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I have a plane-A which sits on the origin and where every point on the plane has a z coordinate of 0 (so there is no rotation of the plane).

I have plane-B in space and I have a a point (which is the origin) on the plane and a normal so it can be rotated in any axis. The point and normal are in relation to plane-A.

What I want to do is switch them, so I now make plane-B the origin and find out the origin-corner-point of plane-A and its normal. I can't figure out the maths - what do I need to do?

hope that makes sense.

EDIT:

I have plane-A & plane-B in the same 3D space

I have plane-A which I represent with a point [0,0,0] and a normal vector which is [0,0,1] I think (not too sure if I have this correct, every point on the plane has a z coordinate of 0).

I have plane-B which is not parallel to plane-A for which I have a point [a_x, a_y, a_z] and a normal vector [a_rx, a_ry, a_rz].

I want some sort of transformation such that [a_x, a_y, a_z] is now [0,0,0] and the normal vector for plane-A [a_rx, a_ry, a_rz] is [0,0,1] but the "relationship" between plane-A and plane-B stays the same.

The end product is, after the transformation, to get the plane-A point coordinates and plane-A normal vector.

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    Are you working in 3 dimensions? If the planes are parallel, then you have a fixed distance between them. Otherwise, you've got a reference point in each plane, and a fixed angle between their normal vectors (which is zero if they're parallel). You can use either plane's reference point (e.g. its origin as you call it) and its normal vector to project points from the other plane onto the first plane. What do you mean by corner point (are you considering infinite planes or finite regions)? What are you ultimately trying to do?2012-03-14
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    I have edited the question. I hope it's far more clear.2012-03-14

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