January 13th, 2017, 03:14 AM  #1 
Newbie Joined: Jan 2017 From: Somewhere Posts: 6 Thanks: 1  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! Last edited by Momonomotomo; January 13th, 2017 at 03:31 AM. Reason: Hi guys! 
January 13th, 2017, 11:12 AM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,488 Thanks: 749 
to rotate your spiral $\theta$ degrees clockwise use $x(t) = a t \sin(t\theta)$ $y(t) = a t \cos(t\theta)$ 
January 14th, 2017, 09:34 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,042 Thanks: 1395 
That would rotate it anticlockwise by $\theta$ degrees. One needs to know whether t is in degrees.

January 14th, 2017, 11:14 AM  #4 
Newbie Joined: Jan 2017 From: Somewhere Posts: 6 Thanks: 1 
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. 
January 14th, 2017, 11:41 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,042 Thanks: 1395 
Did you try rotating it through 180°?

January 14th, 2017, 01:54 PM  #6 
Newbie Joined: Jan 2017 From: Somewhere Posts: 6 Thanks: 1 
Yeah, the curves align perfectly (no matter the angle)! Not what I expected...
Last edited by skipjack; January 14th, 2017 at 08:18 PM. 
January 14th, 2017, 02:14 PM  #7 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,488 Thanks: 749  Can you post a picture of what you're after?
Last edited by skipjack; January 14th, 2017 at 08:18 PM. 
January 18th, 2017, 01:33 AM  #8 
Newbie Joined: Jan 2017 From: Somewhere Posts: 6 Thanks: 1 
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. 
January 19th, 2017, 12:39 AM  #9 
Global Moderator Joined: Dec 2006 Posts: 18,042 Thanks: 1395 
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.

January 19th, 2017, 07:39 AM  #10 
Newbie Joined: Jan 2017 From: Somewhere Posts: 6 Thanks: 1 
Thanks, Skip!


Tags 
geometry, maths, parametric, programming 
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