Spherical cap harmonic analysis (SCHA) for characterising the morphology of rough surface patches

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