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invisibleBlade
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Rotating points around a start coordinate

May 2, 2012 8:54 AM

I am playing around with coding a shape fitting game (similar to Tetris). I have a bunch of shapes that are stored as coordinates relative to a start point ({0,0})so an 'L' shape would be {0,1}, {0,2},{1,2}. Is there a simple way that I can calculate the new coordinates that describe the shape after it has been rotated 90 degrees in either direction?

To clarify, a rotation of 90deg clockwise would result in {0,0}, {-1,0},{-2,0}, {-2,1}.

I would like to do this as simply as possible as I am trying to be processor friendly and was thinking that as I am only interested in rotations of 90degree intervals that there might some clever cheat I could use.

I have asked on a few math forums but I get answers about matrices full of math notation that I don't understand. I might be able to do the math but I would like an explanation from a coder rather than a mathmatician if possible

 

Cheers all

374 Views   4 Replies   Latest reply: invisibleBlade, May 3, 2012 2:57 AM
 
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  • _spoboyle
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    1. _spoboyle,
    May 2, 2012 9:18 AM   in reply to invisibleBlade
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    I'm a mathematician but I did notice a patter with the one example you gave

     

    for each point swap the x, yand negate the new x

     

    so

    newX = -oldY

    newY = oldX

     

    it might not work generally I was just going off the example you gave me, if it doesn't and you don't get any responses I'll get back to you with a solution tomorrow, I should be able to reduce the matrices to simple operations

     
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  • invisibleBlade
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    2. invisibleBlade,
    May 2, 2012 9:35 AM   in reply to _spoboyle
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    I see what you mean however I was hoping to be able to calculate the new x/y based only on the old x/y and the rotation. There are only 4 possible rotations for each of the shapes so I could just manually input them all but I wanted a cleaner way to do it.

    Basically, given only the first set of coords and a rotation of 90 degrees I want to be able to calculate the new set of coords.

     

    My math is only slightely worse than my ability to explain my problems, sorry.

     
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  • _spoboyle
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    3. _spoboyle,
    May 3, 2012 1:04 AM   in reply to invisibleBlade
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    you cna't base the new x just on the old x and the new y on the old y. inherently the new x depends on the old y

     

    \begin{align} x'&=x\cos\theta-y\sin\theta\\ y'&=x\sin\theta+y\cos\theta. \end{align}

     

    now cos(90) = 0 and sin(90) = 1

     

    so for rotation of 90

     

    x' = -y

    y' = x

     

    now cos(180) = -1 and sin(180) = 0

    so for rotation 180

    x' = -x

    y' = -y

     

    now cos(270) = 0 and sin(90) = -1

    so for rotation 270

    x' = y

    y' = -x

     
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  • invisibleBlade
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    4. invisibleBlade,
    May 3, 2012 2:57 AM   in reply to _spoboyle
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    Cool, that is starting to make sense I think

    I need to find out more about this but you hve pointed me in the right direction for sure. Thanks for your help.

     
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