I have a question on parametric equation of ellipses.
I would like to rotate an ellipse around a certain point. I managed to find the half of the equation but something is missing…
$$x(t) = 3\cos(α)\cos(t) – 2\sin(α)\sin(t) + u$$
$$y(t) = 3\sin(α)\cos(t) + 2\cos(α)\sin(t) + v$$
where $C(u,v)$ is the center of the ellipse ,$P(h,k)$ is the certain point and $α$ is the angle of the rotation.
I tried many things but nothing worked…
Thanks
Blaxou
Best Answer
Do a rigid body transformation with a rotation matrix for instance. That means use a rotation matrix $R$ that does the job.
Then you simply have to do the following
$$ x' = R \cdot x $$
where $x$ is the position vector
[x,y]and $x'$ is the new position vector after rotation.