This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Simplification and Repair of Polygonal Models Using Volumetric Techniques
April-June 2003 (vol. 9 no. 2)
pp. 191-205

Abstract—Two important tools for manipulating polygonal models are simplification and repair and we present voxel-based methods for performing both of these tasks. We describe a method for converting polygonal models to a volumetric representation in a way that handles models with holes, double walls, and intersecting parts. This allows us to perform polygon model repair simply by converting a model to and from the volumetric domain. We also describe a new topology-altering simplification method that is based on 3D morphological operators. Visually unimportant features such as tubes and holes may be eliminated from a model by the open and close morphological operators. Our simplification approach accepts polygonal models as input, scan converts these to create a volumetric description, performs topology modification, and then converts the results back to polygons. We then apply a topology-preserving polygon simplification technique to produce a final model. Our simplification method produces results that are everywhere manifold.

[1] G. Barequet and S. Kumar, “Repairing CAD Models,” Proc. IEEE Visualization '97, pp. 363-370, Oct. 1997.
[2] G. Barequet and M. Sharir, “Filling Gaps in the Boundary of a Polyhedron,” Computer Aided Geometric Design, vol. 12, no. 2, pp. 207-229, 1995.
[3] J.H. Bohn and W.J. Wozny, “A Topology-Based Approach for Shell-Closure,” Geometric Modeling for Product Realization, P.R. Wilson et al., pp. 297-319, North-Holland, 1993.
[4] P. Danielsson, “Euclidean Distance Mapping,” Computer Graphics and Image Processing, vol. 14, pp. 227-248, 1980.
[5] J. El-Sana and A. Varshney, “Controlled Simplification of Genus for Polygonal Models,” Proc. IEEE Visualization, pp. 403-412, Aug. 1997.
[6] J. El-Sana and A. Varshney, “Topology Simplification for Polygonal Virtual Environments,” IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 2, pp. 133-144, Apr.-June 1998.
[7] C. Erikson, “Error Correction of a Large Architectural Model: The Henderson County Courthouse,” Technical Report TR95-013, Dept. of Computer Science, Univ. of North Carolina at Chapel Hill, 1995.
[8] M. Garland and P.S. Heckbert, “Surface Simplification Using Quadric Error Metrics,” Proc. SIGGRAPH '97, Computer Graphics Proc., Ann. Conf. Series, pp. 209-216, 1997.
[9] M. Garland and P.S. Heckbert, “Simplifying Surfaces with Color and Texture Using Quadric Error Metrics,” Proc. IEEE Visualization '98, pp. 263-269, Oct. 1998.
[10] A. Gelder and J. Wilhelms, “Topological Considerations in Isosurface Generation,” IEEE Trans. Graphics, vol. 13, no. 4, pp. 337-375, Nov. 1994.
[11] S.J. Gortler, R. Grzeszczuk, R. Szeliski, and M.F. Cohen, “The Lumigraph,” SIGGRAPH '96 Proc., pp. 43-54, Aug. 1996.
[12] A. Gueziec, G. Taubin, F. Lazarus, and W. Horn, “Converting Sets of Polygons to Manifold Surfaces by Cutting and Stitching,” Proc. IEEE Visualization 1998, pp. 383-390, Oct. 1998.
[13] L. He, L. Hong, A.E. Kaufman, A. Varshney, and S. Wang, “Voxel-Based Object Simplification,” IEEE Visualization '95 Proc., pp. 296-303, Oct. 1995.
[14] H. Hoppe, “Progressive Meshes,” Proc. SIGGRAPH '96, Computer Graphics Proc., Ann. Conf. Series, pp. 99-108, 1996.
[15] J. Huang, R. Yagel, V. Filippov, and Y. Kurzion, “An Accurate Method for Voxelizing Polygonal Meshes,” Proc. Symp. Volume Visualization, pp. 119-126, Oct. 1998.
[16] A. Jain, Fundamentals of Digital Image Processing. Englewood Cliffs, N.J.: Prentice Hall, 1989.
[17] D. Khorramabdi, “A Walk through the Planned CS Building,” Technical Report UCB/CSD 91/652, Computer Science Dept., Univ. of California at Berkeley, 1991.
[18] M. Levoy, “A Hybrid Ray Tracer for Rendering Polygon and Volume Data,” IEEE Computer Graphics and Applications, vol. 11, no. 2, pp. 33-40, Mar. 1990.
[19] P. Lindstrom and G. Turk, “Evaluation of Memoryless Simplification,” IEEE Trans. Visualization and Computer Graphics, vol. 5, no. 2, pp. 98-115, Apr.-June 1999.
[20] W.E. Lorensen and H.E. Cline, “Marching Cubes: A High Resolution 3-D Surface Construction Algorithm,” Proc. SIGGRAPH '87, Computer Graphics, pp. 163-169, July 1987.
[21] K.L. Low and T.-S. Tan, “Model Simplification Using Vertex-Clustering,” Proc. Interactive 3D Graphics pp. 75-81, Apr. 1997.
[22] D. Luebke and C. Erikson, “View-Dependent Simplification of Arbitrary Polygonal Environments,” Proc. SIGGRAPH '97, Computer Graphics, pp. 199-208, Aug. 1997.
[23] S.R. Marschner and R.J. Lobb, “An Evaluation of Reconstruction Filters for Volume Rendering,” IEEE Proc. Visualization '94, pp. 100-107, Oct. 1994.
[24] S.M. Morvan and G.M. Fadel, “IVECS: An Interactive Virtual Environment for the Correction of .STL files,” Proc. Conf. Virtual Design, Aug. 1996.
[25] T.M. Murali and T. Funkhouser, “Consistent Solid and Boundary Representations from Arbitrary Polygonal Data,” Proc. 1997 Symp. Interactive 3D Graphics, pp. 155-162, Apr. 1997.
[26] J. Rossignac and P. Borrel, “Multi-Resolution 3D Approximations for Rendering Complex Scenes,” Modeling in Computer Graphics: Methods and Applications, pp. 455-465, June 1993.
[27] J. Popovic and H. Hoppe, “Progressive Simplicial Complexes,” Proc. SIGGRAPH '97 Computer Graphics, pp. 217-224, Aug. 1997.
[28] W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, Computer Graphics, pp. 65-70, July 1992.
[29] W.J. Schroeder, “A Topology Modifying Progressive Decimation Algorithm,” Proc. IEEE Visualization '97, pp. 205-212, Oct. 1997.
[30] W.J. Schroeder and W.E. Lorensen, “Implicit Modeling of Swept Surfaces and Volumes,” Proc. Visualization '94, pp. 40-45, Oct. 1994.
[31] J. Shade, S.J. Gortler, L.-w. He, and R. Szeliski, “Layered Depth Images,” Proc. SIGGRAPH '98, Computer Graphics Proc., Ann. Conf. Series, pp. 209-216, 1998.
[32] G.A. Taubin, “Signal Processing Approach to Fair Surface Design,” Proc. SIGGRAPH '95, Computer Graphics, pp. 351-358, July 1995.
[33] S. Wang and A.E. Kaufman, “Volume Sampled Voxelization of Geometric Primitives,” IEEE Visualization '93 Proc., pp. 78-84, Oct. 1993.

Index Terms:
Mesh simplification, mesh repair, volumetric models, morphological operators.
Citation:
Fakir S. Nooruddin, Greg Turk, "Simplification and Repair of Polygonal Models Using Volumetric Techniques," IEEE Transactions on Visualization and Computer Graphics, vol. 9, no. 2, pp. 191-205, April-June 2003, doi:10.1109/TVCG.2003.10002
Usage of this product signifies your acceptance of the Terms of Use.