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This was proved NP-complete in "Optimal Packing and Covering in the Plane are NP-complete" (Fowler, Paterson and Tanimoto, Information Processing Letters 1981). I found a freely available version of the paper here. They give a neat reduction from 3SAT -- I'll summarise this below, but the paper is short and easy-to-read with several diagrams, and I ...


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I tried it on square grayscale images myself (just hoping they would be invertible, which was always the case (not much luck involved here, since invertible matrices lie dense)). I added a few examples so you can judge the inverses yourself. Their precise look of course depends on the particular normalization (I used cv2.normalize and also normalized ...


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We are looking for a curve $$ P(u) = a_3 u^3 + a_2 u^2 + a_1 u + a_0 $$ which satisfies the following properties: $P(0) = P_i$. $P(1) = P_{i+1}$. $P'(0) = P'_i$. $P'(1) = P'_{i+1}$. In terms of the coefficients $a_0,a_1,a_2,a_3$, these are: $a_0 = P_i$. $a_3 + a_2 + a_1 + a_0 = P_{i+1}$. $a_1 = P'_i$. $3a_3 + 2a_2 + a_1 = P'_{i+1}$. In matrix form, this ...


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