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RE: [ai-geostats] TIN, monitoring netwoks and density

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  • Andrew Hunter
    Hi Gregoire, A TIN offers a number of advantages over grid data; first a TIN minimizes data storage requirements by allowing the density of triangles to vary
    Message 1 of 4 , Jan 19, 2005
      Hi Gregoire,

      A TIN offers a number of advantages over grid data; first a TIN minimizes
      data storage requirements by allowing the density of triangles to vary over
      the surface to reflect its variability. The data structure also allows
      surface derivatives such as slope and aspect, or surface normal information
      to be calculated and stored for each triangle, edge or node, thereby
      improving performance of subsequent surface analysis. However, it requires
      that your samples are located appropriately — peaks and troughs are sampled
      at an appropriate interval, and triangle edges are forced to follow
      breaklines within the surface.

      With respect to interpolation of the surface, it largely depends on what
      sort of surface you are willing to accept. Both grids and TINs can easily
      provide continuous surfaces, but the algorithm used to estimate a surface
      value away from a sampled point will determine if the surface is smooth or
      not. Most linear interpolation techniques, that I am aware of, result in
      discontinuities across triangle or grid edges. To maintain a smooth surface
      more complex algorithms such as the Qunitic patch, or the Clough-Tocher
      triangle patch, are required for TINS. For a grid surface the bi-cubic
      Bézier will produce a smooth surface.

      The point I’m trying to get at is that a TIN, or a Grid, is really a data
      storage mechanism for a surface within a computer — each have their
      advantages. It is the model that you overlay on top of the data that will
      allow you to estimate your surface in a manner that is appropriate to your
      application, and it is the model that will determine if it is possible to
      estimate uncertainty, or what ever else you require. Most exact
      interpolators have zero degrees of freedom (dof); hence, estimates of
      uncertainty are not possible. If uncertainty of estimation is what you are
      interested in, then Kriging will provide you with a solution. If you are not
      really concerned with smoothness, a simple linear interpolator will likely
      sufice, but to determine uncertainty of your estimates you will need to
      increase your dof, which will likely result in the interpolator nolonger
      being exact.


      Andrew Hunter

      Andrew Hunter
      PhD Candidate
      Mobile Multi-Sensor Research Group
      Department of Geomatics Engineering, The University of Calgary
      2500 University Dr. N.W. Calgary, Alberta, Canada T2N 1N4
      Tel: (403) 220 8785, Fax: (403) 284 1980
      E-mail: ahunter@...

      -----Original Message-----
      From: sebastiano.trevisani@... [mailto:sebastiano.trevisani@...]
      Sent: Wednesday, January 19, 2005 1:55 AM
      To: Gregoire Dubois
      Cc: ai-geostats@...
      Subject: Re: [ai-geostats] TIN, monitoring netwoks and density

      Maybe, in order to have a quick and "safe" interpolation, the natural
      neighbor method of Dave Watson could perfom better than TIN.
      Sebastiano Trevisani

      Quoting Gregoire Dubois <gregoire.dubois@...>:

      > Dear list,
      > I would appreciate feedback on an issue that is closely related to
      > SIC2004
      > Let us consider a variable (air pollutants, radioactivity) that is
      > measured at regular time intervals by an automatic monitoring network
      > that is structured like a regular grid. In the case one needs maps to
      > be generated on a regular basis, I was wondering what arguments would
      > be against the use of Triangulated Irregular Networks (or any simple
      > linear interpolation algorithm)? As a matter of fact, if TIN cannot
      > be used to assess uncertainties, it can be easily automated and it is
      > an exact interpolator (no risk to smooth out critical values). I thus
      > understand TIN is the most reasonable approach in the case one has a
      > network that is dense enough. Obviously, the "dense enough" obviously
      > needs to be defined properly as I expect it to be the main parameter
      > that will define the need for more advanced interpolation techniques.
      > But with the exception of density, are there any non obvious issues I
      > am missing here?
      > Thank you in advance for any feedback.
      > Best regards,
      > Gregoire

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