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I know that Mathematica isn't built to model 3D, but most of my models are equation-defined so here's my question: is it somehow possible to combine ad-hoc 3D objects as well as ordinary/parametric/closed-form 3-dimensional plots into a single rendering?

I know about the ability to export and recombine elsewhere, but I don't want to do that right now. (Also, for some reason, SolidWorks crashes when importing complicated models.)

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Indeed it's very easy. Just use Show. Here is an example:

adhock = Graphics3D[{Blue, Cylinder[], Red, Sphere[{0, 0, 2}], Black, 
    Thick, Dashed, 
    Line[{{-2, 0, 2}, {2, 0, 2}, {0, 0, 4}, {-2, 0, 2}}], Yellow, 
    Polygon[{{-3, -3, -2}, {-3, 3, -2}, {3, 3, -2}, {3, -3, -2}}], 
    Green, Opacity[.3], Cuboid[{-2, -2, -2}, {2, 2, -1}]}];


parametric = 
  ParametricPlot3D[{(3 + Cos[v]) Cos[u], (3 + Cos[v]) Sin[u], 
    Sin[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}, 
   PlotStyle -> Specularity[White, 50], Mesh -> None];


Show[adhock, parametric]

Mathematica graphics

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  • $\begingroup$ Awesome, thanks! $\endgroup$ – Dmitri Nesteruk Apr 26 '12 at 14:41

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