# Plotting an elliptical arc given 3 points, radius ratio and angle

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 $a/b$ 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 $e=\sqrt(1 - (b/a)^2)$

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

Thanks, tinez

-