Abstract
This paper describes an adaptive and efficient algorithm for polygonization of implicit surfaces, which consists of two steps: initial polygonization and adaptive refinement. The algorithm first generates an initial coarse triangular mesh from implicit surface using a variation of the traditional Marching Cubes (MC) Algorithm. And then the triangles in the coarse mesh are iteratively subdivided by employing a sampling rate that varies spatially according to local complexity of the surface. The new created vertices in refined mesh are projected onto the implicit surface by gradient descent method. Consequently, the algorithm produces the minimum number of polygons required to approximate the surface with a desired precision and the final mesh is simplicial complex. Our algorithm can be used in the real-time environment of visualization of implicit surfaces.
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References
Blinn, J.F.: A generalization of algebraic surface drawing. ACM Transactions on Graphics 1(3), 235–256 (1982)
Buff, T.: Interval arithmetic and recursive subdivision for implicit surfaces and constructive solid geometry. In: ACM SIGGRAPH 1992, pp. 131–138 (1992)
Pasako, A., Adzhiev, V., Sourin, A., et al.: Function representation in geometric modeling: concepts, implementation and applications. The Visual Computer 2(8), 429–446 (1995)
Bloomenthal, J.: Polygonization of implicit surfaces. Computer Aided Geometric Design 5(4), 341–355 (1988)
Roth, S.: Ray casting as a method for solid modeling. Computer Graphics and Image Processing 18(2), 109–144 (1982)
Bloomenthal, J.: An implicit surface polygonizer. In: Heckbert, P. (ed.) Graphics Gems IV, pp. 324–349. Academic Press, New York (1994)
Velho, L.: Simple and efficient polygonization of implicit surfaces. Journal of Graphical Tools 1(2), 5–24 (1996)
Allgower, E., Schmidt, P.: An algorithm for piecewise-linear approximation of an implicitly defined manifold. Journal of Numerical Analysis 22(2), 322–346 (1985)
Wyvill, B., McPheeters, C., Wyvill, G.: Animating soft objects. The Visual Computer 2(4), 235–242 (1986)
Bloomenthal, J.: Surface tiling. In: Bloomenthal, J. (ed.) Introduction to implicit surfaces, vol. 4. Morgan Kaufmann Publisher, Inc., San Francisco (1997)
Wyvill, G., McPheeters, C., Wyvill, B.: Data structure for soft objects. The Visual Computer 2(4), 227–234 (1986)
Yu, Z.S., Wu, Q.D., Li, Q.Y., et al.: Projection based polygonization of implicit surfaces. Journal of Computer-Aided Design and Computer Graphics 33(4), 333–337 (2001) (in Chinese)
Turk, G.: Re-tiling polygonal surface. Computer Graphics 26(2), 55–64 (1992)
Figueiredo, L.H., Gomes, J., Terzopoulos, D., et al.: Physically-based methods for polygonization of implicit surfaces. In: Proceedings of Graphics Interfaces, Vancouver, pp. 250–257 (1992)
Velho, L.: Adaptive polygonization made simple. In: Brazilian Symposium on Computer Graphics and Image Processing, San Carlos, pp. 111–118 (1995)
Ning, P., Hesselink, L.: Adaptive isosurface generation in a distortion-rate framework. Society of photo-optical instrumentation engineers, San Jose, pp. 11–21 (1991)
do Carmo, M.P.: Differential geometry of curves and surfaces. Pearson Education, Inc., London (1976)
Ohtake, Y.: Mesh optimization and feature extraction. Ph.D Thesis, University of Aizu (2002)
Frdric, T., Philippe, M., et al.: Fast polygonization of implicit surfaces. In: Winter School of Computer Graphics, Plzen(Czech Republic), pp. 283–290 (2001)
Hart, J.C.: Ray tracing implicit surfaces. In: Computer Graphics Proceedings, Annual Conference Series, ACM SIGGRAPH 1993, Anaheim, California. Course Notes No. 25, Modelling, Visualizing and Animating Implicit Surfaces, pp. 1–15 (1993)
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Pang, M., Pan, Z., Zhang, M., Zhang, F. (2005). An Adaptive and Efficient Algorithm for Polygonization of Implicit Surfaces. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_27
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DOI: https://doi.org/10.1007/11424857_27
Publisher Name: Springer, Berlin, Heidelberg
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