METHOD FOR RENDERING ALGEBRAICALLY DEFINED TWO-DIMENSIONAL SHAPES BY COMPUTING PIXEL INTENSITY USING AN EDGE MODEL AND SIGNED DISTANCE TO THE NEAREST BOUNDARY

A method of accurately rendering algebraically defined shapes that can be used to render alignment targets, or for other purposes, is disclosed. The method can render shapes as a bitmap image for machine vision alignment training, for computer display for human observation, and for computer printout for documentation. The method can aid in rendering targets on the objects to be located by providing input to a computer-aided design (CAD) system, or by directly controlling devices such as laser engravers. The rendering method is fast, extremely accurate, and can handle substantially arbitrary shapes. Targets are defined by a real-valued function of position in the real plane that gives the distance from that position to the nearest point on a target boundary. The function gives distance as a positive value for points inside the figure, and as a negative value for points outside the figure. An edge model is used to map distance to real-valued image intensity. By choosing appropriate edge model parameters, edge sharpness, focus, video gain, and noise can be modeled.