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Thread: Is my approach to achieve the rotation affine transformation formula right?

  1. #1
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    Is my approach to achieve the rotation affine transformation formula right?

    To achieve the formula that rotates a point theta degrees around an arbitrary rotation axis, We take arbitrary point c on the rotation axis(we know that it's a fixed point), Now T(x) being the function that rotates the point x theta degrees around the rotation axis, we can find a linear transformation L(x) such that  T\left(x\right)-c=L\left(x-c\right) , So A being the corresponding transformation matrix for L(x) we have
    T\left(x\right)=c+A\left(x-c\right)
    =c+A\left(x\right)+A\left(-c\right)
    =c+A\left(x\right)-A\left(c\right)
    =A\left(x\right)+\left(c-A\left(c\right)\right)
    This also proves that rotation is an affine transformation(a linear transformation followed by a translation) , and BTW similar approach can be used to achieve formulas for other affine transformations that have a fixed point(like shear, reflection and scaling)
    Last edited by PooriaMG; May 15th 2017 at 07:30 AM.
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  2. #2
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    Re: Is my approach to achieve the rotation affine transformation formula right?

    is there a question here?
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  3. #3
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    Re: Is my approach to achieve the rotation affine transformation formula right?

    Quote Originally Posted by romsek View Post
    is there a question here?

    So that's a "yup it's perfectly correct"?
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  4. #4
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    Re: Is my approach to achieve the rotation affine transformation formula right?

    Quote Originally Posted by romsek View Post
    is there a question here?
    The question was in the title of the thread. I have not dealt with affine transformations and don't feel like looking up how they differ from linear ones.
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