Invisible wrote:
> OK, so I'm currently failing to figure this out...
> 
> How do you compute the smallest possible (axis-aligned) bounding box for 
> an ellipse (which is not necessarily axis-aligned)?
> 
> Apparently such an ellipse can be represented as
> 
>   X(t) = Xc + A cos t cos K - B sin t sin K
>   Y(t) = Yc + A cos t sin K + B sin t cos K
> 
> Clearly you need to find the minimum and maximum values for X(t) and 
> Y(t). But I am apparently too stupid to do this.

When you're looking for the maximum or minimum of a function the first 
thing to look for is in general a zero in the derivative.

For example for X:

dX/dt = - A cos K sin t - B sin K cos t
so dX/dt = 0 => A cos K sin t = - B sin K cos t
or assuming A cos K  and cos t are not null (you could make special 
cases if needed)
tan t = -B/A tan K

so the bounds for X are
X0 = X( atan(-B/A tan K) )
X1 = X( pi + atan(-B/A tan K) )

Sort and do the same for Y...

-- 
Vincent

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