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January 13th, 2017, 03:14 AM   #1
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Exclamation Parametric?

Hi guys!
Any good place to find lots of parametric geometry equations? (x=Whatever*t , y=Whatever*t) for example, spirals, polygons, weirder stuff...

Also, how can I modify this parametric equation of a spiral so I can draw it rotated by θ degrees?

x=at sin(t)
y=at cos(t)

Any pointers to pages with info about transformations in a 2d plane would be delightful!

I've been trying to find all of this but wasn't successful, any help is appreciated!
Thanks from geometry

Last edited by Momonomotomo; January 13th, 2017 at 03:31 AM. Reason: Hi guys!
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January 13th, 2017, 11:12 AM   #2
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to rotate your spiral $\theta$ degrees clockwise use

$x(t) = a t \sin(t-\theta)$

$y(t) = a t \cos(t-\theta)$
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January 14th, 2017, 09:34 AM   #3
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That would rotate it anticlockwise by $\theta$ degrees. One needs to know whether t is in degrees.
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January 14th, 2017, 11:14 AM   #4
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Thanks for the answers! However, rotating the spiral didn't give me the intended result.
You see, I want to get the path that exists between each layer of the spiral (imagine a ball going from inside out of the spiral avoiding the curves of it).

I had previously plotted the spiral in an online graphic calculator. It used a polar equation, so maybe the value that gave the effect I wanted wasn't rotation, while it looked like it. That's why I was asking for info about 2d transformations, parametric equations...

I've done some research and I basically need to shift the phase of the spiral.

Any help?

TD;DR: I need to shift the phase of the spiral to get the intersecting path of the layers

Last edited by skipjack; January 14th, 2017 at 11:41 AM.
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January 14th, 2017, 11:41 AM   #5
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Did you try rotating it through 180°?
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January 14th, 2017, 01:54 PM   #6
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Yeah, the curves align perfectly (no matter the angle)! Not what I expected...

Last edited by skipjack; January 14th, 2017 at 08:18 PM.
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January 14th, 2017, 02:14 PM   #7
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Quote:
Originally Posted by Momonomotomo View Post
Yeah, the curves align perfectly (no matter the angle)! Not what I expected...
Can you post a picture of what you're after?

Last edited by skipjack; January 14th, 2017 at 08:18 PM.
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January 18th, 2017, 01:33 AM   #8
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Sorry for the delay, here's what I'm after:


Apparently I'm not allowed to reply in my own topic? Maybe it's the link...
Sorry for the delay, I've been trying to post this a few times this week.

Last edited by skipjack; January 19th, 2017 at 12:37 AM.
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January 19th, 2017, 12:39 AM   #9
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I've combined your posts and changed the link to be a direct link to the image. The posts you made yesterday were awaiting approval due to the link, but I wasn't on this site at the time.
Thanks from topsquark
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January 19th, 2017, 07:39 AM   #10
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Thanks, Skip!
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