The variation of curvature can be displayed using a color coded map.
Color coded maps provide a rough idea of the differential properties
of surfaces but are not sufficient to provide detailed machining
information nor permit automation of the machining process or of
fairing algorithms. Iso-curvature curves can also be
used to display and visualize the variation of curvature by computing
the curvature on a lattice and linearly interpolating the contour
points. The iso-curvature curves divide the surface into regions
of specific range of curvature. However discrete color coded maps of
curvature and lattice methods for curvature contouring do not
guarantee to locate all the stationary points (local extrema and
saddle points) of curvature, and hence may fail to provide the correct
topological decomposition of the surface on the basis of curvature to
the manufacturer or to a fairing process.
A robust procedure for contouring curvature of a free-form
parametric polynomial
surface can be found in [255].
The contouring levels should be determined to
faithfully represent the curvature distribution.
To do this, we need to evaluate (8.27),
(8.28) and (8.29).
Example 8.5.1.
In Example 8.2.1 we have examined the range of
Gaussian curvature of a bilinear surface. The contour lines of
Gaussian curvature can be evaluated by setting
with
a
constant satisfying
which can be rewritten as
Since there is no local maxima, minima, nor saddle points of Gaussian
curvature in the domain, the constant curvature lines are concentric
circles in the parameter space with center at (0,0) and radius
.
with 
a
constant satisfying
.