I guess that as soon as you have a translation of the points along the line, even the points on the line will move, because they "slide" up or down that line. Also, it's not necessarily clear to me why points on the line/intersection shouldn't move away from the line.

In reply to Re^4: (OT) moving points from one plane to another by Corion
in thread (OT) moving points from one plane to another by merrymonk

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