2D Euclidean vector rotations

Question

I have a euclidean vector a sitting at the coordinates  0  1   I want to rotate a by 90 degrees  clockwise  around the origin   0  0    If I have a proper understanding of how this should work  the resultant  x  y  coordinates after the rotation should be  1  0   If I were to rotate it by 45 degrees  still clockwise  instead  I would have expected the resultant coordinates to be  0 707  0 707    theta   deg2rad angle    cs   cos theta   sn   sin theta    x   x   cs - y   sn  y   x   sn   y   cs    Using the above code  with an angle value of 90 0 degrees  the resultant coordinates are   -1  1   And I am so damn confused  The examples seen in the following links represent the same formula shown above surely   What have I done wrong  Or have I misunderstood how a vector is to be rotated

User · Answer

Rotating a vector 90 degrees is particularily simple    x  y  rotated 90 degrees around  0  0  is  -y  x    If you want to rotate clockwise  you simply do it the other way around  getting  y  -x

User · Answer

Sounds easier to do with the standard classes   std  complex lt double gt  vecA 0 1   std  complex lt double gt  i 0 1      90 degrees std  complex lt double gt  r45 sqrt 2 0  sqrt 2 0    vecA    i  vecA    r45    Vector rotation is a subset of complex multiplication  To rotate over an angle alpha  you multiply by std  complex lt double gt    cos alpha   sin alpha

User · Answer

you should remove the vars from the function   x   x   cs - y   sn     now x is something different than original vector x y   x   sn   y   cs    create new coordinates becomes  to avoid calculation of x before it reaches the second line   px   x   cs - y   sn   py   x   sn   y   cs

User · Answer

Rotate by 90 degress around 0 0   x    -y y    x   Rotate by 90 degress around px py   x    - y - py    px y     x - px    py

User · Answer

You re calculating the y-part of your new coordinate based on the  new  x-part of the new coordinate   Basically this means your calculating the new output in terms of the new output     Try to rewrite in terms of input and output   vector2 lt double gt  multiply  vector2 lt double gt  input  double cs  double sn       vector2 lt double gt  result    result x   input x   cs - input y   sn    result y   input x   sn   input y   cs    return result      Then you can do this   vector2 lt double gt  input 0 1   vector2 lt double gt  transformed   multiply  input  cs  sn      Note how choosing proper names for your variables can avoid this problem alltogether

[c++] 2D Euclidean vector rotations

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