44972646489 http://1ucasvb.tumblr.com/post/44972646489/the-arc-length-parametrization-of-an-archimedean 19462 The arc-length parametrization of an Archimedean...

The arc-length parametrization of an Archimedean spiral visualized with colors.

I just finished some new code to generate arc-length parametrizations of arbitrary curves. To try it out, I used it on this Archimedean spiral.

Then I got curious: exactly how does the re-parametrization redistributes the points along this curve? In the original parametrization, the points are bunched up in the middle of the spiral, and more spaced on the outside. The arc-length parametrization makes them equally spaced along the whole path. So how do they compare?

First, I tried this with black points, but it was too confusing. Same thing for a few dots highlighted. So I decided to color them all based on the angle in the original parametrization. This is the result.

It is really interesting how the colors are bent around. It seems that the distribution is quite non-uniform, even though the spiral is rather uniform in growth.

I originally rendered this with four times as many frames, but due to the amount of colors and dimensions of the GIF, Tumblr wouldn’t accept it. It was too large. Below is the animation with twice as many frames.

Hint: try squinting! It blurs the colors and it looks really trippy!

1. tincalcetin reblogged this from 1ucasvb
2. a-alexandrecruz reblogged this from the-pure-x-estasy
3. dontrelyon-memories reblogged this from bigcon
4. macaronisaladan reblogged this from 1ucasvb
5. forroldo reblogged this from 1ucasvb
6. xrastacostax reblogged this from 1ucasvb
7. al3yda reblogged this from diaragap
8. jazzmatazz3 reblogged this from 1ucasvb
9. perennialwhitesnakeshuggermugger reblogged this from bluesaders-used-internets-yatai
10. ellielovesunicorns reblogged this from jennielovezjewbby
11. jericaneely reblogged this from maxosz
12. maxosz reblogged this from sighsforcenturies
13. jasonbruv reblogged this from 1ucasvb
14. minnovative reblogged this from 1ucasvb
15. agressiveexpansion reblogged this from 1ucasvb
16. tarapormacho reblogged this from empares
17. you-are-my-lifelml reblogged this from misantropia-ante-todo
18. misantropia-ante-todo reblogged this from mcbrowenshamanes
19. drewuntardislibornozu reblogged this from bizimkisilehayat
20. bizimkisilehayat reblogged this from bizimkisilehayat
21. accioconfusion reblogged this from 1ucasvb
22. monkeychunks reblogged this from 1ucasvb and added:
Groovy, I dig!
23. realidad-perfecta reblogged this from 1ucasvb
24. my-mental-disease reblogged this from keanuquotes
25. iranarchy reblogged this from 1ucasvb
26. tdsratchet reblogged this from bigcon
27. samplinggirl reblogged this from kwwwsk
28. asdfqazwsx reblogged this from kwwwsk
29. kwwwsk reblogged this from bigcon
30. bigcon reblogged this from crapepudding
31. poppybear128 reblogged this from 1ucasvb