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MathGroup Archive 1995

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Re: 3D-Surface-Plot:Help!

  • To: mathgroup at christensen.cybernetics.net
  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1680] Re: [mg1655] 3D-Surface-Plot:Help!
  • From: twj (Tom Wickham-Jones)
  • Date: Mon, 17 Jul 1995 00:14:15 -0400

Hannes Hochmeister writes

>We have to plot the surface of a landfill or a certain landscape in a
>3D-Surface-Plot.
>Also we need a ContourPlot in 3D of this surface.
>In Mathematica Journal, Vol. 4 Issue 2 and 4 are two articles which give a
>solution for the problem, but only when the data are values of a function or
>of a regularely matrix.
>But we have only unregular data (coordinates in x, y, z). In this case
>Mathematica can not find and plot the z-ordinate to the values of x and y.
>
>If you have a solution for this problem, please send an e-mail to:

There is a collection of packages on MathSource that will plot surfaces
and contours over irregular data of the form { p1, p2, ...} where
each pi is a triple {x,y,z} of numbers.   The MathSource number is
0205-041, the title is ExtendGraphics Packages by Tom Wickham-Jones.

It uses a computational geometry approach to triangulate the data
and then forms the appropriate elements for a surface or contours
from this triangulation.   The Interpolate function will not work
since it only works for regular data,  if you knew the functional
form of the data you could use a fitting technique as an alternative.


When you say you want a ContourPlot in 3D if you mean you want
to draw the contour lines, solutions of f(x,y) == z, and then
to plot them in 3D space this can be done by a simple function
demonstrated here.   It is demonstrated with the ContourPlot 

command but it will work with the extended ListContourPlot 

provided in the ExtendGraphics package.

Make3DLines[ c_ContourGraphics, fun_, x_, y_] :=
  Module[ {val},
      First[ Graphics[ c]] /. Line[ pts_] :>
                 ( val = Apply[ Function[{x,y},fun], First[ pts]] ;
                   Line[ Map[ Append[ #, val]&, pts]])
  ]

c = ContourPlot[ x y, {x,-2,2},{y,-2,2}, ContourShading -> False]

Make3DLines[ c, x y, x, y] ;

Show[ Graphics3D[ %]]


Tom Wickham-Jones
WRI



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