Wave Propagation in Linear Media | re-examined

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A.5 Utilities for displaying points in 3D
A Mathematica packages
The Mathematica package Tools3D contains a number of functions that are needed for the
graphical representation of lists of points in R 3 . Such lists are typically the outcome of surface
computations over a rectangular grid being obtained with commands like Table[fx,y,f(x,y)g,
fx,xmin,xmax,dxg, fy,ymin,ymax,dyg]. Therefore all functions in this package assume
that the data is given as two-dimensional lists of points, like
fffx11,y11,z11g,fx12,y12,z12g, ::: ,fx1n,y1n,z1ngg,
ffx21,y21,z21g,fx22,y22,z22g, ::: ,fx2n,y2n,z2ngg,
.
.
.
.
.
.
.
ffxm1,ym1,zm1g,fxm2,ym2,zm2g, ::: ,fxmn,ymn,zmnggg.
This matrix must be rectangular, so each sublist must have an equal number of members.
Some functions check this property with the statement
Apply[SameQ,Map[Length,t]],
which rst counts the number of elements in each row of the list t (by mapping the operation
Length onto each member of the list; note that these members are again lists) and then
evaluates if all entries in the resulting list are identical. The outcome of this statement is
boolean | if it is False, error messages are generated.
The functions of the package have the following goals:
OrderGrid takes an unsorted, at list of three-dimensional points fxi,yi,zig as input
and arranges them in the required two-dimensional array of points. To this end, the
x-values of all points lying on one grid line must be undisturbed such that they can be
grouped together.
Link3DList is useful whenever a surface is computed in more than one chunk and the
results are stored in di erent les. The function requires a list with the lenames, the
name for the output le, and optionally a path specifying where the les are located.
The function then checks whether the output le already exists | and if so issues a
warning | before merging and sorting the les. The function call is Link3DList[fFFileA",FileB",
::: g,OutFile"].
ReSize rearranges a two-dimensional list by taking only every nth element. Depending
on whether the reduction should be uniform or not, the function can be called with
ReSize[list,n] or ReSize[list,m,n] for leaving every mth row and nth column.
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