Sweeping an oval to a vanishing point

Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider the following slanted variant of sweeping recently introduced in [1]: In a single sweep, the sweep-line is placed at a start position somewhere in the plane, then moved continuously according to a sweep vector v (not necessarily orthogonal to the sweep-line) to another parallel end position, and then lifted from the plane. The cost of a sequence of sweeps is the sum of the lengths of the sweep vectors. The optimal sweeping cost of a region is the infimum of the costs over all finite sweeping sequences for that region. An optimal sweeping sequence for a region is one with a minimum total cost, if it exists. Another parameter of interest is the number of sweeps. We show that there exist convex regions for which the optimal sweeping cost cannot be a...

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Adrian Dumitrescu, Minghui Jiang
• Keywords: Convex Regions, CORR 2011, Education, Sweeping Sequence, Sweeps