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Curve Families

Curve families

The range is further constrained by the curve having no inflection points (though curvature is allowed to reach zero at the endpoints) and being symmetrical, as these are visually important features of a real superellipse. It is an especially good choice for making a G2 continuous interpolating spline (for reasons discussed in the thesis), but a weakness is representing curves with significant curvature variation. In general, it requires solution of a quartic equation, and the process is discontinuous; there exist input curves extremely close to each other with very different best fits.

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