RegionNearest¶

Gives the point of a region closest to a given point. For a solid Disk or Ball an exterior point is projected onto the boundary, while an interior point maps to itself.

$ wo 'RegionNearest[Disk[{0, 0}, 1], {3, 0}]'
{1, 0}

$ wo 'RegionNearest[Disk[{0, 0}, 2], {3, 4}]'
{6/5, 8/5}

A Rectangle clamps the point into the box.

$ wo 'RegionNearest[Rectangle[{0, 0}, {2, 2}], {3, 3}]'
{2, 2}