For a line, the radius at any point along the line is infinite, so the curvature at all points along the line is zero.
For a circle or arc, the radius is constant at all points
along the curve, therefore the curvature is also constant and nonzero.
For a spline, the radius, and thus
curvature, are constantly changing along the length of the curve. The curvature at any point on a
surface is a more complex calculation but describes the same information as the curvature of a curve.