TY - JOUR
AB - Motivated by a number of motion-planning questions, we investigate in this paper some general topological and combinatorial properties of the boundary of the union ofn regions bounded by Jordan curves in the plane. We show that, under some fairly weak conditions, a simply connected surface can be constructed that exactly covers this union and whose boundary has combinatorial complexity that is nearly linear, even though the covered region can have quadratic complexity. In the case where our regions are delimited by Jordan acrs in the upper halfplane starting and ending on thex-axis such that any pair of arcs intersect in at most three points, we prove that the total number of subarcs that appear on the boundary of the union is only (n(n)), where(n) is the extremely slowly growing functional inverse of Ackermann's function.
AU - Herbert Edelsbrunner
AU - Guibas, Leonidas
AU - Hershberger, John
AU - Pach, János
AU - Pollack, Richard
AU - Seidel, Raimund
AU - Sharir, Micha
AU - Snoeyink, Jack
ID - 4089
IS - 1
JF - Discrete & Computational Geometry
TI - On arrangements of Jordan arcs with three intersections per pair
VL - 4
ER -