You are currently reviewing an older revision of this page.
IntroductionThis article describes how to approximate superellipses (Lamé curves) in CorelDRAW. The approximations presented are not mathematically rigorous (there are other options if you need that). Rather, they demonstrate simple techniques that can be used to create curves that share the aesthetic of superellipses.Approximating SuperellipsesSuperellipses can be approximated in CorelDRAW using the b-spline tool (introduced in CorelDRAW X5). The basic idea is that if the b-spline's control polyline (the line connecting the b-spline's control points, in order) is an octagon with alternating side lengths, the resulting b-spline will approximate a superellipse.The easiest way to accomplish this is to snap the control points to a grid:The picture above shows a 6x6 grid (I used a graph paper object as a temporary guide, although the normal grid would work). The control points (blue dots) are placed on the verticies of an octagon (shown in blue). The resulting b-spline, shaded in green, approximates a superellipse.The roundness of the superellipse can be changed by adjusting the spacing between the control points:Here is an alternate pattern of control points that approximates a superellipse. It is convenient because it can be created on a simple rectangle. Just snap the control points to the verticies (nodes) and midpoints of the rectangle's edges.Superellipses with n < 2The above approach works well for superellipses with n > 2. To approximate superellipses with 0 < n < 1, you can create a 4-point star with the star tool, and place the control points on its verticies. Once again, the shape ("sharpness") of the star dictates the shape of the resultant b-spline:In this case, the outer verticies must be clamped (hold 'v' while creating, or select them with the Shape Tool and clamp them in the property bar).The case where 1 < n < 2 is harder to approximate simply. You must add an extra control point to slightly "puff out" the sides. Here is an example created on a 17x17 grid: