We introduce additively-weighted straight skeletons as a new generalization of straight skeletons. An additively-weighted straight skeleton is the result of a wavefront-propagation process where, unlike in previous variants of straight skeletons, wavefront edges do not necessarily start to move at the begin of the propagation process but at later points in time. We analyze the properties of add...

We characterize the self-parallel (mitered) offsets of a general nonconvex polytope Q in 3-space and give a canonical algorithm that constructs a straight skeleton for Q.

The straight skeleton of a polygon is the geometric graph obtained by tracing the vertices during a mitered offsetting process. It is known that the straight skeleton of a simple polygon is a tree, and one can naturally derive directions on the edges of the tree from the propagation of the shrinking process. In this paper, we ask the reverse question: Given a tree with directed edges, can it be...

We study the computation of the straight skeleton of a planar straight-line graph (PSLG) by means of the triangulation-based wavefront propagation proposed by Aichholzer and Aurenhammer in 1998, and provide both theoretical and practical insights. As our main theoretical contribution we explain the algorithmic extensions and modifications of their algorithm necessary for computing the straight ...

Modelling Large Urban Environments using traditional modelling techniques would prove too time consuming a process. Consequently a method is required for generating large urban environments quickly without requiring a labour intensive process or expensive data. Some approaches to resolve this problem have been undertaken through the use of procedural modelling or statistics. However the test su...

We describe several RNC algorithms for generating graphs and subgraphs uniformly at random. For example, unla-belled undirected graphs are generated in O(lg 3 n) time using O "n 2 lg 3 n processors if their number is known in advance and in O(lg n) time using O "n 2 lg n processors otherwise. In both cases the error probability is the inverse of a polynomial in ". Thus " may be chosen to trade-...