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TSC

TSC

Name


      TSC

Purpose


      Interpolate an irregularly sampled field using a Triangular Shaped Cloud

Explanation


      This function interpolates an irregularly sampled field to a
      regular grid using Triangular Shaped Cloud (nearest grid point
      gets weight 0.75-dx^2, points before and after nearest grid
      points get weight 0.5*(1.5-dx)^2, where dx is the distance
      from the sample to the grid point in units of the cell size).

Category


      Mathematical functions, Interpolation

Calling Sequence


      Result = TSC, VALUE, POSX, NX[, POSY, NY, POSZ, NZ,
                    AVERAGE = average, WRAPAROUND = wraparound,
                    ISOLATED = isolated, NO_MESSAGE = no_message]

Inputs


      VALUE: Array of sample weights (field values). For e.g. a
              temperature field this would be the temperature and the
              keyword AVERAGE should be set. For e.g. a density field
              this could be either the particle mass (AVERAGE should
              not be set) or the density (AVERAGE should be set).
      POSX: Array of X coordinates of field samples, unit indices: [0,NX>.
      NX: Desired number of grid points in X-direction.
     

Optional Inputs


      POSY: Array of Y coordinates of field samples, unit indices: [0,NY>.
      NY: Desired number of grid points in Y-direction.
      POSZ: Array of Z coordinates of field samples, unit indices: [0,NZ>.
      NZ: Desired number of grid points in Z-direction.

Keyword Parameters


      AVERAGE: Set this keyword if the nodes contain field samples
                  (e.g. a temperature field). The value at each grid
                  point will then be the weighted average of all the
                  samples allocated to it. If this keyword is not
                  set, the value at each grid point will be the
                  weighted sum of all the nodes allocated to it
                  (e.g. for a density field from a distribution of
                  particles). (D=0).
      WRAPAROUND: Set this keyword if you want the first grid point
                  to contain samples of both sides of the volume
                  (see below).
      ISOLATED: Set this keyword if the data is isolated, i.e. not
                  periodic. In that case total `mass' is not conserved.
                  This keyword cannot be used in combination with the
                  keyword WRAPAROUND.
      NO_MESSAGE: Suppress informational messages.
  Example of default allocation of nearest grid points: n0=4, *=gridpoint.
    0 1 2 3 Index of gridpoints
    * * * * Grid points
  |---|---|---|---| Range allocated to gridpoints ([0.0,1.0> --> 0, etc.)
  0 1 2 3 4 posx
  Example of ngp allocation for WRAPAROUND: n0=4, *=gridpoint.
  0 1 2 3 Index of gridpoints
  * * * * Grid points
  |---|---|---|---|-- Range allocated to gridpoints ([0.5,1.5> --> 1, etc.)
  0 1 2 3 4=0 posx

Outputs


      Prints that a TSC interpolation is being performed of x
      samples to y grid points, unless NO_MESSAGE is set.

Restrictions


      Field data is assumed to be periodic with the sampled volume
      the basic cell, unless ISOLATED is set.
      All input arrays must have the same dimensions.
      Position coordinates should be in `index units' of the
      desired grid: POSX=[0,NX>, etc.
      Keywords ISOLATED and WRAPAROUND cannot both be set.

Procedure


      Nearest grid point is determined for each sample.
      TSC weights are computed for each sample.
      Samples are interpolated to the grid.
      Grid point values are computed (sum or average of samples).

Example


      nx=20
      ny=10
      posx=randomu(s,1000)
      posy=randomu(s,1000)
      value=posx^2+posy^2
      field=tsc(value,posx*nx,nx,posy*ny,ny,/average)
      surface,field,/lego

Notes


      Use csc.pro or ngp.pro for lower order interpolation schemes. A
      standard reference for these interpolation methods is: R.W. Hockney
      and J.W. Eastwood, Computer Simulations Using Particles (New York:
      McGraw-Hill, 1981).

Modification History


      Written by Joop Schaye, Feb 1999.
      Check for overflow for large dimensions P. Riley/W. Landsman Dec. 1999



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