We present a new method for line drawing, triangle filling, polygon filling, and antialiasing. Current statistics show that our method improves line drawing and antialiasing about 6 times and polygon filling functions significantly over all existing methods. Specifically, it can improve finding the span extrema of polygons about 2 times and drawing the antialiased polygon edges more than 2 time...

We present an approach to the localization problem, for which polygon distances play an important role. In our setting of this problem the robot is only equipped with a map of its environment, a range sensor, and possibly a compass. To solve this problem, we first study an idealized version of it, where all data is exact and where the robot has a compass. This leads to the pure geometrical prob...

Given an orthogonal polygon P with n vertices, the goal of the watchman route problem is finding a path S of the minimum length in P such that every point of the polygon P is visible from at least one of the point of S. In the other words, in the watchman route problem we must compute a shortest watchman route inside a simple polygon of n vertices such that all the points interior to the polygo...

An algorithm for computing the convex hull of a simple polygon is presented. Its correctness and complexity are also shown. Computational geometry Convex hull Simple polygon Algorithm

The no-fit polygon (NFP) is the set of feasible locations that one polygon may take with respect to another polygon, such that the polygons do not overlap. Feasible locations are required for most of the solutions to two-dimensional packing problems, and also for other problems such as robot motion planning. Efficient methods to calculate the NFP of two convex polygons, or one convex and one no...

In many computer applications areas such as graphics, automated cartography, image processing, and robotics the notion of visibility among objects modeled as polygons is a recurring theme. This paper is concerned with the visibility of a simple polygon from one of its edges. Three natural definitions of the visibility of a polygon from an edge are presented. The following computational problem ...

Let G denote a graph and let K be a subset of vertices that are a set of target vertices of G. The Kterminal reliability of G is defined as the probability that all target vertices in K are connected, considering the possible failures of non-target vertices of G. The problem of computing K-terminal reliability is known to be #P-complete for polygon-circle graphs, and can be solved in polynomial...

In this paper we present a.n efficient pa.ra.Ilel algorithm. for polygon tria.ngu.Ia.tion. The algo-rithm we present runs in O(logn) time using D(n) processors, which is optimal if the polygon is allowed to contain holes. This improves the previous parallel complexity bounds for this problem by a log n factor. If we are also given a trapezoidal decomposition of the polygon as input, then we can...

Based on building polygons (building footprints) on a digital map, we are proposing a GIS (Geographic Information System) and CG integrated system to generate 3-D building models automatically. Most building polygons‟ edges meet at right angles (orthogonal polygon). A complicated orthogonal polygon can be partitioned into a set of rectangles. In order to partition an orthogonal polygon, we prop...