hackerpoet / conics Goto Github PK

Love the video and that you shared your source-code, really brilliant stuff and I'll definitely be digging into that for some inspiration there for my own projects.

This is not a bug report so much as an interesting observation that I was curious about if you might have some insight on.

I was playing around with the executable, hitting spacebar a few times to shuffle through the various animations, when I noticed something interesting in the example with 4 points and a line.

Specifically if I position one point so that it is inside the triangle formed by the other three, and all 4 points are on the same side of the line, then there appears to be no solution:

(Screen capture).

Similarly if two points are on each side of the line then the same thing happens, with no solution if one point is bounded in a triangle of the other three.

However if only one point is on the other side of the line, then there are solutions only when one point is inside the triangle

(Screen capture)

Intuitively I suppose these cases make sense, as I can't think of a way I'd draw a conic to satisfy these points and line either, but I was curious if there might be some deeper insight as to why this behaves the way it does.

In any case, cheers again for sharing all of this!

Black screen trying to run on parallels on mac (m1) might be a emulator problem rather than software

Also not an actual issue, but you might like the Shadertoy I've just put up for the 3 points + 2 lines problem: https://www.shadertoy.com/view/7df3Dl

I only saw your code after doing mine, but I think the algorithm is similar.

Hello! I have viewed your amazing YouTube video on conic sections and was very inspired by it. After a few days I have managed to prove your conjecture that the centers of all possible conics that are tangent to a given quadrilateral lie on a line. I also proved that the centers of all possible conics that pass through four points lie on a hyperbola. I mostly used linear algebra. Please email me at [email protected] or [email protected], I am very excited to share the proof with you!