# Transformation of unit sqaure to circle

1. Mar 25, 2007

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,

2. Mar 25, 2007

### arildno

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. Mar 25, 2007

hmm......so the x' and y' points would be rcos(theta) and rsin(theta) respectivly?
thanks

4. Mar 25, 2007

### arildno

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. Mar 30, 2007

thank you, however im am still a little unsure...sorry....

6. Mar 31, 2007

### HallsofIvy

Staff Emeritus
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. Mar 31, 2007