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Mathematica

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  • $\begingroup$ That is an unanswered question, hopefully not. See my questions here and here $\endgroup$ Commented Oct 4, 2015 at 12:35
  • $\begingroup$ I was going to suggest a Montecarlo method, but then I saw you want to use computational geometry procedures... $\endgroup$ Commented Oct 4, 2015 at 14:57
  • $\begingroup$ @Peltio With the sorts of Monte Carlo volume computations I'm familiar with, you need to be able to tell if any point is inside or outside of the object. How would you do this here? If you can do that, that alone seems valuable enough to post. $\endgroup$ Commented Oct 4, 2015 at 14:59
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    $\begingroup$ Off the top of my head: slice the solid surface into intersection with parallel planes and then use one of those "is point inside a 2D polygon" test to see if it's inside. (@Szabolcs - you could not have seen my comment, so your question is more than justified). An even easier way: 3Dprint the darn satellites and put them into water to measure the displaced volume :-) $\endgroup$ Commented Oct 4, 2015 at 15:02
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    $\begingroup$ In computer graphics there are various techniques for turning a bad triangle mesh into a volumetric representation; see Jacobson et al. (2013) and the references therein. If Mathematica doesn't have a good way to do it, I would export the vertex positions and normals to a point cloud, use MeshLab to create a clean mesh, and import it back into Mathematica. $\endgroup$ Commented Oct 5, 2015 at 1:11