Simple algorithm for drawing filled ellipse in C/C++

Question

On SO, found the following simple algorithm for drawing filled circles:

for(int y=-radius; y<=radius; y++)
    for(int x=-radius; x<=radius; x++)
        i         


        

Answer 1

A fast Bresenham type algorithm, as proposed by this paper, works really well. Here's an OpenGL implementation that I wrote for the same.

The basic premise is that you plot the curve on one quadrant, which we can mirror on to the other three quadrants. These vertices are computed using an error function, similar to what you use in the midpoint circle algorithm for circles. The paper I have linked above has a pretty nifty proof for the equation, and the algorithm distills down to just checking if a given vertex is within an ellipse or not, just by substituting its values in the error function. The algorithm also tracks the tangent line slope of the curve we are drawing in the first quadrant, and increments x or y depending on the slope value - which contributes further to the performance of the algorithm. Here's an image that shows what's going on:

As for filling the ellipse, once we know the vertices in each quadrant (which is essentially mirror reflections across x and y axes), we get 4 vertices for every vertex that we compute - which is sufficient to draw a quad (in OpenGL anyway). Once we draw quads for all such vertices, we get a filled ellipse. The implementation I have given employs VBO for performance reasons, but you don't strictly need it.

The implementation also shows you how to achieve a filled ellipse using triangles and lines instead of drawing quads - the quads are clearly better though, as it is a primitive and we only draw one quad for 4 vertices, as opposed to one triangle per vertex in the triangle implementation.