Motorcycle graphs: canonical quad mesh partitioning
SGP '08 Proceedings of the Symposium on Geometry Processing
Theoretical and practical results on straight skeletons of planar straight-line graphs
Proceedings of the twenty-seventh annual symposium on Computational geometry
Motorcycle graphs: Stochastic properties motivate an efficient yet simple implementation
Journal of Experimental Algorithmics (JEA)
On the structure of straight skeletons
Transactions on Computational Science VI
Generating realistic roofs over a rectilinear polygon
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
On computing straight skeletons by means of kinetic triangulations
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
A faster algorithm for computing motorcycle graphs
Proceedings of the twenty-ninth annual symposium on Computational geometry
Realistic roofs over a rectilinear polygon
Computational Geometry: Theory and Applications
| Hi-index | 0.00 |
We present a new algorithm to compute motorcycle graphs. It runs in $O(n \sqrt{n}\log n)$ time when n is the number of motorcycles. We give a new characterization of the straight skeleton of a nondegenerate 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 $O(n\sqrt{h+1}\log^2 n)$ time. Combining these results, we can compute the straight skeleton of a nondegenerate polygon with h holes and with n vertices, among which r are reflex vertices, in $O(n\sqrt{h+1}\log^2 n+r \sqrt{r} \log r)$ expected time. In particular, we cancompute the straight skeleton of a nondegenerate polygon with n vertices in $O(n\sqrt{n}\log^2n)$ expected time.