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Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls:

Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls:

Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls:

Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls:

Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls:

Although this answers none of the OP's questions—and is in fact entirely tangential—some might enjoy this image from an earlier MO question, Delaunay triangulations and convex hulls: