generation," ACM Computer Graphics, vol. 24, no. 5, pp. 79-86, Nov. 1990.
[42] J. Wilhelms and A. Van Gelder, "Octree for Faster Isosurface Generation," ACM Computer Graphics, vol. 24, no. 5, pp. 57-62, Nov. 1990.
[43] G. Wolberg, Digital Image Warping, IEEE CS Press, 1990.
[44] National Library of Medicine, Electronic Imagings: Report of the Board of Regions.Bethesda, Md.: National Institutes of Health, NIH Publications 90-2197, 1990.

Index Terms:
Object simplification, volume sampling, topology simplification, level-of-detail-based rendering, multiresolution.
Citation:
Taosong He, Lichan Hong, Amitabh Varshney, Sidney W. Wang, "Controlled Topology Simplification," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 2, pp. 171-184, June 1996, doi:10.1109/2945.506228
Usage of this product signifies your acceptance of the Terms of Use.