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Math Help - Coordinate system translation

  1. #1
    Newbie
    Joined
    Jun 2009
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    Coordinate system translation

    Hello everyone. I'm having trouble with what I believe to be a translation issue. Here is the deal.


    Say I have a rectangle in 2D space that is define as follows

    (.38,.42) (.62,.42)
    ________________________
    |....................................|
    |....................................|
    |....................................|
    |....................................|
    |______________________ |
    (.38,.58) (.62,.58)


    I need to translate it to this system:

    (0,0) (1,0)
    ________________________
    |....................................|
    |....................................|
    |....................................|
    |....................................|
    |______________________ |
    (0,1) (1,1)


    The translation has to be somewhat dynamic such that if the rectangle has different dimensions than those listed above, I can still translate to the system (0,0) - (1,1).

    If possible, an algebraic solution for x and y would be even better.

    I'm totally stumped here, can anyone assist?
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  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by dsoltyka View Post
    Hello everyone. I'm having trouble with what I believe to be a translation issue. Here is the deal.


    Say I have a rectangle in 2D space that is define as follows

    (.38,.42) (.62,.42)
    ________________________
    |....................................|
    |....................................|
    |....................................|
    |....................................|
    |______________________ |
    (.38,.58) (.62,.58)


    I need to translate it to this system:

    (0,0) (1,0)
    ________________________
    |....................................|
    |....................................|
    |....................................|
    |....................................|
    |______________________ |
    (0,1) (1,1)


    The translation has to be somewhat dynamic such that if the rectangle has different dimensions than those listed above, I can still translate to the system (0,0) - (1,1).

    If possible, an algebraic solution for x and y would be even better.

    I'm totally stumped here, can anyone assist?
    Lets say that the original co-ordinates are (a,c),(b,c),(a,d),(b,d)

    where in you question a=.38, b=.62, c=.42,d=.58

    and, let x,y be the old co-ordinate axes and X,Y be the new co-ordinate axes

    then, the transformation equations are
    X=\frac{x-a}{b-a}

    Y=\frac{y-c}{d-c}
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  3. #3
    Newbie
    Joined
    Jun 2009
    Posts
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    Forgive my ignorance, but I am unsure how to use those translation formulas to solve my problem.

    I'm confused about the numerators of each one. I'm not sure what values to use for the old axis. Can you possibly provide an example of how .38 can become 0 and .62 can become 1? I'd really love to understand this a bit better, thank you.
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  4. #4
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Quote Originally Posted by dsoltyka View Post
    Forgive my ignorance, but I am unsure how to use those translation formulas to solve my problem.

    I'm confused about the numerators of each one. I'm not sure what values to use for the old axis. Can you possibly provide an example of how .38 can become 0 and .62 can become 1? I'd really love to understand this a bit better, thank you.
    the formula I gave

    X=\frac{x-a}{b-a}

    in your question, a=.38, b=.62

    hence formula for this question becomes

    X=\frac{x-.38}{.62-.38}

    X=\frac{x-.38}{.24}

    if x=.38,X= \frac{.38-.38}{.24}...which is zero.

    if x=.62,X= \frac{.62-.38}{.24}...which is one.
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