- #1
Unrest
- 360
- 1
Hello. This is 2D with arbitrary orientations.
I have a quadratic curve segment defined by 2 end points and another one in between. I can find lots of other points along this curve.
I want to find a close-enough elliptic spline. It is defined by 2 end points and the point of intersection between the tangents through these end points.
The 2 end points must match exactly.One thought I had was to take 6 points on the curve, then solve the equation of the ellipse (Ax2+Bxy+Cy2+Dx+Ey+F=0) with them. But since these points aren't actually on an ellipse, could it be there is no ellipse that passes through all of them?? I heard you need 5 points to uniquely define an ellipse, but don't see how this equation can be solved for just 5.
Even if I can find this parametric equation for the ellipse, how would I find the point of intersection of the two tangents in a numerically stable way? It should also work for the special case of a straight line.
I have a quadratic curve segment defined by 2 end points and another one in between. I can find lots of other points along this curve.
I want to find a close-enough elliptic spline. It is defined by 2 end points and the point of intersection between the tangents through these end points.
The 2 end points must match exactly.One thought I had was to take 6 points on the curve, then solve the equation of the ellipse (Ax2+Bxy+Cy2+Dx+Ey+F=0) with them. But since these points aren't actually on an ellipse, could it be there is no ellipse that passes through all of them?? I heard you need 5 points to uniquely define an ellipse, but don't see how this equation can be solved for just 5.
Even if I can find this parametric equation for the ellipse, how would I find the point of intersection of the two tangents in a numerically stable way? It should also work for the special case of a straight line.
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