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I'm trying to plot an elliptical arc. I know the starting point $P_1$, ending point $P_2$ and a control point $P_3$. I'm also given the ratio of radii $\frac{a}{b}$ and the angle $\theta$ of the ellipse.

As far as I know, I could use the parametric equations to get points on an ellipse:
$x = h + a\cos(t)$
$y = k + b\sin(t)$
and then rotate those points by $\theta$.
However, I don't know how to calculate the center of the ellipse $(h, k)$ nor the radii $a$ & $b$.

My attempts to solve the problem:

  • Rotate given points by $-\theta$ to get non-rotated ellipse
  • Calculate the eccentricity $e=\sqrt{1 - \left(\frac{b}{a}\right)^2}$

Aaand I'm stuck... Can anyone help me out?

Thanks, tinez

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