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I'd like to evaluate this convolution to a function of r, z and r0 giving a density for the resulting region:

$\boldsymbol{\pi}(z) \ast \delta(r-r0)$

WHERE

$\boldsymbol{\pi}(z)$ is an xy planar region at z

and

$\delta(r-r_0)$ is a spherical shell of radius r0 .

I've tried a number of approaches, including:

  • Convolve[DiracDelta...
  • Regions and/or ShellRegion
  • RegionDilation/RegionErosion
  • variations on FromSphericalCoordinates and others I've probably forgotten.

Failing a solution to my specific challenge, are there any examples of, at least, multidimensional Convolve with radial DiracDelta between surfaces of different dimensionality (of course, both residing in the same embedding space)?

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  • $\begingroup$ Please include the code you have tried and the problems you encountered. $\endgroup$
    – bbgodfrey
    Commented Feb 24, 2022 at 1:17
  • $\begingroup$ OK but it will take me a while to reconstruct my failed approaches because I didn't save them. $\endgroup$ Commented Feb 24, 2022 at 1:18

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