Benjamin Schmitt
Galina Pasko
ABSTRACT
Models of implicit surfaces and curves trimmed by a solid are discussed in the context of dimensionally heterogeneous object modeling. Both a carrier surface and a trimming solid are modeled using the function representation. Algorithms for polygonization of trimmed surfaces and curves, as well as ray-tracing of trimmed surfaces are described. Illustrative and CAD related examples are given.
- Adzhiev, V., Kartasheva, E., Kunii, T., Pasko, A., Schmitt, B. 2002. Cellular-functional modeling of heterogeneous objects, Proc. 7th ACM Symposium on Solid Modeling and Applications, Saarbrucken, Germany (June 17--21, 2002), Konwoo Lee and N. M. Patrikalakis (Eds.), ACM Press, pp. 192--203. Google Scholar
Digital Library
- Bloomenthal, J., et al., 1997 Introduction to implicit surfaces, Morgan Kaufmann Publishers Inc. San Francisco, CA, USA, ISBN 155860233X Google ScholarDigital Library
- Bowyer, A. 1994. SVLIS Set-Theoretic Kernel Modeller. Introduction and User Manual, Information Geometers, Winchester, UK.Google Scholar
- DeRose, T., Kass, M., Truong T. 1998, Subdivision surfaces in character animation, Proceedings of SIGGRAPH 98 pp. 85--94. Google ScholarDigital Library
- Fomenko, A. T., and Kunii, T. L. 1997. Topological modeling for visualization. Springer-Verlag, Tokyo and Heidelberg.Google Scholar
- Hosaka, M. 1992 Modeling of Curves and Surfaces in CAD/CAM, Springer-Verlag, Berlin. Google ScholarDigital Library
- HyperFun Project: www.hyperfun.orgGoogle Scholar
- Kumar, S., and Manocha, D. 1995. Efficient rendering of trimmed NURBS surfaces, Computer-aided Design Journal, Elsevier Science, 27(7), pp 509--521.Google Scholar
- Kumar, V., D. Dutta, D. 1997. An approach to modelling multi-material objects, Fourth Symposium on Solid Modelling and Applications, ACM SIGGRAPH, pp. 336--345. Google ScholarDigital Library
- Litke, N., Levin, A., and Schröder, P. 2001, Trimming for subdivision surfaces, Computer Aided Geometric Design, 18(5), pp. 463--481. Google ScholarDigital Library
- Lorensen, W. E., and Cline, H. E. 1987. Marching cubes: A high resolution 3d surface construction algorithm. Proceedings of SIGGRAPH '87, Computer Graphics, 21(4):163--196. Google ScholarDigital Library
- Mantyla, M. 1988. An introduction to solid modeling. Computer Sciences Press, College Park, MD. Google ScholarDigital Library
- Pasko, A., Pilyugin, V., Pokrovskiy, V. 1988 Geometric modeling in the analysis of trivariate functions, Computers and Graphics, 12(3/4):457--465.Google ScholarCross Ref
- Pasko, A., Adzhiev, V., Sourin, V. and Savchenko, V. 1995. Function representation in geometric modeling: concepts, design and applications. The Visual computer journal, 11, p. 429--446.Google Scholar
- Pasko, A. A. 1998. On Escher's spirals - Polygonization of 2-manifolds with boundaries, Implicit Surfaces '98, Eurographics/ACM SIGGRAPH Workshop (Seattle, USA, 15--16 June 1998), J. Bloomenthal and D. Saupe (Eds.), University of Washington, ISSN 1024-0861, 1998, pp. 77--80.Google Scholar
- A. Pasko, V. Adzhiev, Schmitt, B., and Schlick, C. 2002. Constructive hypervolume modelling. Graphical Models, Special issue on volume modeling, 63:413--442. Google ScholarDigital Library
- PovRay, Persistence of Vision. www.povray.orgGoogle Scholar
- Rossignac, J. 1996. CSG formulation for identifying and for trimming faces of CSG models, CSG'96 Set-theoretic Solid Modeling: Techniques and Applications, Information Geometers, UK, 1--14.Google Scholar
- Rvachev, V. L. 1987. Theory of R-functions and some applications. Naukova Dumka, Kiev, 1987 (in Russian)Google Scholar
- Snyder, J. 1992 Generative Modelling for Computer Graphics and CAD. Academic Press, 1992. Google ScholarDigital Library
Index Terms
- Rendering trimmed implicit surfaces and curves
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