A Simple Algorithm for Lattice Point Counting in Rational Polygons
نویسنده
چکیده
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.
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