Time-optimal visibility-related algorithms of meshes with multiple broadcasting

Given a sequence of objects in the plane along with a viewpoint O, the visibility problem involves determining the portion of each object that is visible to an observer positioned at O. The main contribution of this work is to provide time-optimal solutions to this problem for two classes of objects, namely disks and iso-oriented rectangles in the plane. This problem is of importance in various fields like computer graphics, VLSI design, and robot navigation. Additionally, the visibility algorithm provides the basis for a time-optimal algorithm to triangulate a set of points in the plane. Specifically, all algorithms presented involve an input of size n and run in O(log n) time on a mesh with multiple broadcasting of site n×n. This is the first instance of time-optimal solutions for these problems on this architecture