Curvature

Definition of the surface curvature at a point:

For two-dimensional surfaces embedded in R3, consider the intersection of the surface with a plane containing the normal vector at a point and another arbitrary vector tangent to the surface. This intersection is a plane curve and has a curvature. This is the Normal curvature. The maximum and minimum values of the normal curvature at a point are called the principal curvatures, k1 and k2, and the extremal directions are called principal directions.

It is possible to draw some typical surface curvatures:

Also the first principal curvature directions can be shown as unitary vectors.