Piecewise linear paths among convex obstacles

Let B be a set of n arbitrary possibly intersecting convex obstacles in Rd. It is shown that any two points which can be connected by a path avoiding the obstacles can also be connected by a path consisting of Ond,1bd=2+1c segments. The bound cannot be improved below nd; thus in R3 , the answer is between n3 and n4 . For open disjoint convex obstacles, a n bound is proved. By a well-known reduction, the general case result also upper bounds the complexity for a translational motion of an arbitrary convex robot among convex obstacles. In the planar case, asymptotically tight bounds and e cient algorithms are given.

• Type: Conference
• Year: 1993
• Where: STOC
• Authors: Mark de Berg, Jirí Matousek, Otfried Schwarzkopf
• Keywords: Algorithms, Convex Obstacles, Intersecting Convex Obstacles, Open Disjoint Convex, STOC 1993