Motorcycle Graphs and Straight Skeletons

We present a new algorithm to compute motorcycle graphs. It runs in O(n √ n log n) time when n is the number of motorcycles. We give a new characterization of the straight skeleton of a non–degenerate polygon. For a polygon with n vertices and h holes, we show that it yields a randomized algorithm that reduces the straight skeleton computation to a motorcycle graph computation in expected O(n √ h + 1 log2 n) time. Combining these results, we can compute the straight skeleton of a non–degenerate polygon with h holes and with n vertices, among which r are reflex vertices, in O(n √ h + 1 log2 n + r √ r log r) expected time. In particular, we can compute the straight skeleton of a non–degenerate polygon with n vertices in O(n √ n log2 n) expected time. Key words: Computational Geometry – Randomized Algorithm – Straight Skeleton Medial Axis – Motorcycle graph

• Type: Journal
• Year: 2007
• Where: ALGORITHMICA
• Authors: Siu-Wing Cheng, Antoine Vigneron
• Keywords: ALGORITHMICA 2007, Motorcycle Graph, Non–degenerate Polygon, Straight Skeleton