Wave Propagation in Linear Media | re-examined

A.5 Utilities for displaying points in 3D
Disp3DList displays surfaces consisting of three-dimensional points by calling the function
ListSurfacePlot3D, which is part of the standard package Graphics`Graphics3D`.
Disp3DContour generates a contour plot of the list of points. In this case, the regularity
of the list is checked for the convenience of the user. The reason is that the built-in
function ListContourPlot would simply not evaluate (without a warning) if the list
passed to it was not regular.
Movie takes the surface and returns cuts in parallel to the x-z plane by increasing the
y-coordinate. If no special value for PlotRange is given, this option is set so as to cover
the extrema, being invariant for all pictures. The user can override this default with
another range. Note that in order to allow this, the user's options must be written
before the default values in the call of the function ListPlot.
(* Copyright: Copyright 1994, CAD-Div., IGEE, Vienna Univ. of Techn. *)
(*:Version: Mathematica 2.2.1 *)
(*:Title: 3DTools *)
(*:Author: Thilo Sauter *)
(*:Keywords: *)
(*:Requirements: None. *)
(*:Warnings: The Functions defined herein require the 3D-Lists to
lie on a rectangular x/y grid *)
(*:Summary: This package contains functions useful for managing and
displaying lists of 3D points. The reordering function
OrderGrid is based on the package ListToArray by Jason F.
Harris.
*)
BeginPackage["Tools3D`","Graphics`Graphics3D`"]
OrderGrid::usage =
"Takes a list {{x1,y1,z1},{x2,y2,z2}...} and orders it to the
two-dimensional form {{{x1,y11,z11},{x1,y12,z12},..},{{x2,y21,z21},..},..}
of 3D-points."
ReSize::usage =
"ReSize[list,n] keeps only every nth row and column of a two-dimensional
list. ReSize[list,{m,n}] takes every mth row and nth column."
Link3DList::usage =
"Link3DList[Names,Output,(Path)] needs a list of filenames, a name for
the output file and an optional path where to look for the files. The files
must be a two-dimensional list of 3D-points, the output file has the same
form (generated by OrderGrid)."
Disp3DList::usage =
"Display a surface consisting of points {x,y,z} over a rectangular
x/y grid (two-dimensional list of 3D-points)"
Disp3DContour::usage =
"Disp3DContour[list,(opts)] produces a contour plot of a list of points {x,y,z}
over a rectangular and equidistant x/y grid (two-dimensional list of 3D-points)"
Movie::usage =
"Movie[list,(opts)] produces an animation of a rectangular list of points
{x,y,z} with {x,z}-Frames and incremented y-value"
Link3DList::fewlists = "At least two files needed";
Link3DList::reggrid = "Warning: Grid not regular!";
Disp3DContour::reggrid = "Grid not regular!";
Begin["`Private`"]
OrderGrid[a_List] := Module[{xvals,asort},
asort = Sort[a];
xvals = Union[Flatten[Cases[asort,{x_,y_,z_}->x]]];
Map[Cases[asort,{#,y_,z_}]&, xvals]];
TakeOther[l_List,n_] := Map[First[#]&,Partition[l,n]];
ReSize[l_List,{n_,m_}] := TakeOther[Map[TakeOther[#,m]&,l],n];
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