in reply to Re^3: (OT) moving points from one plane to another
in thread (OT) moving points from one plane to another

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.

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Re^5: (OT) moving points from one plane to another
by BrowserUk (Patriarch) on Jul 10, 2009 at 07:56 UTC
    This sends the X-Y plane to the X-Y plane

    You're right. Rotation alone won't deal with parallel planes. I guess that's why I included:

    (assuming they are not parallel)

    The nice thing about rotation-only examples, as a starting point, is that they are easy to visualise, whilst getting away from thinking in terms of rotations occuring (only) around the orthogonal axis. Once you've mastered thinking in terms of rotations around arbitrary vectors, then applying a translation, once the points are in the same plane, comes fairly naturally. Reflections and sheers are somewhat harder to visualise (for me at least), but if you take simple steps, you get there.

    Of course, if you're one of those that is comfortable just manipulating numbers in the abstract, then just applying someone elses formulae is all you need. But I find that without some grounding in visualising the way transforms combine it is nearly impossible to acquire a confidence in the results. And if you need to modify those formulae--to impose one or more constraints on the freedom of motion--then it is neigh impossible if you do not understand how the formulae work. YMMV.

    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.
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Re^5: (OT) moving points from one plane to another
by merrymonk (Hermit) on Jul 10, 2009 at 12:20 UTC
    I have just tried both cases my creating planes from each set of co-ordinates given.
    Interestingly the first case worked fine by rotating points about the x-axis.
    The second case failed (and was trapped) since these planes are parallel.
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      Please define "worked fine". Did the 3 specified starting points actually go to the 3 specified target points? If not, then I don't think you've solved your stated problem.

      For the first example, if you rotate about the x-axis, then all points on the x-axis have to go back to the x-axis. But in the specification I gave for that example (1, 0, 0) which starts on the x-axis is supposed to wind up at (0, 0, 1) on the z-axis. So you can't possibly do that by rotating around the x-axis.

[reply]
        Thanks for your continued interest.
        I was a bit overstating the result!
        what I meant was, the points had been rotated to the correct plane.
        I do have to position them correctly in that plane.
        However, as I know how to do this it is not a problem for me.
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