Abstract
A bisector of two sets is the set of points equidistant form them. Bisectors arise naturally in several areas of computational geometry. We show that bisectors of weakly linearly separable sets inE d have many properties of interest. Among these, the bisector of a restricted class of linearly separated sets is a homeomorphic image of the linear separator. We also give necessary and sufficient conditions for the existence of a particular continuous map from (a portion of) any linear separator to the bisector.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
F. L. Bookstein, The Line-Skeleton,Comput. Graphics and Image Process., Vol. 11, pp. 123–137, October 1979.
L. Guibas and J. Stolfi, Primitives for the Manipulation of General Subdivisions and the Computation of Voronoi Diagrams,ACM Trans. Graphics, vol. 4, no. 2, pp. 74–123, April 1985.
T. Husain,Topology and Maps, New York: Plenum, 1977.
P. Kelly and M. Weiss,Geometry and Convexity: A Study in Mathematical Methods, New York: Wiley, 1979.
D. T. Lee, Medial Axis Transformation of a Planar Shape.,IEEE Trans. Pattern Anal. Mach. Intell., vol. 4, no 4, pp. 363–369, July 1982.
D. T. Lee and R. L. Drysdale, III, Generalization of Voronoi diagrams in the Plane.,SIAM J. Comput., vol. 10, no. 1, pp. 73–87, February 1981.
D. Leven and M. Sharir, Intersection and Proximity Problems and Voronoi Diagrams, in J. T. Schwartz and C. Yap, editors,Algorithmic and Geometric Aspects of Robotics, pp. 187–228. Hillsdale, New Jersey: Erlbaum, 1987.
F. P. Preparata and M. I. Shamos,Computational Geometry: An Introduction, New York: Springer-Verlag, 1985.
V. Srinivasan and L. R. Nackman, Voronoi Diagram for Multiply-Connected Polygonal Domains I: Algorithm,IBM J. Res. Develop., vol. 31, no. 3, pp. 361–372, May 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nackman, L.R., Srinivasan, V. Bisectors of linearly separable sets. Discrete Comput Geom 6, 263–275 (1991). https://doi.org/10.1007/BF02574688
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02574688