Geometry Expressions

First create a parametric curve with X=f(T), Y=g(T).

Now create a tangent to the curve at parametric location t.

Create the normal.

Construct the envelope of the normal as t varies. This is the evolute curve, the locus of the centers of curvature.

Put a point on the evolute at parametric location t.

Create the circle of curvature.

View the coordinates of the center of curvature.

Copy as Java

And paste into a code editor.

Note we have placeholder generic functions f() and g() and numerical approximations to their first and second deivatives, which appear in the formula for the center of curvature.