Rotate an ellipse around a certain point
1,020
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.
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Author by
Blax
Updated on December 05, 2020Comments

Blax over 1 year
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

cgiovanardi over 5 yearsThere are a lot of questions and answers here in this site. Just write "rotated ellipse" in the Q&A box. For example math.stackexchange.com/questions/1477762/…

Blax over 5 years@cgiovanardi I'm searching for rotated ellipse around a certain point ;) If you find the answer of the question on an another question, don't hesitate to let me know :D

Hypergeometricx over 5 yearsDid you mean $\alpha$ rather than $a$ in $x(t)$?

Blax over 5 yearsYep, I forgot to change it sorry ;)

cgiovanardi over 5 years@Blaxou Maybe this math.stackexchange.com/questions/426150/… ?


Blax over 5 yearsThe problem is that I can't use matrixes

Armen Avetisyan over 5 yearsYou don't have to use a matrix. Just do something like $x(t)' = x(t) \cdot cos(a)  y(t)*sin(a)$ and $y(t)' = x(t) \cdot sin(a) + y(t) \cdot cos(a)$.