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I would like to create a rectangle from two given 3D points (they are placed on rectangle diagonal). Those points lies on the same plane with given normal. I was able to do it on axis aligned planes, but now I would like to do it on any plane.

Any ideas if this is possible and how?

user1577566
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    Your task is impossible without an additional criterion, such as the direction of one pair of edges: Given two points in the $(x,y)$-plane, there is a $1$-parameter family of rectangles having these points on a diagonal. – Andrew D. Hwang Nov 29 '13 at 14:02
  • Can I detrmine such direction? Let's say I want edges to be axis aligned, can it be done then? – user1577566 Nov 29 '13 at 14:19
  • A generic plane (specifically, one having equation $ax+by+cz=d$ with $a$, $b$, $c$ all non-zero) contains no line parallel to a coordinate axis. Even if you only want the edges of your rectangle to be parallel to a coordinate plane, your task is impossible for planes $P$ that are not themselves parallel to a coordinate plane (the same class as before): Two non-parallel planes determine a line of intersection, and the three directions in $P$ defined by the Cartesian coordinate planes are mutually non-perpendicular. – Andrew D. Hwang Nov 29 '13 at 14:43
  • Ok, that's a shame :( I think I will stick to that axis aligned drawing. Thank you for help :) – user1577566 Nov 29 '13 at 14:45

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If $A,C$ are your two points, let $S$ be the sphere with $AC$ as diameter. Let $O$ be its center. Then pick any $B\in S$ and let $D$ be the other point of intersection of the line $BO$ and $S$. Then $ABCD$ is a rectangle. If you have an additional restriction in form of a plane through $A,C$, then the sphere becomes a circle (by intersection), but that still leaves you with a one-parameter faimily (as hinted by user86418).

Hagen von Eitzen
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