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Re: GEOSTATS: Coordinate conversions (off-topic)

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  • Noemi Barabas
    Hi Simon, This may not be the best solution but a possible alternative: I have just recently started working on a problem with similar issues of coordinate
    Message 1 of 2 , Jul 18, 2000
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      Hi Simon,

      This may not be the best solution but a possible alternative:
      I have just recently started working on a problem with similar issues of
      coordinate conversion and distortion, although the spatial nature of my
      problem is somewhat different from yours. I am unbending a river so that
      kriging is done in a domain that follows the course of the river instead
      of going over land. I have converted the coordinates (which were already
      in meters and on a small scale geographically) by applying a grid
      generation scheme. (Gridgen is one software that can be used).

      Grid generation is widely used in the field of flow simulation in channels
      or around bodies where boundary conditions apply along irregular surfaces
      (hydrodynamics, aeronautics etc).

      The physical boundary is defined into four segments that correspond to the
      four sides of a rectangle. An equal number of grid points are laid out
      along each of the pairs of facing boundaries. Various algorithms (Laplace
      transforms to linear interpolation, depending on the problem) calculate
      grid lines between the extreme grid point pairs. The grid is generated in
      the original coordinate system, so each sample has to be assigned to the
      nearest grid point within limits of resolution and coordinate precision.

      In flow field simulations, the differential equations and boundary
      conditions are transformed based on the mathematical relationship between
      the two coordinate systems. This is not necessary in this application, as
      all grid points to be estimated are calculated before kriging.
      Semivarogram calculation, modeling and kriging takes place in the
      transformed space and the results need merely be mapped to the original
      coordinate points corresponding to the initial grid generation output.

      An excellent book on the theory is:
      Numerical grid generation : foundations and applications
      by Thompson, Joe F. (1985)
      Published New York : North-Holland : Elsevier Science Pub. Co.

      Gridgen is available from Pointwise for a free 90 day trial period:
      www.pointwise.com


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