Function representation for sweeping by a moving solid

IEEE Transactions on Visualization and Computer Graphics

Volumn 2, Issue 1, 1996, Pages 11-18

  Sourin, Alexi I ^a   A pasko, Alexander ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Function representation; R functions; Solid modeling; Sweeping, implicit functions

Indexed keywords

ALGORITHMS; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; SET THEORY; VISUALIZATION;

CARTESIAN COORDINATES; FUNCTION REPRESENTATION; IMPLICIT FUNCTIONS; R FUNCTIONS; SOLID MODELING; SWEEPING;

COMPUTER GRAPHICS;

EID: 0030105492     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/2945.489382     Document Type: Article

References (33)

1. J.R. Rossignac"Trough the Cracks of the Solid Modeling Milestone," Object Modeling to Advanced Visual Communication, S. Coquillart, W, Strasser and P. Stucki, eds., Focus on Computer Graphics Series, Springer Verlag, 1994, pp. 1-75
2. W.P. Wang, and K.K. Wang"Geometric Modeling for Swept Volume Of Moving Solids," IEEE Trans. Computer Graphics and Applications, vol. 6, 12, pp. 8-17,1986.
3. K.C. Hui"Solid Sweeping In Image Space-Application in NC Simulation," The Visual Computer, vol. 10, 6, pp. 306-316, 1994.
4. R.B. Jerard, S.Z. Hussaini, R.L. Drysdale, and B. Schaudt"Approximate Methods for Simulation and Verification of Numerically Controlled Machining Programs," The Visual Computer, no. 5, pp. 329-348,1989.
5. W.P. Wang"Solid Modeling for Mold Design and Manufacture," Technical Report No. 44, Cornell Univ., Ithaca, N.Y., Jan. 1984.
6. K.C. Hui, and S.T. Tan"Mould Design With Sweep Operations-A Heuristic Search Approach," Computer-Aided Design, vol. 24, 2, pp. 81-91,1992.
7. S. Sawai, and Y. Kakazu"Mould Design: Automatic Generation of The Shape of Cavity and Core," CSG 94 Set-Theoretic Solid Modeling: Techniques and Applications, Information Geometers. Winchester, 1994, pp. 337-350.
8. T. Lozano-Perez"Spatial Planning: A Configuration Space Approach," IEEE Tmns. Computers, vol. 32, 2, pp. 108-120,1983.
9. J.R. Rossignac, and A.A.G. Requicha"Constant-Radius Blending in Solid Modeling," Computers in Mechanical Engineering, vol. 3, 1, pp. 65-73,1984.
10. J.R. Rossignac, and A.A.G. Requicha"Offsetting Operations in Solid Modeling," Computer Aided Geometric Design, vol. 3, 2, pp. 129-148,1986.
11. A.E. Middleditch"Ray Casting Set-Theoretic Rolling Sphere Blends," Computer-Aided Surface Geometry and Design, The Mathematics of Surfaces IV, A.Bowyer, ed., Oxford: Clarendon Press, 1994, pp. 261-280.
12. J. Menon, R.J. Marisa, and J. Zagajac"More Powerful Solid Modeling Through Ray Representations," IEEE Trans. Computer Graphics and Applications, vol. 14, 3, pp. 22-35,1994.
13. K. Sambandan"Geometry Generated by Sweeps Of Polygons and Polyhedra," Technical Report No. 66, Cornell Univesiry, Ithaca, N.Y., p. 156, August, 1990.
14. J.J. van Wijk"Ray Tracing of Objects Defined by Sweeping a Sphere," Computers and Graphics, vol. 9, 3, pp. 283-290,1985.
15. P. K. Ghosh"A Unified Computational Framework for Minkowski Operations," Computers ana. Graphics, vol. 17, 4, pp. 357378,1993.
16. R.R. Martin"The Geometry of the Helical Canal Surface," Compuler-Aided Surface Geometry and Design, The Mathematics of Surfaces TV, A. Bowyer, ed. Oxford: Clarendon Press, 1994, pp. 17-32.
17. S.J. Parry-Barwick, A. Bowyer"Minkowski Sums Of SetTheoretic Models," CSG 94 Set-Theoretic Solid Modeling: Techniques and Applications, Information Geometers. Winchester, 1994, pp. 101116.
18. R.R. Martin and P.C. Stephenson"Sweeping of Three-Dimensional Objects," Computer-Aided Design, vol. 22, 4, pp. 223-234,1990.
19. K.C. Hui"Solid Modeling with Sweep-CSG Representation," CSG 94 Set-Theoretic Solid Modeling: Techniques and Applications, Information Geometers, Winchester, 1994, pp. 119-131.
20. C.M. Hoffmann"Implicit Curves and Surfaces in CAGD," IEEE Computer Graphics and Applications, vol. 13, 1, pp. 79-88,1993.
21. J.F. Blirtn"A Generalization of Algebraic Surface Drawing," ACM Trans. Graphics, vol. 1, 3, pp. 235-256,1982.
22. G. Wyvffl, C. McPheeters, B. Wyvill"Data Structure for Soft Objects," The Visual Computer, vol. 2, 4, pp. 227-234,1986.
23. J. Bloomental, and B. Wyvill"Interactive Techniques For Implicit Modeling," Computer Graphics, vol. 24, 2, pp. 109-116,1990,
24. I.A. Essa, S. Sclaroff, and A. Pentland"A Unified Approach For Physical And Solid Modeling For Graphics and Animation," Proc. EUROGRAPHICS '92, Computer Graphics Forum, vol. 11, no, 3, pp. 129-138,1992.
25. V.L. Rvachev, Methods of Logic Algebra in Mathematical Physics. Kiev: Naukova Dumka Publishers, 259p, 1974.
26. V. Shapiro"Theory of R-Functions and Applications: A Primer" TR CPA88-3. Cornell Univ., Ithica, N.Y., 1988, p. 27p.
27. A.A. Pasko"Conceptual and Instrumental Tools For A Direct Method of Multidimensional Geometric Problems Solving with a Computer," PhD dissertation, Moscow Engineering Physics Institute, Moscow, 1988.
28. A.A. Pasko, V.V. Savchenko, V.D. Adzhiev, and A.I. Sourin"Multidimensional Geometric Modeling and Visualization Based on the Function Representation of Objects," Univ. Aizu, Technical Report 93-1-008,1993, p. 47.
29. V. Shapiro"Real Functions For Representation of Rigid Solids," Computer Aided Geometric Design, vol. 11, 2, pp. 153-175,1994. -
30. A.A. Pasko, V.D. Adzhiev, A.I. Sourin, V.V. Savchenko"Function Representation In Geometric Modeling: Concepts, Implementations and Applications," The Visual Computer, vol. 11, 8,1995, pp. 429-446.
31. A.A. Pasko, V.V. Savchenko"Blending Operations For The Functionally Based Constructive Geometry," CSG 94 Set-theoretic Solid Modeling: Techniques and Applications, Information Geometers-4 Winchester, 1994, pp. 151-161.
32. C.E. Weatherburn"Differential Geometry of Three Dimensions." Cambridge Univ. Press, 1927.
33. R.T. Farouki"Hierarchical Segmentations Of Algebraic Curves And Some Applications," Mathematical Methods m Computer Aided Geometric Design, T. Lyche and L. Schumaker, eds. Academic Press, 1989, pp. 239-248.