Transformation of unit sqaure to circle

[unique_pavadrin]

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

 

[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.

 

[unique_pavadrin]

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

 

[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.

 

[unique_pavadrin]

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

 

[HallsofIvy]

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.

 

[unique_pavadrin]

thank you HallsofIvy