  We use spherical cap harmonic (SCH) basis functions to analyse and
reconstruct the morphology of scanned genus-0 rough surface patches with open
edges. We first develop a novel one-to-one conformal mapping algorithm with
minimal area distortion for parameterising a surface onto a polar spherical cap
with a prescribed half angle. We then show that as a generalisation of the
hemispherical harmonic analysis, the SCH analysis provides the most added value
for small half angles, i.e., for nominally flat surfaces where the distortion
introduced by the parameterisation algorithm is smaller when the surface is
projected onto a spherical cap with a small half angle than onto a hemisphere.
From the power spectral analysis of the expanded SCH coefficients, we estimate
a direction-independent Hurst exponent. We also estimate the wavelengths
associated with the orders of the SCH basis functions from the dimensions of
the first degree ellipsoidal cap. By windowing the spectral domain, we limit
the bandwidth of wavelengths included in a reconstructed surface geometry. This
bandlimiting can be used for modifying surfaces, such as for generating finite
or discrete element meshes for contact problems. The codes and data developed
in this paper are made available under the GNU LGPLv2.1 license.
