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Homework Help: Transformation of unit sqaure to circle

  1. Mar 25, 2007 #1
    I was wondering if anybody knew how to transform a unit square (point A (0,0) point B (1,0) point C (1,1) point D (0,1)) into a circle using a transformation matrix, or if there is a special name for this case.
    Many thanks,
    unique_pavadrin
     
  2. jcsd
  3. Mar 25, 2007 #2

    arildno

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    Well, look closely on the standard polar coordinates transformation.
    This takes a rectangle onto a circle.

    So, all you need to do is to map the unit square onto that rectangle, and you're done.
     
  4. Mar 25, 2007 #3
    hmm......so the x' and y' points would be rcos(theta) and rsin(theta) respectivly?
    thanks
     
  5. Mar 25, 2007 #4

    arildno

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    Yes, with r varying between 0 and some upper limit, and the angle between 0 and 2pi.

    This is a rectangle in the (r,theta)-plane.
     
  6. Mar 30, 2007 #5
    thank you, however im am still a little unsure...sorry....
     
  7. Mar 31, 2007 #6

    HallsofIvy

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    Since this transformation maps a line (side of the square) into an arc of a circle, it is not "linear" and cannot be written as a matrix multiplication.
     
  8. Mar 31, 2007 #7
    thank you HallsofIvy
     
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