Search algorithm for determining the range of the possible collision of conver polygons

Let P = (P
0
, P
1
, …, P
n−1
) and Q = (q
0
, q
1
, …, q
m−1
) be two arbitrary convex polygons in plane. In this paper, the author studies the problems of how to quickly determine their possible collision range and movable range. In the paper, a new sufficient and necessary condition for deciding possible collision is proposed, and the basic characters of the oblique supporting lines are investigated, and on these grounds the problem to determine the possible collision range is transformed into that of searching the supporting points on the sets of convex polygon vertexs. Using the strategy of searching simultaneously the sets of vertexes of P and Q, the author constructs the fast algorithm for finding the supporting points, the time-complexity of which is O(log
²
(m + n)). Based on these results, the algorithms to quickly determine the range are given, which possess the time-complexity of O(log
²
(m + n)).