Finding minimal convex nested polygons

Finding the Set of All Minimal Nested Convex Polygons

Finding largest rectangles in convex polygons

We consider the following geometric optimization problem: find a maximum-area rectangle and a maximum-perimeter rectangle contained in a given convex polygon with n vertices. We give exact algorithms that solve these problems in time O(n). We also give (1 − ε)-approximation algorithms that take time O(ε−3/2 + ε−1/2 log n) for maximizing the area and O(ε−3 + ε−1 log n) for maximizing the perimeter.

Stock Cutting Of Complicated Designs by Computing Minimal Nested Polygons

This paper studies the following problem in stock cutting: when it is required to cut out complicated designs from parent material, it is cumbersome to cut out the exact design or shape, especially if the cutting process involves optimization. In such cases, it is desired that, as a first step, the machine cut out a relatively simpler approximation of the original design, in order to facilitate...

On Minimal Triangulations of Products of Convex Polygons

We give new lower bounds for the minimal number of simplices needed in a triangulation of the product of two convex polygons, improving the lower bounds in [Bo&al05].

Finding the Minimum Distance Between Two Convex Polygons

suppose that a provisional path of coordinated motion has been planned for two rigid polyhedral bodies B1 and B2 in 3-space. Then there will exist functions RI(t), R*(t), x1(t), x2(t) of a parameter t designating time such that the set of points occupied by Bj at time t is Rj(t)Bj + xj(t). TO verify the validity of the proposed motion, one can proceed as follows: find the minimum distance 6 bet...