Equitable subdivisions within polygonal regions

Shellability of a Poset of Polygonal Subdivisions

Cartograms and Circular-Arc Simplification of Polygonal Subdivisions

Cartograms are proportional drawings of maps where the areas of all countries correspond to prescribed weights. Besides the property of being a proportional representation it is essential for the quality of a cartogram that the countries are not too badly deformed. A good clarity can only be achieved if all countries can easily be identified by the reader due to the fact that their principal to...

Integration within Polygonal Finite Elements

Engineering mechanics formulations of aerospace industry problems overwhelmingly rely upon spatial averaging techniques. Crucial applications in the area of dynamic response analysis and stochastic estimation of material degradation can be cited as important cases. Integration procedures on finite domains underlie physically acceptable averaging processes. Unlike one-dimensional cases, integral...

Multi-guard covers for polygonal regions

We study the problem of finding optimal covers of polygonal regions using multiple mobile guards. By our definition, a point is covered if, at some time, it lies within the convex hull of the guards from which it is visible. The definition captures our desire that guards both “see” and “surround” points that they cover. Guards move along continuous timeparameterized curves within a polygonal re...

Covering Simple Polygonal Regions by Ellipses

We study the problem of how to cover simple polygonal rectilinear regions by a small set of axis–parallel ellipses. This question is well motivated by a special pattern recognition task where one has to identify ellipse shaped protein spots in 2–dimensional electrophoresis images. We present and discuss various algorithmic approaches towards this problem ranging from a brute force method, to a ...