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Apparently, RegionProduct should allow you to generate convolution-generated shapes. For instance, take a 1D curve and a sphere, and the region product I would expect to obtain is the 1D curve thickened by the sphere shape. But RegionProduct of a 1D curve in 3D and a 3D sphere is actually in 6D space.

Is there some way to obtain the convolution region I just described?

Edit the logical operation that I would want to do is a morphological Dilation, but when passing a geometrical region to this function, it complains that it "is neither a rectangular array nor an image"

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  • $\begingroup$ That sounds like a morphological filter, like dilation. $\endgroup$ Oct 21, 2014 at 23:16
  • $\begingroup$ can you provide a reference or an example? I can't find anything on Google or Wolfram portal $\endgroup$
    – lurscher
    Oct 22, 2014 at 2:18
  • $\begingroup$ What keywords did you search? en.wikipedia.org/wiki/Mathematical_morphology. Much of the literature is focused on 2D and image processing. $\endgroup$ Oct 22, 2014 at 2:19
  • $\begingroup$ the point is that I can't find a way to take two regions and make this new region with them $\endgroup$
    – lurscher
    Oct 22, 2014 at 3:05
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    $\begingroup$ In this context of regions in Euclidean space, this operation is more commonly known as the Minkowski sum. There doesn't appear to be a built-in method for it. If TransformedRegion accepted two regions as input, you could have done TransformedRegion[r1, r2, Function[{p1, p2}, p1 + p2]], but that doesn't work right now. $\endgroup$
    – user484
    Oct 22, 2014 at 4:48

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