Nonlinear Transformation of a Region 

Transform a disk by a nonlinear transformation .

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X r0 = Disk[{1, 1}, 4];

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X f = {Indexed[#, 1] Indexed[#, 2], Indexed[#, 1] + Indexed[#, 2]} &;

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X r1 = TransformedRegion[r0, f];

Visualize the region and a point in the region before the transformation.

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X p = {-2, 2};

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X RegionPlot[r0, Epilog -> {Red, Point[p]}]

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Visualize the region and point after the transformation.

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X RegionPlot[r1, Epilog -> {Red, Point[f[p]]}]

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