Bézier circle approximation
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Bézier curves can approximate a circle, but not fit
perfectly. A common approximation is to use four Bézier
curves, one per quadrant, each with inner control points a distance from the end points (where
is the circle radius), and
in a direction tangent to the circle at the end points. This will ensure the
midpoints of the Bézier curves are on the circle, and that the first
derivative is continuous. The radial error in this approximation will be
about 0.0273 percent of the circle’s radius.
[edit]
References
- Approximation of circular arcs by cubic polynomials, [Goldapp:1991]
- Good approximations of circles by curvature-continuous Bézier curves, [Dokken:1990]
