Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

This paper presents a survey as well as a new sweep-circle algorithm, on plane sweep algorithms for computing the Delaunay triangulation. The algorithms examined are: Fortune’s sweep-line algorithm, Zalik’s sweep-line algorithm, and a sweep-circle algorithm proposed by Adam, Kauffmann, Schmitt, and Spehner. We test implementations of these algorithms on a number of uniform and none-uniform dist...

Voronoi diagrams are among the most important data structures in geometric modeling. Among many efficient algorithms for computing 2D Voronoi diagrams, Fortune’s sweepline algorithm (Fortune, 1986 [5]) is popular due to its elegance and simplicity. Dehne and Klein (1987) [8] extended sweepline to sweepcircle and suggested computing a type of transformed Voronoi diagram, which is parallel in nat...

A new algorithm based on the sweep plane approach to determine the machined part geometry in 5-axis machining with general APT tools is presented. Undercut and overcut can be determined. Collision detection between the toolholder, workpiece and workpiece fixture can also be detected. The subtraction of the removed material is obtained for each sweep plane by using a stencil buffer. A flat plane...

We provide a sweep coverage algorithm for routing mobile sensors that communicate with a central data sink. This algorithm improves on its predecessors by reducing the number of unnecessary scans when different points of interest (POIs) have different requirements for the time interval within which they must be scanned (sweep period). Most sweep coverage algorithms seek to minimize the number o...