Transformation of unit sqaure to circle

  • #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
 

Answers and Replies

  • #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.
 
  • #3
hmm......so the x' and y' points would be rcos(theta) and rsin(theta) respectivly?
thanks
 
  • #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.
 
  • #5
thank you, however im am still a little unsure...sorry....
 
  • #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.
 
  • #7
thank you HallsofIvy
 

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