Methods for Searching Mutual Visible-Intervals on Moving Object

Computing visible information, such as a visible surface determination, is a significant problem and has been mainly studied in the fields of computational geometry and/or computer graphics[2, 4, 6, 10, 11, 13]. Furthermore, recently, one might be attracted to problems for dealing with continuously moving objects in a geometrical space [1, 9, 12, 14]. In this paper, we propose two indexing methods, called an Mutual Visible Intervals search tree (MVI-tree) and an Mutual Visible Intervals search list (MVI-list). Using each index, one can efficiently find “mutual visible-surfaces” of two moving objects from a query time. “Mutual visible surfaces” are subregions which are “visible” each other. We give algorithms for constructing an MVI-tree and an MVI-list from a set M of two convex polygons M0 with n0 vertices and M1 with n1 vertices, in the case where every convex polygon moves by uniform motion. An MVItree of M can be constructed in time O(N logN) using space O(N) and an MVI-list of M can be constructed in time O(N) using space O(N), where N is the total number of vertices and N = n0 + n1. “Mutual visible intervals”, i.e. “one-dimensional mutual visible surfaces”, of M at a query time can be found in time O(logN) using an MVI-tree or an MVI-list. Keyword Spatio-Temporal Index, Visible Surface Determination, Mutual Visible Intervals, Moving Object, MVI-tree, MVI-list