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This thread considers mathematical methods here to make the 3D object smooth but this question consider how to achieve the goal of smoothing a 3D object in Mathematica.

I want to get smoother geometrical objects, some messing up here. Suppose for example a tetrahedron where I would like to make the corners rounded with either convolution or interpolation. I would have to select two control points on different faces and then select one adjusting point -- I could use a NURBS aka spline approximation with a polynomial then aka Mathematica's BezierCurve[...] command. Now I am trying to do a ready command that would do this for me without me traversing different vertices and making sure of selecting right faces for control/adjusting points. Example data about the coordinates with the tetrahedron's faces here.

Does Mathematica have some ready function to do Interpolation or Convolution for geometric objects?


I think the by-far-easiest solution is to use Convex hull but it hides some information if you have a lot of details. This is an answer in progress.

Different methods

  1. Convex hull of a 3D object?
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    $\begingroup$ Could you post some simple example to play with? $\endgroup$ – István Zachar Mar 22 '13 at 15:19
  • $\begingroup$ Here's a simple, but not very good approach: << PolyhedronOperations`; Graphics3D@ Nest[Truncate[#, .2] &, N@PolyhedronData["Tetrahedron", "Faces"], 5] $\endgroup$ – Szabolcs Mar 22 '13 at 15:21
  • $\begingroup$ Use a RegionFunction that includes points within some epsilon>0 of the boundary? $\endgroup$ – Daniel Lichtblau Mar 23 '13 at 23:02

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