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## Using Geomview as Mathematica's Default 3D Display

The package ``Geomview.m'` arranges for Geomview to be the default display program for 3D graphics in Mathematica. To load it, give the command `<< Geomview.m` to Mathematica. Thereafter, whenever you display 3D graphics with `Plot3D` or `Show`, Mathematica will send the graphics to Geomview.

Loading ``Geomview.m'` implicitly loads ``OOGL.m'` as well, so you can use the `Geomview` and `WriteOOGL` as described above after loading ``Geomview.m'`. You do not have to separately load ``OOGL.m'`.

    % math
    Mathematica 2.0 for SGI Iris
    Copyright 1988-91 Wolfram Research, Inc.
     -- GL graphics initialized --

    In[1] := <<Geomview.m

    In[2] := Plot3D[x^2 + y^2, {x, -2, 2}, {y, -2, 2}]

    Out[2] := -SurfaceGraphics-

This invokes geomivew and loads the graphics object into it.

    In[3] := Plot3D[{x*y + 6, RGBColor[0,x,y]}, {x,0,1}, {y,0,1}]

    Out[3] := -SurfaceGraphics-

This replaces the previous Geomview object by the new object.

    In[4] := Geomview[{%2,%3}]

    Out[4] := {-SurfaceGraphics-, -SurfaceGraphics-}

This displays both objects at once. You also can have more than one Mathematica object at a time on display in Geomview, and have separate control over them, by using the `Geomview` command with a name, See section Using Mathematica to generate OOGL files.

    In[5] := Graphics3D[ {RGBColor[1,0,0], Line[{ {2,2,2},{1,1,1} }] }]

    Out[5] := -Graphics3D-

    In[6] := Geomview["myline", %5]

This addes the `Line` specified in `In[5]` to the existing Geomview display. It can be controlled independently of the "Mathematica" object, which is currently the list of two plots.

    In[7] := <<GL.m

If you're on an SGI, loading `GL.m` returns Mathematica to its usual 3D graphics display. The following plot will appear in a normal static Mathematica window.

    In[8] := ParametricPlot3D[{Sin[x],Sin[y],Sin[x]*Cos[y]}, {x,0,Pi},{y,0,Pi}]

    Out[8] := -Graphics3D-

We can return to Geomview graphics at any time by reloading ``Geomview.m'`.

    In[9] := <<Geomview.m

    In[10] := Show[%8]

    Out[10] := -Graphics3D-

    In[11] := ParametricPlot3D[
    	   {(2*(Cos[u] + u*Sin[u])*Sin[v])/(1 + u^2*Sin[v]^2),
    	   (2*(Sin[u] - u*Cos[u])*Sin[v])/(1 + u^2*Sin[v]^2),
    	   Log[Tan[v/2]] + (2*Cos[v])/(1 + u^2*Sin[v]^2)},
    	  {u,-4,4},{v,.01,Pi-.01}]

    Out[11] := -Graphics3D-

This last plot is Kuen's surface, a surface of constant negative curvature. Parametrization from Alfred Gray's Modern Differential Geometry of Curves and Surfaces textbook.

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