Parabola Shenanigans
TODO: Should probably merge this with parabola-arc-line.md and make it more medial-axis centric
Intersection of line and parabola
TODO
https://math.stackexchange.com/a/1359003/4506
Tangent of a parabola at a given point
TODO
Assumes point lies on the parabola
Uses normal of line between focus and closest point on directrix from the test point.
Parabola circle intersection
I think this will only be for cases where the parabola intersects once
TODO
Arcs
We can extend this to arcs by using my point_lies_on_arc function
The medial axis of an inwards pointing arc and a line
This is an answer to this StackExchange question which I'm posting here instead as the answer I posted there was downvoted and deleted with no reason given.
- Focus is arc centre
- Directrix is line offset by arc radius
Medial axis between
| A | B | Medial shape |
|---|---|---|
| Line | Line | Line |
| Line | Point | Parabola with focus at point and directrix on line |
| Line | Convex arc | Parabola with focus at projection of arc centre on line and directrix parallel to line and tangent to arc |
| Non-concentric arc | Non-concentric arc | Hyperbola |
| Concentric-ish arc | Concentric-ish arc | Ellipse with foci on arc centres |