Hidden surface removal for rectangles

Abstract

A simple but important special case of the hidden surface removal problem is one in which the scene consists of n rectangles with sides parallel to the x- and y-axes, with viewpoint at z=∞ (that is, an orthographic projection). This special case has application to overlapping windows in computer displays. An algorithm with running time O( n log n + k log n) is given for static scenes, where k is the number of line segments in the output. Algorithms are given for a dynamic setting (that is, rectangles may be inserted and deleted) that take time O(log 2 n log log n + k log 2 n) per insert or delete, where k is now the number of visible line segments that change (appear or disappear). Algorithms for point location in the visible scene are also given.