The trimming of FASS fractal curve in arbitrary boundary layer

Aiming at a limitation that the FASS (space-filling, self-avoiding, simple and self-similar) curve, fractal laser scanning-path can only fill in a square region, which is a method presented to realize the trimming of FASS fractal curve in arbitrary boundary layer by means of judging the intersection points between parameterized arbitrary boundary and a FASS fractal curve. The related algorithm concerned with determining intersection points is investigated according to the recursion feature of the fractal curve and in the process of traversing fractal curve, the rule of judging intersection points is ascertained to make the laser-scanning beam walk along the fractal curve inside the desired boundary. This provides the basis for getting the arbitrary boundary layers in CNC system by fractal scanning-path.