Visibility Queries among Horizontal Segments - A Dynamic Data Structure

Consider the following interactive computer game. A set of blue horizontal segments is drawn in a window. The player must draw in the window, within a few seconds, a red segment that is not visible from the bottom edge nor the top edge of the window's boundary. If the red segment drawn by the player is visible, then the player does not get any points for this move# otherwise, the number of points is proportional to the length of the segment. After computing the score for this move, the red segment is removed, and either a new blue segment is added to the scene or an existing blue segment is deleted from the scene. The player must now draw again a red segment for the new scene, get points for this move, and so on. The main algorithmic difficulty in the implementation of this game, is to determine at each round whether or not the red segment drawn by the player is visible from one of the horizontal edges of the window's boundary. We propose a data structure that overcomes t