Discrete Approximation of Continuous Convex Blobs
Louis Hodes · SIAM Journal on Applied Mathematics · 1970
Given a pattern of squares on a grid for approximating arbitrary figures, one would like to have a criterion for determining whether that pattern could have been produced by a convex figure. The main result shows that an intuitively sparse criterion, the midpoint convexity property,is actually stronger than an intuitively neat global criterion, that of having a convex smallest bounding polygon. We also show that any pattern produced by a convex figure can be produced by a convex polygonal figure with its vertices at the corners of squares.