## Bézier Curves

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wtg62
Posts: 174
Joined: Mon Jan 27, 2014 11:30 pm
Location: Texas, United States

### Bézier Curves

Yet another experiment, https://dl.dropboxusercontent.com/u/556 ... ezier.html
Bézier Curves of any degree can be visualized! You can also visualize straight lines, but that's sort of pointless.
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testtubegames
Posts: 1078
Joined: Mon Nov 19, 2012 7:54 pm

### Re: Bézier Curves

Cool - I now understand Bezier Curves better than I ever did before.

...that is, until I did one of order 100. Got real trippy real fast
Screen Shot 2015-08-15 at 9.10.33 PM.png (339.59 KiB) Viewed 16447 times
Pretty psychedelic!

wtg62
Posts: 174
Joined: Mon Jan 27, 2014 11:30 pm
Location: Texas, United States

### Re: Bézier Curves

Hah, try doing one with each point going around the canvas in each corner, one in the upper right, upper left, bottom left, bottom right, and repeat that for a lot of points. The visualization looks really cool.
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A Random Player
Posts: 523
Joined: Mon Jun 03, 2013 4:54 pm

### Re: Bézier Curves

wtg62 wrote:Hah, try doing one with each point going around the canvas in each corner, one in the upper right, upper left, bottom left, bottom right, and repeat that for a lot of points. The visualization looks really cool.
Try a square or pentagon, too! Whoaaa, spinning squares. Relates to geometric sequences in some way. (Haha, because it's very geometric?)
Also try a back-and-forth pattern. (Ex. (-100, -50), (100, -40), (-100, -30), (100, -20), etc. in Cartesian coordinates - very rough, and horizontal/vertical scale won't matter a lot). It's a straight line, except when it's not.
Similarly, try something like (-100, -50), (100, -50), (100, -40), (-100, -40), (-100, -30), (100, -30), etc.

If you think about it, Bézier Curves are just a 2D glorified binomial theorem
\$1 = 100¢ = (10¢)^2 = (\$0.10)^2 = \$0.01 = 1¢ [1]
Always check your units or you will have no money!

wtg62
Posts: 174
Joined: Mon Jan 27, 2014 11:30 pm
Location: Texas, United States

### Re: Bézier Curves

The canvas is 1024x512, so the corners are at (0,0), (1024,0), (0,512), and (1024,512).
If you want to consider the center of the canvas as (0,0), then the corners are (-512,-256), (512,-256), (-512,256), & (512,256).
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