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The curvature of a planar curve at a point 
is defined as the reciprocal
of the radius, 
, of the ``best fit'' circle that touches the curve at
and whose center intersects the line that is normal to the tangent of
the curve at (see Figure 32). Note that the curvature
of a straight line is 
everywhere since the ``best fit'' circle at any
point has infinite radius.
Consider a surface with a surface normal at point . The intersection of
a plane containing the surface normal and the surface defines a curve with
a certain curvature at . Imagine the plane being rotated about the
surface normal. At some angle 
to an axis that intersects and
is perpendicular to the surface normal, the curve defined by the plane and
the surface will have a maximum curvature 
at , (see
Figure 33). At 
the curve will have a
minimum curvature 
at . The surface curvature is represented
by 
. Thus, surface curvature has three degrees
of freedom.
