The circle-brush algorithm

Brushing commonly refers to the drawing of curves with various line widths in hit-mapped graphics systems. It is best done with circles of suitable diameter so that a constant line width, independent of the curve's slope, is obtained. Allowing all possible integer diameters corresponding to all possible integer line widths results in every second width having an odd value. Thus, the underlying circle algorithm must be able to handle both integer and half-integer radii. Our circle-brush algorithm handles both situations and produces a “best approximation”: All grid points produced simultaneously minimize (1) the residual, (2) the Euclidean distance to the circle, and (3) the displacement along the grid line from the intersection with the circle. Our circle-brush algorithm was developed in careful consideration of its implementation in VLSI.