An Optimal Algorithm for Finding the Kernel of a polygon

摘要

The kernel K(P) of a simple polygon P wah n verUces is the locus of the points internal to P from which all verUces of P are wslble Equwalently, K(P) is the mtersectmn of appropriate half-planes determined by the polygon's edges Although it is known that to find the intersection of n generic half-planes requires time O(n log n), we show that one can exploit the ordering of the half-planes corresponding to the sequence of the polygon's edges to obtain a kernel finding algorithm which runs m time O(n) and is therefore optimal