On the Polygon Containment Problem on an Isometric Grid

Xiangzhi Wei, Bao Zhao, Ajay Joneja, Juntong Xi

Abstract: This paper addresses the issue of placing a simple polygon (upon translation and rotation) on an isometric triangular grid such that the polygon contains the maximum number of triangles in its closure. This solves the problem left open in two recent papers titled “On the problem of the automated design of large-scale robot skin” and “An improved algorithm for the automated design of large scale robot skin” published in the IEEE Transactions on Automation Science and Engineering . Based on the properties of the grid, an improved algorithm is also presented. We also present some experimental results describing the use of this algorithm.