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Issue No.04 - April (1987 vol.7)
pp: 23-30
Peter Wilson , General Electric Company
ABSTRACT
The question of what is the "best" form of geometry for use in CAD systems and for data exchange between systems has often been argued with much intuition but few facts. I will present here some numerical stability results for several formulations of conic curves with the conclusion that the point/vector/scalar representation performs best. This also leads to a form of referential geometry that has significant advantages for use in geometric modeling systems.
INDEX TERMS
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CITATION
Peter Wilson, "Conic Representations for Shape Description", IEEE Computer Graphics and Applications, vol.7, no. 4, pp. 23-30, April 1987, doi:10.1109/MCG.1987.276868
REFERENCES
1. Apr. 1968 Initial Graphics Exchange Specification (IGES) NBS
2. Sept. 1984 Experimental Solids Proposal (ESP) IGES internal rpt., NBS
3. CAM-I Geometric Modeling Project Boundary File Design (XBF-2) Oct. 1982
4. Mar. 1984 SET Specifications Rev 1.1 (Standard d'Exchange et de Transfert) (An English translation is available from NBS, Gaithersburg, Md.)
5. E.B.Birchfield and H.H.King, "Product Data Definition Interface (PDDI)," Proc. USAF CIM Industry Days, 1985 Apr. 1985
6. A Reporting of the PDES Initiation Activities , NBS May 1986 IGES internal rpt.
7. A.Dresden, Solid Analytical Geometry and Determinants , Dover Publications 1964
8. I.D.Faux and M.J.Pratt, Computational Geometry for Design and Manufacture , 1981 (distributed by Halsted Press, a division of John Wiley & Sons, New York, N. Y.)
9. G.A.Allen, "Parametric Geometry for Solid Modeling," Jan. 1984 Geometric Representation: Which Way to Go?
10. R.N.Goldman, "Two Approaches to a Computer Model for Quadric Surfaces," IEEE CG&App. 21-24 Sept. 1983
11. R.H.Johnson, "Analytic Geometry for Solid Modeling," Jan 1984 Geometric Representation: Which Way to Go?
12. J.Z.Levin, "A Parametric Algorithm for Drawing Pictures of Solid Objects Composed of Quadric Surfaces," Comm. ACMpp. 555-563 Oct. 1976
13. A.P.Morgan, A Method for Computing all Solutions to Systems of Polynomial Equations , General Motors Research Publication GMR-3651 July 1981
14. H.U.Pfeifer, Computer Aided Design , Sept. 1985pp. 311-318
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