Abstract
Computing surface intersections is a fundamental problem in geometric modeling. Any boolean operation can be seen as an intersection calculation followed by a selection of the parts necessary for building the surface of the resulting object. A robust and efficient algorithm to compute intersection on subdivision surfaces (surfaces generated by the Loop scheme) is proposed here. This algorithm relies on the concept of a bipartite graph which allows the reduction of the number of faces intersection tests. Intersection computations are accelerated by the use of the bipartite graph and the neighborhood of intersecting faces at a given level of subdivision to deduce intersecting faces at the following levels of subdivision.
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References
Abdel-Malek, K., and Yeh, H. J. “Determining Intersection Curves between Surfaces of Two Solids.” Computer Aided Design, 28, pp. 539–549, 1996.
Bajaj, C. L., Hoffmann, C. M., Hopcroft, J. E., and Lynch, R. E. “Tracing Surface Intersec-tions.” Computer Aided Geometric Design, 5, pp. 285–307, 1988.
Barnhill, R. E., Farin, G., Jordan, M., and Piper, B. R. “Surface / Surface Intersection.” Computer Aided Geometric Design, 4, pp. 3–16, 1987.
Biermann, H., Kristjansson, D., and Zorin, D. “Approximate Boolean Operations on Free-Form Solids.” in CAGD 2000, Oslo, Norway, 2000.
Boender, E. “A Survey of Intersection Algorithms for Curved Surfaces.” Computer & Graphics, 15, pp. 99–115, 1991.
Bondy, A., and Murty, U. S. R. (1976), Graph Theory with Apllications, ed. Inc. American Elsevier Publishing Co., New York.
Chandru, V., and Kochar, B. S., “Geometric Modeling: Algorithms and New Trends.” in Chapter Analytic Techniques for Geometric Intersection Problems, PA, Philadelphia: SIAM, pp. 305–318,1987.
DeRose, T., Kaas, M., and Truong, T. “Subdivision Surfaces in Character Animation.” in SIGGRAPH Proceedings, pp. 85–94, 1998.
Krishnan, S., Narkhede, A., and Manocha, D. “Boole: A System to Compute Boolean Combinations of Sculptured Solids.” Technical Report, Department of Computer Science, University of North California, 1994.
Linsen, L. “Netbased Modelling.” in SCCG 2000, Slovakia, pp. 259–266, 2000.
Litke, N., Levin, A., and Schröder, P. “Trimming for Subdivision Surfaces.” Technical Report, Caltech, 2000.
O’Brien, D. A., and Manocha, D. “Calculating Intersection Curve Approximations for Subdivision Surfaces”. 2000. http://www.cs.unc.edu/~brien/courses/comp258/project.html.
Patrikalakis, N. M. “Surface-to-Surface Intersections.” IEEE Computer Graphics & Applications, 13, pp. 89–95, 1993.
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Lanquetin, S., Foufou, S., Kheddouci, H., Neveu, M. (2003). A Graph Based Algorithm for Intersection of Subdivision Surfaces. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_40
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DOI: https://doi.org/10.1007/3-540-44842-X_40
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