When a surface is parametrized in orthogal coordinates, Euler's formula relates the normal curvature of a curve at a point to the angle the the unit tangent vector makes with the first coordinate unit vector and the principal curvatures κ1 and κ2 at the point, specifically kn(t0) = cos(theta(t0))^{2}*κ1 + sin(theta(t0))^{2}*κ2. The demo illustrates this for a curve on a torus of revolution.