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Evaluation of Memoryless Simplification
April-June 1999 (vol. 5 no. 2)
pp. 98-115

Abstract—This paper investigates the effectiveness of the Memoryless Simplification approach described by Lindstrom and Turk [14]. Like many polygon simplification methods, this approach reduces the number of triangles in a model by performing a sequence of edge collapses. It differs from most recent methods, however, in that it does not retain a history of the geometry of the original model during simplification. We present numerical comparisons showing that the memoryless method results in smaller mean distance measures than many published techniques that retain geometric history. We compare a number of different vertex placement schemes for an edge collapse in order to identify the aspects of the Memoryless Simplification that are responsible for its high level of fidelity. We also evaluate simplification of models with boundaries, and we show how the memoryless method may be tuned to trade between manifold and boundary fidelity. We found that the memoryless approach yields consistently low mean errors when measured by the Metro mesh comparison tool. In addition to using complex models for the evaluations, we also perform comparisons using a sphere and portions of a sphere. These simple surfaces turn out to match the simplification behaviors for the more complex models that we used.

[1] C. Bajaj and D.R. Schikore, “Error-Bounded Reduction of Triangle Meshes with Multivariate Data,” Proc. Visual Data Exploration and Analysis III, SPIE, vol. 2656, pp. 34-45, Jan. 1996.
[2] A. Ciampalini, P. Cignoni, C. Montani, and R. Scopigno, “Multiresolution Decimation Based on Global Error,” The Visual Computer, vol. 13, no. 5, pp. 228-246, 1997.
[3] P. Cignoni, C. Rocchini, and R. Scopigno, “Metro: Measuring Error on Simplified Surfaces,” Computer Graphics Forum, vol. 17, no. 2, pp. 167-174, June 1998.
[4] J. Cohen, A. Varshney, D. Manocha, G. Turk, H. Weber, P. Agarwal, F.P. Brooks Jr., and W.V. Wright, "Simplification Envelopes," Computer Graphics Proc. Ann. Conf. Series (Proc. Siggraph '96), pp. 119-128, 1996.
[5] J. Cohen, M. Olano, and D. Manocha, Simplifying Polygonal Models Using Successive Mappings Proc. Visualization '97, pp. 395-402, Oct. 1997.
[6] J. Cohen, M. Olano, and D. Manocha, “Appearance-Preserving Simplification,” Proc. Siggraph, pp. 115-122, July 1998.
[7] M. Garland and P.S. Heckbert, "Surface Simplification Using Quadric Error Metrics," Proc. Siggraph 97, ACM Press, New York, 1997, pp. 209-216.
[8] M. Garland and P. Heckbert, “Simplifying Surfaces with Color and Texture Using Quadric Error Metrics,” Proc. Visualization 98, pp. 263-269, Oct. 1998.
[9] T.S. Gieng, B. Hamann, K.I. Joy, G.L. Schussman, and I.J. Trotts, Smooth Hierarchical Surface Triangulations Proc. Visualization '97, R. Yagel and H. Hagen, eds., pp. 379-386, 1997.
[10] A. Guéziec, “Surface Simplification with Variable Tolerance,” Proc. Second Ann. Int'l Symp. Medical Robotics and Computer Assisted Surgery, pp. 132-139, Nov. 1995.
[11] B. Hamann, "A Data Reduction Scheme for Triangulated Surfaces," Computer Aided Geometric Design, vol. 11, no. 2, pp. 197-214 1994.
[12] H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Mesh Optimization,” Proc. SIGGRAPH '93, pp. 19-26, 1993.
[13] H. Hoppe, “Progressive Meshes,” Proc. SIGGRAPH '96, pp. 99-108, 1996.
[14] C.E. Dowling, C. Hockemeyer, and A.H. Ludwig, “Adaptive Assessment and Training Using the Neighbourhood of Knowledge States,” Intelligent Tutoring Systems, C. Frasson, G. Gauthier, and A. Lesgold, eds., pp. 578–586, 1996.
[15] K.J. Renze and J.H. Oliver, “Generalized Surface and Volume Decimation for Unstructured Tessellated Domains,” Proc. VRAIS '96, pp. 111-21, Mar. 1996.
[16] R. Ronfard and J. Rossignac, “Full-Range Approximation of Triangulated Polyhedra,” Proc. Eurographics '96, Computer Graphics Forum, vol. 15, no. 3, pp. 67-76, Aug. 1996.
[17] W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, pp. 65-70, 1992.
[18] W. Schroeder, “A Topology Modifying Progressive Decimation Algorithm,” IEEE Visualization, pp. 205-212, 1997.

Index Terms:
Model simplification, surface approximation, level of detail, geometric error, optimization.
Citation:
Peter Lindstrom, Greg Turk, "Evaluation of Memoryless Simplification," IEEE Transactions on Visualization and Computer Graphics, vol. 5, no. 2, pp. 98-115, April-June 1999, doi:10.1109/2945.773803
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