2013 IEEE 54th Annual Symposium on Foundations of Computer Science (1991)

San Juan, Puerto Rico

Oct. 1, 1991 to Oct. 4, 1991

ISBN: 0-8186-2445-0

pp: 49-58

J. Matousek , Dept. of Appl. Math., Charles Univ., Praha, Czechoslovakia

ABSTRACT

It is shown that for every fixed delta >0 the following holds: if F is a union of n triangles, all of whose angles are at least delta , then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2/sup alpha (n)/ log n) is given. Several applications of these results are presented.

INDEX TERMS

randomized algorithm, fat triangles, linearly many holes, connected components, complexity

CITATION

M. Sharir,
E. Welzl,
N. Miller,
S. Sifrony,
J. Matousek,
J. Pach,
"Fat triangles determine linearly many holes (computational geometry)",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 49-58, 1991, doi:10.1109/SFCS.1991.185347