How do i implement a circle filling algorithm in opengl?

Question

It should be of the form circle(float xcenter, float ycenter, float radius).

Answer 1

There's a gluDisk, but it has a somewhat different signature than you've given. It always centers the disk on the origin, and expects you to use glTranslate if that's not where you want your disk. It's also a bit more versatile in other ways -- the disk it draws can have a hole in the center, which you (apparently) don't care about, as well as a "loops" parameter to draw more than one disk at a time. That makes adapting it to what you've asked for just a bit more work than you'd like:

void circle(float xcenter, float ycenter, float radius) {
    GLUquadric* quad = gluNewQuadric();

    glMatrixMode(GL_MODELVIEW);
    glPushMatrix();
    glLoadIdentity();
    glTranslatef(xcenter, ycenter);

    gluDisk(quad, 0, radius, 256, 1);
    glPopMatrix();
    gluDeleteQuadric(quad);
}

I'd say this is right at the point that it's open to question whether it's easier to just do like @genpfault said, and draw a circular triangle-fan yourself.