M.J. van Kreveld

Spatial information retrieval and geographical ontologies an overview of the SPIRIT project

A large proportion of the resources available on the world-wide web refer to information that may be regarded as geographically located. Thus most activities and enterprises take place in one or more places on the Earths surface and there is a wealth of survey data, images, maps and reports that relate to specific places or regions. Despite the prevalence of geographical context, existing web search facilities are poorly adapted to help people find information that relates to a particular location. When the name of a place is typed into a typical search engine, web pages that include that name in their text will be retrieved, but it is likely that many resources that are also associated with the place may not be retrieved. Thus resources relating to places that are inside the specified place may not be found, nor may be places that are nearby or that are equivalent but referred to by another name. Specification of geographical context frequently requires the use of spatial relationships concerning distance or containment for example, yet such terminology cannot be understood by existing search engines. Here we provide a brief survey of existing facilities for geographical information retrieval on the web, before describing a set of tools and techniques that are being developed in the project SPIRIT : Spatially-Aware Information Retrieval on the Internet (funded by European Commission Framework V Project IST-2001-35047).

Determining the castability of simple polyhedra

Abstract. A polyhedron P is castable if its boundary can be partitioned by a plane into two polyhedral terrains. Castable polyhedra can be manufactured easily using two cast parts, where each cast part can be removed from the object without breaking the cast part or the object. If we assume that the cast parts are each removed by a single translation, it is shown that for a simple polyhedron with n vertices, castability can be decided in

Concatenable segment trees

O(n^2\log n)

Watertight scenes from urban LiDar and planar surfaces

time and linear space using a simple algorithm. A more complicated algorithm solves the problem in

Scale-Dependent Definitions of Gradient and Aspect and their Computation

O(n^{3/2+\epsilon})

Connected component and simple polygon intersection searching

time and space, for any fixed ε > 0. In the case where the cast parts are to be removed in opposite directions, a simple O(n2)-time algorithm is presented. Finally, if the object is a convex polyhedron and the cast parts are to be removed in opposite directions, a simple

Intersection queries in sets of disks

O(n \log^2n)

A simple and efficient algorithm for high-quality line labeling

algorithm is presented.

Rectangular cartogram computation with sea regions

In this paper a variant of a segment tree is devised on which, in addition to insertions, deletions and stabbing queries, the operations concatenate and split can be performed efficiently. Insertions, concatenations and splits take O(log n) time, deletions take O(log2n) time, stabbing queries take O(k + log n) time (where k is the number of answers to the query), and the structure uses O(n log n) space to store. The technique is based on a new general data structure that stores sets of objects, the union-copy structure, on which the operations union (of two sets), copy (of a set), insert (of an object in one or more sets), delete (of an object from all sets in which it occurs) and enumerate (of a set) can be performed efficiently.

Shortest path queries in rectilinear worlds of higher dimension

The demand for large geometric models is increasing, especially of urban environments. This has resulted in production of massive point cloud data from images or LiDAR. Visualization and further processing generally require a detailed, yet concise representation of the scenes surfaces. Related work generally either approximates the data with the risk of over‐smoothing, or interpolates the data with excessive detail. Many surfaces in urban scenes can be modeled more concisely by planar approximations. We present a method that combines these polygons into a watertight model. The polygon‐based shape is closed with free‐form meshes based on visibility information. To achieve this, we divide 3‐space into inside and outside volumes by combining a constrained Delaunay tetrahedralization with a graph‐cut. We compare our method with related work on several large urban LiDAR data sets. We construct similar shapes with a third fewer triangles to model the scenes. Additionally, our results are more visually pleasing and closer to a human modelers description of urban scenes using simple boxes.