Cartographic line simplification and polygon CSG formulæ in O(n log∗ n) time

An O(n log log n)-Time Algorithm for Triangulating a Simple Polygon

Given a simple n-vertex polygon, the triangulation problem is to partition the interior of the polygon into n-2 triangles by adding n-3 nonintersecting diagonals. We propose an O(n log logn)-time algorithm for this problem, improving on the previously best bound of O (n log n) and showing that triangu-lation is not as hard as sorting. Improved algorithms for several other computational geometry...

Finding the largest axis aligned rectangle in a polygon in o(n log n) time

An O(log log n) Time Algorithm to Compute the Kernel of a Polygon

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...

Computing the straight skeleton of a monotone polygon in O(n log n) time

The straight skeleton of a simple polygon is defined as the trace of the vertices when the initial polygon is shrunken in self-parallel manner [2]. In this paper, we propose a simple algorithm for drawing the straight skeleton of a monotone polygon. The time and space complexities of our algorithm are O(nlogn) and O(n) respectively.

Geodesic-Preserving Polygon Simplification

Polygons are a paramount data structure in computational geometry. While the complexity of many algorithms on simple polygons or polygons with holes depends on the size of the input polygon, the intrinsic complexity of the problems these algorithms solve is often related to the reflex vertices of the polygon. In this paper, we give an easy-todescribe linear-time method to replace an input polyg...