Question

This is a common interview question (according to some interview sites) but I can find no normal answers on the Internet – some are wrong and some point to complex theory I expect not to be required in an interview (like the Bresenham algorithm).

The question is simple:

The circle equation is: x² + y² = R².
Given R, draw 0,0-centered circle as best as possible without using any
floating point (no trig, square roots, and so on, only integers)

Answer 1

From the second method on this page:

for each pixel, evaluate
x²+y² and see if
it is in the range from
R²-R+1 to R²+R
inclusive. If so, color the pixel on
the screen, and if not, don’t.

Further details and explanation given on the aforementioned page, but the crux is that you are looking for pixels that are a distance between R-0.5 and R+0.5 from the origin, so the distance squared is x²+y² and the threshold distances squared are R²-R+0.25 and R²+R+0.25.

For other methods, Google “draw a circle using integer arithmetic only”.