How can I efficiently plot the inside of an ellipse?
Following @Evil's comment, I suggest two steps. For each ellipse $E$:

(1) Computing a bounding box $B$ for $E$.

(2) For each row of pixels in $B$, walk left-to-right until a pixel $p_1$
is discovered to be inside $E$.
Then walk right-to-left until $p_2$ is in $E$.
Then all the pixels from $p_1$ to $p_2$ are in $E$
(because of convexity).

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The most difficult step is computing a bounding box for the ellipse.
You likely don't need it exactly. 
Here are two sources:


"How do you calculate the axis-aligned bounding box of an ellipse?."
"How do you find a tight-fitting, axis-aligned, bounding box of a rotated ellipse in AS3?."