Bezier Circle

Approximate a circle with cubic Bezier curves: here’s a simple method, written in Processing. The key to approximating the circle is a constant, kappa, that will help us calculate the distance from a Bezier anchor point on the circle to its associated control point, off the circle. Kappa is the distance between the anchor point and the control point divided by the circle radius, when the circle is divided into 4 sectors of 90 degrees. See these notes by G. Adam Stanislav for the math.

Circle approximated by five Bezier curves. Click to view applet.

Notes: Kappa is scaled by the number of sectors into which the circle is divided (k = 4 * kappa / sectors). Four sectors is the minimum required to get a good approximation. With a little bit of work it should be possible to create a circle with unequal sectors, scaling kappa by the portion of the circle occupied by each sector. From there, one could make various sorts of blobs by scaling the the control points and anchor points around the center of the original circle.

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