A Simple Algorithm for Lattice Point Counting in Rational Polygons

We propose a simple algorithm for lattice point counting in
rational polygons. A rational polygon is one whose vertices have rational
coordinates. The algorithm decomposes a given polygon into right
trapezoids and counts the number of lattice points in the right trapezoids.
Each right trapezoid can be dissected into a rectangle and a right-angled
triangle in the obvious way. The number of lattice points in the rectangle
is easy to determine, and we find that a short recursive function computes
the number of lattice points in the right-angled triangle. We also
give an algorithm for counting lattice points on line segments.

By: Hiroki Yanagisawa

Published in: RT0622 in 2007


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