Convexity in (Zn,L∞): results

I have written an implementation of the wavefront algorithm for (Z²,L_∞). You will need Boost to compile it. The mode of usage is the same as the algorithm for (Z²,L₁). The figure shows the L_∞ wavefront hulls for several sets, confront them with the corresponding L₁ hulls.

Note that there is no particular inclusion relationship between L₁ and L_∞ wavefronts hulls: some times H_wave,L1(X) is included in H_wave,L∞(X), some other times it is the other way around, and in a third class of situations neither hull is included in the other. The union of both hulls seems to yield results closer to our geometric, "round" intuition of what convexity must look like; the question remains whether this operation defines a valid convexity operator.