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Math Help - linear algebra, rotation matrix

  1. #1
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    linear algebra, rotation matrix

    hello,

    i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


    A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

    If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

    thanks
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  2. #2
    MHF Contributor
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    Rotation matrix

    Hello closetnerd
    Quote Originally Posted by closetnerd View Post
    hello,

    i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


    A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

    If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

    thanks
    I'm afraid not, because every 2 x 2 matrix will map (0, 0) onto itself, and you'll want (-2, 2) to map onto itself, it that is to be the centre of rotation.

    Grandad

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  3. #3
    Junior Member ursa's Avatar
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    hello,

    i'm wondering if it is possible to find a rotation matrix that does not rotate about the origin.


    A and B shows the standard rotation of a square about the origin. C is a square not about the origin, if i apply the rotation matrix, i end up with D, however I'd like to end up with E.

    If C had the coordinates c1 (-1,1) c2 (-1, 3), c3 (-3, 3), c4 (-3, 1). It would be a rotation about (-2, 2). Is this possible?

    thanks
    hi
    first you shift your point to the origin by using translation matrix
    then apply rotation matrix and finally apply inverse of translation matrix
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  4. #4
    MHF Contributor
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    Rotation matrix

    Hello -

    My answer assumes that you are using matrix multiplication only. Matrix addition will allow you to shift the origin, of course.

    Grandad
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