Approximating vertices of a convex polygon with grid points in the polygon
In this paper, we consider the problem of approximating a vertex of a convex polygon by an integer point in the polygon. We show that the nearest grid point in a convex polygon to a vertex can be found if it exists, or decided to be nonexistent, in time O(n+logl), where l is the diameter of the polygon and n is the number of the polygon's vertices. The underlying technique used is the continued fraction expansion.
KeywordsGrid Point Convex Polygon Grid Line Continue Fraction Expansion Integer Lattice
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