A set of points with connectivity information is called point-set data. PS-curves(point-sequence curves), rectangular array data, and triangular net data are representative forms of point-set data. Fairing of point-set data is an essential step in processing laser-scanned data. Investigated in this thesis are various aspects of difference fairing methods for point-set data.
First, EOD (even-order-difference) fairing of PS-curve is analyzed using a DFT (discrete Fourier-transform) filter. A DFT-filter corresponding to an EOD-fairing operation is derived, and then a method for determining “optimal" damping factor for EOD-fairing is proposed based on the concept of filtering measure. Validity of the“theoretical" damping factor is demonstrated by systematic fairing experiments. Difference fairing of array data is treated as a “ tensor product" fairing of PS-curves. When an EOD fairing results in oscillations, a $2^{nd}$ difference moving-average method is applied to the faired PS-curve as an additional postprocessing'operation to remove the oscillations.
For fairing of triangular-net data, a modified forth difference fairing scheme is proposed. In this scheme, a forth difference at each vertex is computed by blending the position of the current vertex, positions and “ tangent vectors" of its neighbor vertices, and fairing is confined to the normal vector direction of the current vertex. The proposed fairing method was applied to various types of triangular net data, and it was found to be superior to existing fairing methods.
