ALPHA-KERNEL PROBLEM WITH FUZZY VISIBILITY

Abstract

This paper proposes a new visibility concept,fuzzy visibility reflecting that the visibility property varies according to the condition of application areas. The concept of alpha-visibility is defined on the basis of the fuzzy theory. For two points p and q, p is alpha-visible from q if the visibility degree between them is no less than alpha is an element of [0,1]. If there exists a point from which all points in a polygon are alpha-visible, then it is said that the visibility value of the polygon is alpha. The alpha-kernel problem is constructing the region such that ail points inside simple polygon can be alpha-visible from any point of the region. An optimal algorithm is given for the alpha-kernel problem with O(n) time complexity. For a given simple polygon we present O(n) algorithms for computing the maximum and minimum visibility values of the polygon.