7 papers found.

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Point feature map labeling is a geometric visualization problem, in which a set of input points must be labeled with a set of disjoint rectangles (the bounding boxes of the label texts). It is predominantly motivated by label placement in maps but it also has other visualization applications. Typically, labeling models either use internal labels, which must touch their feature...

For a polyhedron \(P\) let \(B(P)\) denote the polytopal complex that is formed by all bounded faces of \(P\). If \(P\) is the intersection of \(n\) halfspaces in \(\mathbb R ^D\), but the maximum dimension \(d\) of any face in \(B(P)\) is much smaller, we show that the combinatorial complexity of \(P\) cannot be too high; in particular, that it is independent of \(D\). We show...

Suppose we want to compute the Delaunay triangulation of a set P whose points are restricted to a collection ℛ of input regions known in advance. Building on recent work by Löffler and Snoeyink, we show how to leverage our knowledge of ℛ for faster Delaunay computation. Our approach needs no fancy machinery and optimally handles a wide variety of inputs, e.g., overlapping disks...

Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible convex hulls, measured by length and by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We give polynomial time...

We study variants of the potato peeling problem on meshed (triangulated) polygons. Given a polygon with holes, and a triangular mesh that covers its interior (possibly using additional vertices), we want to find a largest-area connected set of triangles of the mesh that is convex, or has some other shape-related property. In particular, we consider (i) convexity, (ii...

We investigate the concept of a median among a set of trajectories. We establish criteria that a “median trajectory” should meet, and present two different methods to construct a median for a set of input trajectories. The first method is very simple, while the second method is more complicated and uses homotopy with respect to sufficiently large faces in the arrangement formed...

Spatially aggregated data is frequently used in geographical applications. Often spatial data analysis on aggregated data is performed in the same way as on exact data, which ignores the fact that we do not know the actual locations of the data. We here propose models and methods to take aggregation into account. For this we focus on the problem of locating clusters in aggregated...