Lineart: Difference between revisions
From wikiluntti
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<math>R(\rho, \theta) = \int \it f(x,y) \delta( \rho - x \cos\theta + y \sin\theta) dx dy</math> | <math>R(\rho, \theta) = \int \it f(x,y) \delta( \rho - x \cos\theta + y \sin\theta) dx dy</math> | ||
== | == Virtually Passed YT == | ||
White canvas <math>R</math> with <math>N</math> nails around the circumference and add straight black lines between the nails. | White canvas <math>R</math> with <math>N</math> nails around the circumference and add straight black lines between the nails. | ||
Video: The Mathematics of String Art | |||
* 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> | * 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>. | ||
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** Pseudoinverse gives not binary result. Greedy algorithm. | ** Pseudoinverse gives not binary result. Greedy algorithm. | ||
* FFT in part II gives much better results | * FFT in part II gives much better results | ||
Video: How To Make a Computer Create Something Beautiful: String Art | |||
* Radon transform | |||
== References == | == References == | ||
Revision as of 15:38, 24 October 2024
Introduction
String art
- Radon transform (inverse of)
- 2d FFT
- Optimization
Radon Transform
The sum of the intensities in each direction (a line integral).
The new image will be
Virtually Passed YT
White canvas with nails around the circumference and add straight black lines between the nails.
Video: The Mathematics of String Art
- Starting nail angle and ending nail angle . Maximum number of lines is
- Convert image array to vectors, and make the linear combination: . Solve .
- Problems:
- Line darkness; from step function to some other.
- Pseudoinverse gives not binary result. Greedy algorithm.
- FFT in part II gives much better results
Video: How To Make a Computer Create Something Beautiful: String Art
- Radon transform
References
- https://elderlawattorneyblog.com/dharruk/circle-string-art-instructions.php
- TOP 5 EASIEST STRING ART PICTURES #1 | DIY TUTORIAL | MANDALA IN CIRCLE | 3 COLOURS https://www.youtube.com/watch?v=5gbwxqFnWek
- https://geometryexpressions.com/downloads/StringArt.pdf
- https://ar5iv.labs.arxiv.org/html/2008.10693
- https://ccicada.org/wp-content/uploads/2023/09/String-Art-Creating-Constructing-and-Computing.pdf
- https://arxiv.org/pdf/2008.10693
- https://quenell.org/PSU/pubpdf/stringart.pdf
- https://www.stringartlaboratory.com/post/beginners-guide-to-string-art-understanding-its-origins-basic-tools-and-materials
- https://chessapig.github.io/files/hyperbolic_string_art.pdf
- https://polypad.amplify.com/lesson/string-art
- https://plus.maths.org/content/bridges-string-art-and-bezier-curves
- https://meangreenmath.com/2023/01/20/parabolas-from-string-art-part-7/
- https://www.peterwonka.net/Publications/pdfs/2018.EG.Birsak.StringArt.pdf
- https://yetanothermathprogrammingconsultant.blogspot.com/2024/01/string-art.html
