9.2 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 9.1 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.