Initially the position of the shape was in (100, 100). I am rotating (say 30 degrees) the shape as shown in the image below. I have found the starting point of the rotated object. Is there a formula to find the point of the shape when the rotation was 0 degree? Any help?
How to find a point after rotation?
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geometry
analytic-geometry
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0Rotating w.r.t the center of the rectangle. – 2012-06-11
1 Answers
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Rotating any point $(x,y)$ on a plane about the origin by $\theta$ degrees (counter-clockwise) is given by $ \left[ \begin{array}{c} x' \\ y' \\ \end{array} \right] = \left[ \begin{array}{cc} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{array} \right] \left[ \begin{array}{c} x \\ y \\ \end{array} \right], $ where $(x',y')$ denotes your new position.
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0No problem! For more information on rotational matrices: http://www.youtube.com/results?search_query=rotational+matrix&oq=rotational+matrix&aq=f&aqi=g1&aql=&gs_l=youtube.3..0.146.3160.0.3174.20.15.0.2.2.0.255.1914.4j6j3.14.0...0.0.bifGYUjQsg4 – 2012-06-11