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Computing Rational Bisectors
November/December 1999 (vol. 19 no. 6)
pp. 76-81
Bisector construction plays an important role in many geometric computations. This article explains how to compute rational bisectors of point-surface and sphere-surface pairs.

1. H. Persson, "NC Machining of Arbitrary-Shaped Pockets," Computer-Aided Design, Vol. 10, No. 3, May 1978, pp. 169-174.
2. D. Dutta and C. Hoffmann, "On the Skeleton of Simple CSG Objects," ASME J. of Mechanical Design, Vol. 115, No. 1, Mar. 1993, pp. 87-94.
3. G. Elber and M.-S. Kim, "The Bisector Surface of Freeform Rational Space Curves," ACM Trans. on Graphics, Vol. 17, No. 1, Jan. 1998, pp. 32-49.
4. G. Elber and M.-S. Kim, "Bisector Curves of Planar Rational Curves," Computer-Aided Design, Vol. 30, No. 14, Dec. 1998, pp. 1089-1096.
5. R. Farouki and R. Ramamurthy, "Specified-Precision Computation of Curve/Curve Bisectors," Int'l J. of Computational Geometry and Applications, Vol. 8, Nos. 5-6, Oct.-Dec. 1998, pp. 599-617.
6. R. Farouki and J. Johnstone, "The Bisector of a Point and a Plane Parametric Curve," Computer-Aided Geometric Design, Vol. 11, No. 2, Apr. 1994, pp. 117-151.
7. H. Pottmann, "Rational Curves and Surfaces with Rational Offsets," Computer-Aided Geometric Design, Vol. 12, No. 2, Mar. 1995, pp. 175-192.
8. R. Farouki and T. Sakkalis, "Pythagorean Hodographs," IBM J. of Research and Development, Vol. 34, No. 5, Sep. 1990, pp. 736-752.
9. D. Dutta, R. Martin, and M. Pratt, "Cyclides in Surface and Solid Modeling," IEEE Computer Graphics and Applications, Vol. 13, No. 1, Jan. 1993, pp. 53-59.
10. M. Peternell and H. Pottmann, "Computing Rational Parameterizations of Canal Surfaces," J. of Symbolic Computation, Vol. 23, Nos. 2-3, 1997, pp. 255-266.
11. H. Pottmann, W. Lü, and B. Ravani, "Rational Ruled Surfaces and Their Offsets," Graphical Models and Image Processing, Vol. 58, No. 6, Nov. 1996, pp. 544-552.
12. Irit 7.0 User's Manual, Technion, 1997, http://www.cs.technion.ac.il~irit.

Citation:
Gershon Elber, Myung-Soo Kim, "Computing Rational Bisectors," IEEE Computer Graphics and Applications, vol. 19, no. 6, pp. 76-81, Nov.-Dec. 1999, doi:10.1109/38.799747
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