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Issue No.02 - March/April (2005 vol.25)
pp: 36-45
Galina I. Pasko , Kanazawa Institute of Technology
Alexander A. Pasko , Hosei University
Tosiyasu L. Kunii , Kanazawa Institute of Technology
ABSTRACT
We propose new analytical formulations of bounded blending operations for the function-based constructive shape modeling. The blending set operations are defined using R-functions and displacement functions with the localized area of influence. The shape and location of the blend is defined by control points on the surfaces of two solids or by an additional arbitrary bounding solid also defined by a real-valued function. The proposed blending using a bounding solid can be applied to a single selected edge, a vertex, or another blend. We introduce new types of blends such as a multiple blend with the disconnected bounding solid and a partial edge blend. We show that the proposed operations can replace pure set-theoretic operations in the solid model without rebuilding the entire construction tree data structure. The proposed blending is shown to have versatile applications in interactive design. Influence of all parameters on the blend shape and location is illustrated.
INDEX TERMS
Geometric modeling, shape, blending, implicit surfaces, R-functions
CITATION
Galina I. Pasko, Alexander A. Pasko, Tosiyasu L. Kunii, "Bounded Blending for Function-Based Shape Modeling", IEEE Computer Graphics and Applications, vol.25, no. 2, pp. 36-45, March/April 2005, doi:10.1109/MCG.2005.37
REFERENCES
1. J. Bloomenthal et al., eds., Introduction to Implicit Surfaces, Morgan Kaufmann, 1997.
2. J. Rossignac and A. Requicha, "Constant-Radius Blending in Solid Modeling," Computers in Mechanical Eng., vol. 3, no. 1, 1984, pp. 65-73.
3. J. Woodwark, "Blends in Geometric Modeling," Proc. Mathematics of Surfaces II, Clarendon Press, 1987, pp. 255-297.
4. A. Pasko and V. Savchenko, "Blending Operations for the Functionally Based Constructive Geometry," Proc. Set-theoretic Solid Modeling: Techniques and Applications, CSG 94 Conf., Information Geometers, 1994, pp. 151-161.
5. A. Pasko et al., "Function Representation in Geometric Modeling: Concepts, Implementation, and Applications," The Visual Computer, vol. 11, no. 8, 1995, pp. 429-446.
6. A. Requicha, "Representations of Rigid Solids: Theory, Methods, and Systems," Computing Surveys, vol. 12, no. 4, 1980, pp. 437-465.
7. V. Rvachev, Theory of R-functions and Some Applications, Naukova Dumka, 1987 (in Russian).
8. V. Shapiro, "Real Functions for Representation of Rigid Solids," Computer Aided Geometric Design, vol. 11, no. 2, 1994, pp. 153-175.
9. G. Pasko et al., "Virtual Shikki and Sazaedo: Shape Modeling in Digital Preservation of Japanese Lacquer Ware and Temples," Proc. Spring Conf. Computer Graphics SCCG 01, IEEE CS Press, 2001, pp. 147-154.
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