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Issue No.01 - January/February (1990 vol.10)
pp: 50-58
<p>The computational requirements and accuracy of two methods for finding the intersection of Bezier surfaces are examined. In both methods, the existence of an intersection curve is confirmed by using the convex hull property of such surfaces. The first method evaluates the intersection by recursive subdivision of two patches with overlapping hulls. The second method detects a point on the intersection curve and then incrementally traces the intersection in the parametric spaces of the two surfaces. With both methods, the intersection of a pair of first-order planar patches must be solved analytically. The intersection is approximated by first-order Bezier patches in the first case and by planar triangles in the second. Overall, the method of incremental tracing is shown to give more accurate results than the method of recursive subdivision.</p>
Nadim M. Aziz, Reda Bata, Sudarshan Bhat, "Surfaces: Bezier Surface/Surface Intersection", IEEE Computer Graphics and Applications, vol.10, no. 1, pp. 50-58, January/February 1990, doi:10.1109/38.45810
1. Q.S. Peng, "An Algorithm for Finding the Intersection Lines Between Two B-Spline Surfaces,"Computer-Aided Design, Vol. 16, No. 4, July 1984, pp. 191-196.
2. J.M. Lane and R.F. Riesenfeld, "A Theoretical Development for the Computer Generation of Piecewise Polynomial Surfaces,"IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 2, No. 1, Jan. 1980, pp. 35-46.
3. E. Cohen, T. Lyche, and R. Riesenfeld, "Discrete B-Spline and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics,"Computer Graphics and Image Processing, Vol. 14, No. 2, Oct. 1988, pp. 87-111.
4. D. Lasser, "Intersection of Parametric Surfaces in the Bernstein-Bezier Representation,"Computer-Aided Design, Vol. 18, No. 4, May 1988, pp. 162-192.
5. S.L. Hanna, J.F. Abel, and D.P. Greenberg, "Intersection of Parametric Surfaces by Means of Look-Up Tables,"CG&A, Vol. 3, No. 7, Oct. 1983, pp. 39-48.
6. M.B. Phillips and G.M. Odell, "An Algorithm for Locating and Displaying the Intersection of Two Arbitrary Surfaces,"CG&A, Vol. 4, No. 9, Sept. 1984, pp. 48-58.
7. P. G. Comba, "A procedure for detecting intersections of three-dimensional objects,"J. ACM, vol. 15, no. 3, pp. 354-366, July 1968.
8. M. E. Mortenson,Geometric Modeling. New York: Wiley, 1985.
9. N.M. Aziz, R. Bata, and S.P. Bhat, "Methods of Bezier Surface-Surface Intersections," Eng. Report, Eng. Graphics Program, Clemson Univ., Clemson, S.C., 1987.
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