A linear time algorithm for minimum conic link path in a simple polygon

• The studied problem is the generalization of the well-known straight line version.
• A linear time algorithm for the problem is proposed.
• The result has inherently broadened applications than that of its degenerate case.
• Practitioners in the fields of computational geometry may find merits herein.

We consider the problem of finding, in a simple polygon, from a starting point to a destination point, a piecewise path consisting of conic sections. By considering only one type of conic section, i.e., circular, elliptic, hyperbolic, or parabolic curves, we present an O(n) time algorithm for computing the path with the minimum number of conic sections. The studied problem is the generalization of the straight line link path version. The results can be conducted in versatile applications: the hidden surface removal problem in CAD/CAM, the contour tracing, the red-blue intersection problem, the robot motion planning, and related computational geometry applications. The linear time property is most vital for those applications need to take instant reaction.