Curves and Surfaces > Curves > Special Curves > Analysis
Interesting curves from an analysis standpoint.
Ck Continuous Curves with continuous derivatives.
Regular Curves Regular curves have nonzero acceleration everywhere.

Ck Continuous

A curve with continuous derivatives up to order k is said to be Ck continuous. An example is the parabola, which is infinitely differentiable.

Regular Curves

Regular curves have nonzero acceleration at all points (i.e., the second derivative of the curve never vanishes.) An example of a regular curve is the circle. The cycloid, however, is non-regular at its cusps.