This gallery contains curves made with the include file I wrote.

These curves are generated from the vector of curvature described as follows.

P * <0, 1 + cos( S ), 0>

This vector is always parallel to the y-axis, so these curves are on the plane paralell to the x-z plane.
The curve is closed if P is a rational number.

In the case of plane curve (i.e. the vector of curvature always points to the constant direction),
the turning angle of the curve from S0 to S1 is described as follows, where theta is the turning angle (in radians) and F(S) is (signed) carvature of the curve.

These are other types of curve made with my include file.
Some curves are generated by reducing the value of N on purpose.