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Aug 14th, 2018
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  1. rd = RegionDistance @ ParametricRegion[{x, x^2}, {{x, 0, 1}, {y, 0, 1}}];
  2.  
  3. ContourPlot[Evaluate@rd[{x, y}], {x, 0, 1}, {y, 0, 1},
  4. Contours -> 10, Exclusions -> None,
  5. Epilog -> {Plot[x^2, {x, 0, 1}, PlotStyle -> Directive[Thick, Red]][[1]]}]
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