Computing Distances and Nearest Points 

Compute the distance to the nearest point in a mesh.

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X mesh2d = BoundaryDiscretizeGraphics[Text[Style["\[Pi]", Bold]], _Text, MaxCellMeasure -> 0.1]; pt2d = {0, 0};

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X RegionDistance[mesh2d, pt2d]

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Plot the distances.

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X df = RegionDistance[mesh2d]; {Plot3D[df[{x, y}], {x, -5, 5}, {y, -4, 4}, MeshFunctions -> {#3 &}, Mesh -> 5], ContourPlot[df[{x, y}], {x, -5, 5}, {y, -4, 4}, Contours -> {{0.5, Red}, {1, Green}, {1.5, Blue}}]}

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Visualize nearest points on the mesh.

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X pts = Table[4 {Cos[k 2 \[Pi]/24], Sin[k 2 \[Pi]/24]}, {k, 0., 23}]; nst = RegionNearest[mesh2d][pts]; Legended[Show[mesh2d, Graphics[{{Thin, Gray, Line[Transpose[{pts, nst}]]}, {Red, Point[pts]}, {Blue, Point[nst]}}]], PointLegend[{Red, Blue}, {"start", "nearest"}]]

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