Christmas gift, arc through 3 points

[mabad 19]

A good while back, a member of the Cafe asked for a solution to have an arc always pass through three points.

At the time I wrote a COFFEE script, which was quite hairy, but did the job (in most cases )

After the release of C4D R20 COFFEE did not work anymore and decided to give a go to that script using Python.

To get better equations on how to locate the arc, I got to this page, which had the math to get it always working.

So I coded the script, and today as a gift for the C4D community, I want to make it available for you all.

Just open the file and move the points A, B and C around. The arc will follow the points. Point B is always the middle point.

 

Have fun with it. If you find the script useful, please let me know.

ThreePointArc_R20_python.c4d

[Hrvoje 5,501]

Thanks for sharing!

[Eterea 6]

Thank you so much, Mabad!

[jed 432]

I find the concept that any 3 points always lie on a circle a bit mind-blowing.

 

Sounds like the kind of theorem someone in ancient Greece would spend their whole life trying to prove (or disprove).

[jed 432]

@mabad I used your code to make this

 

 

3points.c4d

[mabad 19]

Hey @jed, very interesting idea.

 

I suppose that making the circles in 3D, instead of 2D, and letting the 4th circle pass through the 3 points would be so crazy, that the effect you got there would not be so smooth. I like it.

The concept of an arc/circle passing through three points is similar to the one that says that through 2 points can only pass a line, but with a twist

 

@Eterea, you gave me the idea of building this one. Thanks for using it in your clip, it was probably for much less than a second, but the result was very good. I loved that video.

[jed 432]

@mabad thanks for comment. The soundtrack is Cubase - my new year's resolution is to stop using commercial music in clips.

 

 

[Eterea 6]

11 hours ago, mabad said:

@Eterea, you gave me the idea of building this one. Thanks for using it in your clip, it was probably for much less than a second, but the result was very good. I loved that video.

Yeah! Your script was fantastic to create the solar arcs for my Lux Aeterna animation.

 

Thank you so much for this, Mabad! :-)