Rendering trimmed implicit surfaces and curves

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.

REFERENCES

• 1: Valery Adzhiev , Elena Kartasheva , Tosiyasu Kunii , Alexander Pasko , Benjamin Schmitt, Cellular-functional modeling of heterogeneous objects, Proceedings of the seventh ACM symposium on Solid modeling and applications, June 17-21, 2002, Saarbrücken, Germany [doi>10.1145/566282.566311]
• 2: Jules Bloomenthal , Brian Wyvill, Introduction to Implicit Surfaces, Morgan Kaufmann Publishers Inc., San Francisco, CA, 1997
• 3: Bowyer, A. 1994. SVLIS Set-Theoretic Kernel Modeller. Introduction and User Manual, Information Geometers, Winchester, UK.
• 4: Tony DeRose , Michael Kass , Tien Truong, Subdivision surfaces in character animation, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.85-94, July 1998 [doi>10.1145/280814.280826]
• 5: Fomenko, A. T., and Kunii, T. L. 1997. Topological modeling for visualization. Springer-Verlag, Tokyo and Heidelberg.
• 6: M. Hosaka, Modeling of curves and surfaces in CAD/CAM, Springer-Verlag New York, Inc., New York, NY, 1992
• 7: HyperFun Project: www.hyperfun.org
• 8: Kumar, S., and Manocha, D. 1995. Efficient rendering of trimmed NURBS surfaces, Computer-aided Design Journal, Elsevier Science, 27(7), pp 509--521.
• 9: Vinod Kumar , Debasish Dutta, An approach to modeling multi-material objects, Proceedings of the fourth ACM symposium on Solid modeling and applications, p.336-345, May 14-16, 1997, Atlanta, Georgia, United States [doi>10.1145/267734.267812]
• 10: Litke, N., Levin, A., and Schröder, P. 2001, Trimming for subdivision surfaces, Computer Aided Geometric Design, 18(5), pp. 463--481.
• 11: William E. Lorensen , Harvey E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, ACM SIGGRAPH Computer Graphics, v.21 n.4, p.163-169, July 1987
• 12: M. Mantyla, Introduction to Solid Modeling, W. H. Freeman & Co., New York, NY, 1988
• 13: Pasko, A., Pilyugin, V., Pokrovskiy, V. 1988 Geometric modeling in the analysis of trivariate functions, Computers and Graphics, 12(3/4):457--465.
• 14: 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.
• 15: 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.
• 16: Alexander Pasko , Valery Adzhiev , Benjamin Schmitt , Christophe Schlick, Constructive hypervolume modeling, Graphical Models, v.63 n.6, p.413-442, November 2001 [doi>10.1006/gmod.2001.0560]
• 17: PovRay, Persistence of Vision. www.povray.org
• 18: 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.
• 19: Rvachev, V. L. 1987. Theory of R-functions and some applications. Naukova Dumka, Kiev, 1987 (in Russian)
• 20: John M. Snyder, Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis, Academic Press Professional, Inc., San Diego, CA, 1992

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.3 Picture/Image Generation

Additional Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism

General Terms:
Algorithms

Keywords:
function representation, geometric modeling, implicit surfaces, polygonization, ray-tracing, trimming