The box that an ellipse fits is easily calculated if there are no rotation, or if the rotation is ${x*90^o}$ (where x is an integer) is easy.
For a (major radius) and b (minor radius), it is :
Xmax = a Ymax = b
or it is :
Xmax = b Ymax = a
But how to do it in a general case, when the rotation angle is not a multiple of 90 degrees?
The limits to ellipse are like on the next image:
I am given all ellipse's parameter (as described in wiki) :
- ellipses formula:
$x_{0}=a\cdot \cos (\varphi )$
$y_{0}=b\cdot \sin (\varphi )$- where: a=major radius, b=minor radius, $\varphi \in [0,\pi ]$
- rotation formula:
$x_{1}=x_{0}\cdot \cos (\Theta )-y_{0}\cdot \sin (\Theta )$
$y_{1}=x_{0}\cdot \sin (\Theta )+y_{0}\cdot \cos (\Theta )$- where $\Theta$=ellipse's rotation
All parameters (a, b and $\Theta$) are known.
If you like you can also use the canonical form for ellipse: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$