       Plotting surface from array of points

• To: MathGroup at yoda.physics.unc.edu
• Subject: Plotting surface from array of points
• From: Robert Villegas <VILLEGAS at knox.bitnet>
• Date: Tue, 19 May 1992 08:19 CDT

```     Bappaditya Banerjee asked about generating a surface from a list of
ordered triples {x, y, z}.

In the case you gave, {{1,4,7},{2,5,8},{3,6,9}}, the three points are
collinear, so there isn't enough to determine a surface from those alone.  If
you had three non-collinear points, you could draw the triangle having
them as vertices with Polygon:

Show[Graphics3D[ Polygon[{p1, p2, p3}] ]]

where p1, p2, and p3 are three-element lists of numbers (ordered triples).  To
situate the object in the usual x, y, and z axes, include the option Axes ->
Automatic above.

In general, if you have a two-dimensional array of points in xyz-space,
you need something different from ListPlot3D.  Unlike ListPlot, ListPlot3D
does not accept _points_ in space; it takes an array of real numbers
indicating the _values_ of a function z = f(x, y) at the lattice points of a
rectangle in the xy-plane.  That is,

ListPlot3D[{ {z11, z12, ..., z1m}, . . . , {zn1, zn2, ..., znm} }]

will plot a surface described by the function f whose values are

f(1, 1) = z11; f(1, 2) = z12; . . . ; f(1, m) = z1m
.              .                      .
.              .                      .
.              .                      .
f(n, 1) = zn1; f(n, 2) = zn2; . . . ; f(n, m) = znm

When what you have is an array of points, not values, there is a function
called MakePolygons in the package ParametricPlot3D.m from version 1 of
Mathematica, and it is also in the first edition of _Programming in
Mathematica_ by Roman Maeder.  If you don't have the first version of either
the program or the book, I could send you a copy of the code in a text file.
Or, perhaps it is in the Yoda archive so you could FTP it; I haven't checked.
Whichever, I can easily look it up and send it if you need it.

Robby Villegas
Knox College
(Villegas at Knox.Bitnet)

```

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