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 convex rope problem, posed by Peshkin and Sanderson in IEEE J. Robotics Automat, 2 (1986) pp. 53-58, is to find the counterclockwise and clockwise convex ropes starting at the vertex a and ending at the vertex b of a simple polygon, where a is on the boundary of the convex hull of the polygon and b is visible from infinity. In this paper, we present a linear time algorithm for solving this ...

In this paper, we study a new problem of convex drawing of planar graphs with non-convex boundary constraints. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. We also prove that every four-connected plane graph whose boundary is fixed with a crown-shaped polygon a...

Based on the planar polygon shape classification, we propose a method—Standardized Binary String Descriptor of Convex Polygon—for classification of convex polygons, making it more precise. Thus, the model database space is pruned and the number of shape models compared with, when doing match query and similarity query, is reduced. Furthermore, the number of equivalence class of convex polygon f...

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...

A floodlight of size α is a light source that projects light in a cone of size α . In this paper we study the problem of illuminating a convex polygon using floodlights. We give an O(n 2 ) time algorithm to find an optimal pair of floodlights to illuminate a convex polygon P with n vertices; that is a pair of floodlights to illuminate a convex polygon in such a way that the sum of their sizes i...

A half-plane probe through a polygon measures the area of intersection between a half-plane and the polygon. We dev elop techniques based on xray probing to determine convex n-gons in 7n + 7 half-plane probes. We also show n + 1 half-plane probes are sufficient to verify a specified convex polygon and prove linear lower bounds for determination and verification.

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In th...