Lineart: Difference between revisions

Revision as of 15:08, 24 October 2024

String art

The sum of the intensities in each direction (a line integral).

$\rho =x\cos \theta +y\sin \theta$

The new image will be

$R(\rho ,\theta )=\int {\it {f(x,y)\delta (\rho -x\cos \theta +y\sin \theta )dxdy}}$

White canvas $R$ with $N$ nails around the circumference and add straight black lines between the nails.

Starting nail angle $\psi _{1}$ and ending nail angle $\psi _{2}$ . Maximum number of lines is ${n \choose 2}={\frac {N(N-1)}{2}}$
Convert image array to vectors, and make the linear combination: $Ax=b$ . Solve $\min _{x}|Ax-b|^{2}$ .

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 White canvas <math>R</math> with <math>N</math> nails around the circumference and add straight black lines between the nails.
 * Starting nail angle <math>\psi_1</math> and ending nail angle <math>\psi_2</math>. Maximum number of lines is <math>{n \choose 2} = \frac{N(N-1)}{2}</math>
-* Convert image array to vectors, and make the linear combination: <math>Ax = b</math>. Solve <math> \min_x \| Ax-b\|^2</math>.
+* Convert image array to vectors, and make the linear combination: <math>Ax = b</math>. Solve <math> \min_x | Ax-b |^2</math>.
 == References ==