New answers tagged matrices
2
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 ...
2
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 ...
1
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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