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Math Help - Rotating points around a known center

  1. #1
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    Rotating points around a known center

    I don't know if this is the right forum, but here we go.

    I have the situation where I have several known points in the plane that I want to rotate 45 degrees counterclockwise around a known center which is not (0,0). How do I do this, i.e. how do I find the new coordinates for each point?

    I am using Matlab, if that matters.
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  2. #2
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    Actually, I figured it out on my own. But now I have a different problem. I am plotting an ellipse in Matlab, and I want to rotate it 45 degrees, now clockwise, around it's center. Any ideas?
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  3. #3
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    Say the point is (1,1).
    And we want to find how it rotates ("a rotation matrix", but if that terms confuses you, ignore it).

    Draw a new coordinate system having (1,1) in its center pararrel and perpindicular to the original system.

    Then point (x,y) relative to the new coordinate system gets mapped to,
    x'=sqrt{2}/2*x-sqrt{2}/2*y
    y'=sqrt{2}/2*x+sqrt{2}/2*y

    Thus, (x',y') is the new coordinate relative to the new coordinate system.
    But relative to the old coordinate system it is,
    (x'+1,y'+1)
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  4. #4
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    Hello, changing_seasons!

    I think I've worked this out correctly . . .


    I have several known points in the plane that I want to rotate 45° CCW
    around a known center which is not (0,0).
    How do I find the new coordinates for each point?
    Let P(x,y) be any point.
    Let C(h,k) be the given center.

    We will need two quantities:
    . . . . . . . . . . . . - - - . . .______________
    The distance CP: . r .= .√(x - h)² + (y - k)²
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . y - k
    The angle θ that CP makes with the positive x-axis: . tan θ .= .------
    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x - h

    Then: . x' .= .h + r·cos(θ + 45°)
    . . . . . .y' .= .k + r·sin(θ + 45°)

    . . I think . . .

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  5. #5
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    Thanks for the help guys, but I found a way to solve both my problems.
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