Re: (OT) moving points from one plane to another

From the 3 points on the first plane you can determine its equation. Ditto, for the three mapped point on the second plane.

With the equations of both planes, you can determine the line where they intersect (assuming they are not parallel).

That line forms the axis of rotation; and the angle between the planes, the angle of rotation. You know have all the information required to build the matrix for the affine transformation that you can then apply to the rest of the points in the original plane to map them to their new positions.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

RIP PCW

Comment on Re: (OT) moving points from one plane to another

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Re^2: (OT) moving points from one plane to another by merrymonk (Hermit) on Jul 09, 2009 at 09:54 UTC
Thank you for that. It may have given me the way forward. I have found a reference http://inside.mines.edu/~gmurray/ArbitraryAxisRotation/ArbitraryAxisRotation.pdf that gives the matrix for rotation about an arbitary axis. I am hoping that your references and this will solve the problem.	[reply]
Re^2: (OT) moving points from one plane to another by tilly (Archbishop) on Jul 09, 2009 at 16:44 UTC
You are assuming that points on the intersecting line do not move. This is a huge assumption that is almost always wrong.	[reply]
Re^3: (OT) moving points from one plane to another by BrowserUk (Patriarch) on Jul 09, 2009 at 17:56 UTC
This is a huge assumption that is almost always wrong. Care to expand on that by showing us a practical example? Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error. "Science is about questioning the status quo. Questioning authority". In the absence of evidence, opinion is indistinguishable from prejudice. RIP PCW	[reply]
Re^4: (OT) moving points from one plane to another by tilly (Archbishop) on Jul 09, 2009 at 21:50 UTC
Let me give an example mapping the X-Y plane to the X-Z plane: `(0, 0, 0) -> (0, 0, 0) (1, 0, 0) -> (0, 0, 1) (0, 1, 0) -> (-1, 0, 0)` [download] Your approach would notice the 90 degree rotation in planes. But would assume that since `(1, 0, 0)` is in both planes that it gets mapped to itself. For another interesting example consider the following mapping: `(0, 0, 0) -> (1, 0, 0) (1, 0, 0) -> (2, 0, 0) (0, 1, 0) -> (1, 1, 0)` [download] This sends the X-Y plane to the X-Y plane but no point remained still. Your approach has no idea how to handle it.	[reply] [d/l] [select]
Re^5: (OT) moving points from one plane to another by BrowserUk (Patriarch) on Jul 10, 2009 at 07:56 UTC
Re^5: (OT) moving points from one plane to another by merrymonk (Hermit) on Jul 10, 2009 at 12:20 UTC
Re^6: (OT) moving points from one plane to another by tilly (Archbishop) on Jul 10, 2009 at 16:09 UTC
Some notes below your chosen depth have not been shown here
Re^4: (OT) moving points from one plane to another by Corion (Patriarch) on Jul 09, 2009 at 18:03 UTC
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.	[reply]