Lineart: Difference between revisions
From wikiluntti
| Line 21: | Line 21: | ||
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. | ||
* 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> | * Convert image array to vectors, and make the linear combination: <math>Ax = b</math>. Solve <math>min_x | Ax-b |^2</math>. | ||
== References == | == References == | ||
Revision as of 15:09, 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
Video: The Mathematics of String Art
White canvas with Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle N} nails around the circumference and add straight black lines between the nails.
- Starting nail angle Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi_1} and ending nail angle Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi_2} . Maximum number of lines is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {n \choose 2} = \frac{N(N-1)}{2}}
- Convert image array to vectors, and make the linear combination: Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Ax = b} . Solve Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle min_x | Ax-b |^2} .
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
