VISUALIZATION OF APOLLONIUM CIRCLES IN GEOMETRIC MODELING OF PARALLEL APPROACH METHOD ON PLANE
This article presents a mathematical model of the pursuit task with a simple movement on the plane, using the method of parallel approximation and the model of behavior of both the pursuing and the pursued objects of the task. For each moment of time, the Apollo circle and related characteristic lines are constructed. In the given geometrical model for the predetermined trajectory of the pursued object there is an optimal trajectory of the pursuer object. During a certain period, the object must decide in what direction and at what speed it must move, depending on the location of its target, to minimize the time to reach the stalker object. As a result of this article we have achieved formalization and algorithmizing of the method of parallel rapprochement of the pursuer and his goal. Modeling was performed in MathCAD programming and mathematical modeling environment. By results of creation of mathematical model, the animation roller where it is possible to look through moving and transformation of circle of Apolonia and the characteristic points and lines connected with it has been made. As a result of work of programs, the animated images of movement of objects, references to which are resulted in the text of article are received.