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TSC

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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