Abstract

The problem of smooth-surface approximation from discrete data values is discussed. For the particular interpolation requirements of the cable net generation problem, a method of polar-coordinate smoothing spline functions is developed. Next a Newton-iterative method of automatic equal mesh generation is developed which uses the polar spline representation of the cable net surface. This method produces complete specification of the cable grid node locations and cable segments, including the irregular-length grid elements intersecting the net edge cables. Examples are presented to illustrate how the interpolation procedure functions and how the mesh generation procedure couples with the surface interpolation procedure to produce a satisfactory complete initial geometry specification.

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