Mesh region with Rick Astley

A example of creating and using boundary mesh for solving equations on them.

Smile!

img = (*VB[*)(FrontEndRef["438babff-4e1b-415b-ba6b-edeb3d6f288f"])(*,*)(*"1:eJxTTMoPSmNkYGAoZgESHvk5KRCeEJBwK8rPK3HNS3GtSE0uLUlMykkNVgEKmxhbJCUmpaXpmqQaJumaGJom6SYlmiXppqakJhmnmKUZWVikAQCXhRbB"*)(*]VB*);

Apply a filter

MeanShiftFilter[img, 5, 1] // Binarize // ColorNegate

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Create a mesh region

ξ = ImageMesh[%]

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Compute eigenfunctiions of the wave equation

{vals, funs} = NDEigensystem[
   {-Laplacian[u[x, y], {x, y}], 
    DirichletCondition[u[x, y] == 0, True]}, 
   u[x, y], Element[{x, y}, ξ], 6];

Plot different time slots

Grid@
 Partition[
  Table[ContourPlot[funs[[i]], Element[{x, y}, ξ], 
    PlotRange -> All, ImageSize->300, PerformanceGoal->"Speed", PlotLabel -> vals[[i]], 
    PlotTheme -> "Minimal"], {i, Length[vals]}], 3]

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