Given four points in $\mathbb{R}^2$, is there an efficient method to determine if the convex hull contains an integral point $(m,n)\in\mathbb{Z}^2$? If it helps, I can assume the convex hull is a quadrilateral.
Integral point inside a quadrilateral
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geometry
integer-lattices
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0Not sure if this is much help, but it could be possible to split the quadrilateral into two triangles and use Pick's theorem. http://en.wikipedia.org/wiki/Pick's_theorem (but this only works if the vertices of the quadrilateral are integer points.) – 2012-07-11
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0@OldJohn Yes thanks, but in my application the vertices will be general rational points. Raymond's reference below to Yanagisawa's paper might be helpful. – 2012-07-12