A weighting function approach to modeling of irregular surfaces Academic Article uri icon

abstract

  • A novel approach is presented for efficient mathematical modeling of discretely measured irregular surfaces. The technique is applicable to modeling of arbitrary surfaces; it is shown to be especially well suited for modeling of fine-structure topographic surfaces. The macroscopic features of the method are as follows. (1) Given a set of discrete coordinate measurements, an average least squares mathematical model for the surface geometry is determined. (2) The model consists of an arbitrarily large family of locally valid surface functions that join smoothly; nth-order continuity is satisfied everywhere. (3) Each locally valid surface function can typically be reduced to a low-degree polynomial of two variables; thus an efficient and consistent mathematical model for local surface calculations is provided. (4) The method sequentially operates on a moderate to small subset of the measured data; it is therefore applicable to an arbitrarily large set of observed data. These features and associated computational devices are discussed in the light of numerical results obtained by using actual geodetic data sets. These results demonstrate that the method is a versatile, accurate, and efficient means for obtaining general-purpose mathematical models of irregular surfaces.

author list (cited authors)

  • Junkins, J. L., Miller, G. W., & Jancaitis, J. R.

publication date

  • January 1, 1973 11:11 AM