*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Given an open subset in -D space and two compact subsets and of , where is derived from by a continuous motion, is it possible to move to while remaining entirely inside ?

**References**

Buchberger, B.; Collins, G. E.; and Kutzler, B. ``Algebraic Methods in Geometry.'' *Annual Rev. Comput. Sci.* **3**, 85-119, 1988.

Feinberg, E. B. and Papadimitriou, C. H. ``Finding Feasible Points for a Two-point Body.'' *J. Algorithms* **10**, 109-119, 1989.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/sofa/sofa.html

Leven, D. and Sharir, M. ``An Efficient and Simple Motion Planning Algorithm for a Ladder Moving in Two-Dimensional
Space Amidst Polygonal Barriers.'' *J. Algorithms* **8**, 192-215, 1987.

© 1996-9

1999-05-25