1 research outputs found
Generalized kernels of polygons under rotation
Given a set of orientations in the plane, two points inside
a simple polygon -see each other if there is an
-staircase contained in that connects them. The
-kernel of is the subset of points which -see all
the other points in . This work initiates the study of the computation and
maintenance of the - of a polygon as we rotate
the set by an angle , denoted -. In particular, we design efficient algorithms for (i)
computing and maintaining - while
varies in , obtaining the angular intervals
where the - is not empty and (ii) for
orthogonal polygons , computing the orientation such that the area and/or the perimeter of the
- are maximum or minimum. These
results extend previous works by Gewali, Palios, Rawlins, Schuierer, and Wood.Comment: 12 pages, 4 figures, a version omitting some proofs appeared at the
34th European Workshop on Computational Geometry (EuroCG 2018