We show how to represent a simple polygon P by a grid (pixel-based) polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P , a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the bounda...

Guarding a polygon with few guards is an old and well-studied problem in computational geometry. Here we consider the following variant: We assume that the polygon is orthogonal and thin in some sense, and we consider a point p to guard a point q if and only if the minimum axis-aligned rectangle spanned by p and q is inside the polygon. A simple proof shows that this problem is NP-hard on ortho...

Given a planar polygon (or chain) with a list of edges {e1, e2, e3, . . . , en−1, en}, we examine the effect of several operations that permute this edge list, resulting in the formation of a new polygon. The main operations that we consider are: reversals which involve inverting the order of a sublist, transpositions which involve interchanging subchains (sublists), and edge-swaps which are a ...

“Trixel Buffers is a new spatial data-structure for fast point in multiple polygon inclusion queries. The algorithm utilizes a pre-processing step in which the inside/outside status of a quadtree ́s leaf triangles without polygon geometry is pre-computed automatically; at run-time point queries lying within these triangles simply inherit their inclusion status. If a point query lies in a leaf tr...