1. Random and goal oriented walk models To simulate human movement in a street network, we setup some random walkers which can hop from one street to another arbitrarily. The hopping behaviour is defined at a topological level in which individual streets are represented as nodes and street intersections as links of a connectivity graph (Figure 1). On the other hand, the simulation has yet to be...

A directed graph is upward planar if it can be drawn in the plane such that every edge is a monotonically increasing curve in the vertical direction, and no two edges cross. An undirected graph is recti-linear planar if it can be drawn in the plane such that every edge is a horizontal or vertical segment, and no two edges cross. Testing upward planarity and rectilinear planarity are fundamental...

At high frequencies, the sound propagation can be approximated by the propagation of sound particles which are reflected and absorbed at the boundaries. This propagation follows then a transport process. In urban canyons, this transport process can be reduced to a diffusion process. The resultant model allows one to obtain the spatial distribution of the acoustical energy in a street for a very...

A summary of research in urban feature extraction being conducted under a MURI (multi-disciplinary research initiative) program sponsored by the U.S. Army Research Office is provided. Most of the paper focuses on extraction of rectilinear building models. Feature extraction from aerial images is difficult due to problems of segmentation, 3-D inference and shape description. A system for buildin...

Street network vector data is represented as Regular Closed Network. The combinatorial structure of the Regular Closed Network is modelled through abstract cell complex. Two abstraction operators and two refinement updates are cited to define the street elimination operator and street refinement operator. Two alternative progressive representation models for street network vector data are propo...

The OpenStreetMap (OSM) project is a prime example in the field of Volunteered Geographic Information (VGI). Worldwide, several hundred thousand people are currently contributing information to the ―free‖ geodatabase. However, the data contributions show a geographically heterogeneous pattern around the globe. Germany counts as one of the most active countries in OSM; thus, the German street ne...

Many complex networks erase parts of their geometry as they develop, so that their evolution is difficult to quantify and trace. Here we introduce entropy measures for quantifying the complexity of street orientations and length variations within planar networks and apply them to the street networks of 41 British cities, whose geometric evolution over centuries can be explored. The results show...

We present a general rectilinear Steiner tree problem in the plane and prove that it is solvable on the Hanan grid of the input points. This result is then used to show that several variants of the ordinary rectilinear Steiner tree problem are solvable on the Hanan grid, including | but not limited to | Steiner trees for rectilinear (or iso-thetic) polygons, obstacle-avoiding Steiner trees, gro...

In this paper, a three-layer force-directed self-organizing map is designed to resolve the circuit placement problem with arbitrarily shaped rectilinear modules. The proposed neural model with an additional hidden layer can easily model a rectilinear module by a set of hidden neurons to correspond the partitioned rectangles. With the collective computing from hidden neurons, these rectilinear m...

This paper discusses three rectilinear (that is, axis-parallel) covering problems in d dimensions and their variants. The first problem is the Rectilinear Line Cover where the inputs are n points in R and a positive integer k, and we are asked to answer if we can cover these n points with at most k lines where these lines are restricted to be axis parallel. We show that this problem has efficie...