I understand that I can subdivide the curve down so that I am drawing single pixel lines, but that is again drawing lines. What I am looking for is Bezier curve code that draws a Bezier similarly to Bresenham's line drawing code. In other words, the initial pixel is calculated and the rest are incrementally derived from some function. The curve would be plotted pixel by pixel by pixel.
My interest in this is really just personal. I have no need for it, but it always bothered me that I could not find any examples. I am just really curious if this has ever been done, and if so, I would like to see the code.
Well, if your line segments are only a single pixel long they're... uh.... just pixels. They're sequentially plotted from the function that is the Bezier curve. You're probably not going to find something as simple and elegant as a Bresenham algorithm for Bezier curves because the curvature is neither constant like a circle, nor easily predictable like an ellipse. You could possibly derive it to obtain the curvature (the curvature can be described as the rate of change of the tangent to the curve with respect to the arc-length, or dT/ds) and match curvature to a pixel pattern, but that just seems needlessly complex. Some quick googling turned up http://www.gamedev.net/topic/156180-curvature-of-a-bezier-solved/ in which a poster posted about how to find the curvature of a Bezier; couldn't say how accurate or correct it is, but it might be a place to start. Seems like, if you know the curvature at pixel N, then you should be able to use it to calculate pixel N+1. But, again, it's probably just easier to evaluate the curve for very small increments of t instead.