Expressions for the geodesic curvature and speed of a function may be entered in the control window. The speed function is defined by f(t), and the geodesic curvature is defined by g(t).

A plot of f(t) against t is displayed in the f(t) window.

A plot of g(t) against t is displayed in the g(t) window.

The curve defined by these geodesic curvature and speed functions is displayed in the Curve: X(t) window. The curve originates at the origin in the direction of the positive x-axis, and is colored by curvature. The curve is displayed for values of t from -1 to t0. The value of t0 may be changed in the control window.
Change the value of t0 as in earlier demos.