Compute Region Distance 

Compute distance from a point in any dimension.

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X RegionDistance[Cylinder[{{0, 0, 0}, {0, 0, 1}}, 1], {1, 2, 3}]

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X RegionDistance[Ball[{0, 0, 0, 0, 0}, 1], {1, 2, 3, 4, 5}]

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Compute distance formulas in any dimension.

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X RegionDistance[Rectangle[], {x, y}]

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X RegionDistance[Ball[{0, 0, 0, 0}, 1], {w, x, y, z}]

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Create a distance function that can be reapplied to multiple points.

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X f = RegionDistance[ Pyramid[{{0, 0, 0}, {2, 0, 0}, {2, 2, 0}, {0, 2, 0}, {1, 1, 2}}]]

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X options = {Mesh -> None, Axes -> False, Boxed -> False, BoxStyle -> GrayLevel@0.7, Contours -> {0.25, 0.5, 1}, ContourStyle -> ColorData[94, "ColorList"], Lighting -> "Neutral", BaseStyle -> Opacity[0.5], BoxRatios -> Automatic};

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X ContourPlot3D[f[{x, y, z}], {x, -1, 3}, {y, -1.5, 3}, {z, -1.5, 3}, Evaluate[options]]

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Visualize iso-distances for other basic regions.