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Interval Methods for Processing Geometric Objects
February 1984 (vol. 4 no. 2)
pp. 7-17
S. Mudur, Tata Institute of Fundamental Research
P. Koparkar, University of Bombay
In this approach, the parametric form is applied without the usual computational nightmare. The key is to view the parametric range as an interval, relying on subdivision algorithms.

1. R. E.Moore, Interval Analysis , Prentice-Hall 1966
2. E. R.Hansen, “A Globally Convergent Interval Method for Computing and Bounding Real Roots,” BIT Vol. 18, No. 4, pp. 415-424 1978 Nordisk Tidskrift for Informations Behandling
3. T. M.Apostol, Mathematical Analysis , Addison-Wesley 1958
4. P. A.Koparkar and S. P.Mudur, “A New Class of Algorithms for Processing Parametric Curves,” Computer-Aided Design Vol. 15, No. 1, pp. 41-45 1983
5. P. A.Koparkar and S. P.Mudur, Computational Techniques for Processing Parametric Surfaces , National Centre for Software Development and Computing Techniques 1983 (submitted for publication)
6. I.Braid, Designing with Volumes , Cantab Press 1973
7. I. D.Faux and M. J.Pratt, Computational Geometry for Design and Manufacture , Ellis-Horwood 1979
8. J. M.Lane and R. F.Riesenfeld, “A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces,” IEEE Trans. PAMI Vol. 2, No. 1, pp. 36-46 1980
9. J.Lane and L.Carpenter, “A Generalized Scanline Algorithm for the Computer Display of Parametrically Defined Surfaqes,” Computer Graphics and Image Processing Vol. 11, No. 3, pp. 290-297 1979
10. J. F.Blinn, Computer Display of Curved Surfaces Dec. 1978
11. T.Whitted, Computer Graphics , 1978 Vol. 12, supplement to Siggraph 78
12. E.Catmull, A Subdivision Algorithm for Computer Display of Curved Surfaces Dec. 1974

Citation:
S. Mudur, P. Koparkar, "Interval Methods for Processing Geometric Objects," IEEE Computer Graphics and Applications, vol. 4, no. 2, pp. 7-17, Feb. 1984, doi:10.1109/MCG.1984.275931
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