ISAAC 1992: Algorithms and Computation pp 269-278

# Approximating vertices of a convex polygon with grid points in the polygon

• H. S. Lee
• R. C. Chang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 650)

## Abstract

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.

## Keywords

Grid Point Convex Polygon Grid Line Continue Fraction Expansion Integer Lattice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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