4points+line question

[JohannesMP]

trafficstars

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!

[matthewarcus]

If you have points on either side of the tangent line, then the curve must be a hyperbola (since it can't cross the tangent line), so you probably need to think about where the asymptotes might go.