Heuristic Algorithm for The Toolpath Planning Amongasequencedofellipses in 2D

Robot toolpath planning in insdustry 4.0 nowadays becomes a popular topic in the forums. This paper fisrt depicts the difficulty about computing the distance from a point to an ellipse in 2D. Then the author proposed a closed-form general solution for the distance of one point and one ellipse in 2D with time consumed O(1). Based on the heuristic method computing the shortest path among point-ellipse-point, the author advelops an efficient algorithm computing the near-shortest path touring n sequenced ellipses. Since the result of this paper is sufficiently general, it can be conducted in a variety of applications: in the fields of Computer-Aided Design and Manufacturing, Computer Graphics, Layered Manufacturing, 3D Printing, Prototyping, Robot Motion (Path) Planning, Wireless Sensor Networking, Multimedia Animation, Geodesy, Astronomy, Physics, Electromagnetics, and Fluid mechanics.Finally, this paper callsfor a solution, a need for the optimization: a closed-form general solution for point-ellipse-point problem. Once the general solution can be obtained in the future, the heuristic algorithm can be modified to an exact optimal algorithm soon. Keywords - Shortest Distance, Distance From a Point to a Parabola, Computational Geometry.