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Vector rotation

  1. Apr 2, 2005 #1
    Hi! I'm trying to implement a FPS-camera. I need to calculate a new vector from another one, rotated a.

    This is of cource in 2D. Is this correct:
    x' = x * ||v|| sin a / y
    y' = - y ||v|| cos a / x
  2. jcsd
  3. Apr 2, 2005 #2
    if you want to rotate a vector (x, y) of an angle a to get a vector (x', y') you just need this:

    x' = x*cos(a) - y*sin(a)
    y' = x*sin(a) + y*cos(a)
  4. Apr 2, 2005 #3
    Ahh! Exactly what I was looking for.

    EDIT: Hello there! I found that my copy of Core Algorithms in Game Programming has a matrix for my 3D rotation.
    Last edited: Apr 2, 2005
  5. Apr 2, 2005 #4
    Consider two vectors which lenght is the same (rotation doesn't change the lenght, I think) and build two similar trinagles by add two lines from thier heads to the x-axes. Name them v=(x, y) and u=(a,b). Then obiously x/a =y/b. x=ay/b=a*||v|| sin(Pi - a)/b = x=a * ||v|| sin a /b In a similar way one can derive the other equation. Where is my error?
  6. Apr 2, 2005 #5


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    Sin(pi- a)? But a isn't an angle, it is a length. Where did you get this?
  7. Apr 2, 2005 #6
    I don't understand your description. A diagram would be helpful.
  8. Apr 2, 2005 #7
    Woops! It should be the angle between the vectors. Call it alpha istead. My own diagram tricked me.

    EDIT: When I think about it. Shouldn't it be (Pi-alpha)/2. :blushing: Oops.
    EDIT2: Can you even assume they're equal? I think I've made a complete fool of myself.

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    Last edited: Apr 2, 2005
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