There has been lots of research in the field of fuzzy spatial data and the topology of fuzzy spatial objects. In this contribution, an extension to the 9-intersection model is presented, to allow for the relative position of overlapping fuzzy regions to be determined. The topology will be determined by means of a new intersection matrix, and a set of numbers, expressing the similarity between t...

A unit disk graph is an intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric representation (specifying the coordinates of the disk centers).

We present an algorithm generating a collection of fat arcs which bound the zero set of a given bivariate polynomial in Bernstein– Bézier representation. We demonstrate the performance of the algorithm (in particular the convergence rate) and we apply the results to the computation of intersection curves between implicitly defined algebraic surfaces and rational parametric surfaces.

Euler diagrams allow the visual representation of set systems and their intersection relations. Every set is represented by a collection of closed curves such that elements of two or more collections intersect if and only if the intersection of the corresponding sets is non-empty. In the area-proportional case each intersection’s area conveys numerical information. There exist several well-form...

The kernel of a polygon P is the set of all points that see the interior of P . It can be computed as the intersection of the halfplanes that are to the left of the edges of P . We present an O(log log n) time CRCW-PRAM algorithm using n/log log n processors to compute a representation of the kernel of P that allows to answer point containment and line intersection queries efficiently. Our appr...

We provide an answer to an open problem concerning the representation of preferences by intervals. Given a finite set of elements and three relations on this set (indifference, weak preference and strict preference), necessary and sufficient conditions are provided for representing the elements of the set by intervals in such a way that 1) two elements are indifferent when the interval associat...

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection. Secondly, to obtain centered solutions for systems of uncertain linear equations, we compute th...

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data). We use...

In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets’ boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based s...