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# Department of Science, Math, & Technology

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Polar Coordinates
Posted: Posted September 20th, 2019
Edited September 20th, 2019 by Xhin
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I'll hopefully have time to say something more intelligence later, but for now: very cool pictures. Nice work on the math.

Posted September 21st, 2019 by EN
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I’d like to see what you can do with setts and brecans and tartans and plaids, using polar coordinates or inversions or other transformations similar to those you’ve posted about here!

Posted September 24th, 2019 by chiarizio
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Again, cool pictures. Do you have any experience with linear algebra? You can do some cool transformations with that too. Check out the discrete cat map (https://en.wikipedia.org/wiki/Arnold%27s_cat_map#The_discrete_cat_map) for one example.

In my first programming class (Java), one of our later assignments was to build different image filters as a kind of knock-off photoshop. That was one of my favorite tasks as we got to be creative and come up with whatever ways we wanted to alter pictures. Your polar stuff reminds me of that. It's clear that you're having a lot of fun with this. Do you have any larger plans for these besides your github?

Posted September 25th, 2019 by EN
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@chiarizio: Good idea!

Using this sett as the base:

Polar Reflection

Rectangular Inversion

Polar Kaleidoscope

Cubic Transformation

Miscellaneous

This is what happens if you run the inverse of the polar kaleidoscope code -- it assumes an image is polar does a cartesian transformation. This plugin still needs some work.

One of the settings of my improved polar inversion plugin. I'm not even sure what all the settings are yet or which ones are distinct.

These are a lot more experimental and involve manipulating the angle and distance with other variables.

Posted September 25th, 2019 by Xhin
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You can do some cool transformations with that too. Check out the discrete cat map (https://en.wikipedia.org/wiki/Arnold%27s_cat_map#The_discrete_cat_map) for one example.

That's a pretty neat effect. I implemented it (once I figured out that "mod 1" meant "modulo x by the width and modulo y by the height, that is).

The original formula calls for destination[x,y] = source[2*x+y, x+y], however you can apparently change that 2 into anything else -- 3 takes a while but does return to the original cat. 4 should as well -- with a bunch of iterations I got a frame where there's *nine cats* (and some pixel variations between them), which is pretty weird.

I also tried things like source[2*x+y,x+y*2] and [3*x+y,x+y*4] -- these are giving similar order-->chaos-->order effects so they'll probably return to normal eventually, but I lack the patience to iterate them long enough to check.

Posted September 25th, 2019 by Xhin
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It is just so beautiful 😍!

What does it do to, for instance, the Royal Stuart tartan?

Posted September 25th, 2019 by chiarizio
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@chiarizio: here are some settings I quite liked for the Royal Stuart tartan

Source Image

Polar Reflection

Polar Kaleidoscope

Rectangular Inversion

Cubic Transformation

Posted September 26th, 2019 by Xhin
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What does it look like on a still image of EN's mycard..

Posted September 26th, 2019 by Moonray
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@Moonray: Extremely cool, as it turns out.

Source Image

Polar Reflection

Polar Kaleidoscope

Rectangular Inversion

Cubic Transformation

Miscellaneous

An inverted polar transformation with some tweaked settings.

• distance /= angle
• distance *= x or y (I think the top part is y and the bottom part is x)

Plus some miscellaneous stuff to make it more complex, scale it down to where it's visible and/or tweak various parameters there.

• Posted September 26th, 2019 by Xhin
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Can you do it to a MOVING EN’s card? And keep it moving?

Posted October 31st, 2019 by chiarizio
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