- #1

- 11

- 0

Please I need some help with this:

Is it possible to transform a circle into a rectangle? If so what would be the expressions of x' and y' in terms of x and y.

Thank you in advance!

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Carol_m
- Start date

- #1

- 11

- 0

Please I need some help with this:

Is it possible to transform a circle into a rectangle? If so what would be the expressions of x' and y' in terms of x and y.

Thank you in advance!

- #2

- 160

- 2

Though the transformation exists, finding it explicitly is another matter entirely. According to Mathworld it can be explicitly written down using elliptic functions but I don't know how much use that is.

- #3

- 11

- 0

Thank you very much for your reply. Could you please give me a reference to this so I can find the explicit formula?

Thanks again!

- #4

- 53

- 0

Have you tried using the transformation from polar coordinates to rectangular coordinates?

- #5

jasonRF

Science Advisor

Gold Member

- 1,465

- 525

So one approach is to map a circle to the upper half plane using a Mobius transformation, then use a Schwarz-Christoffel to map the upper half plane to rectangle. Both of these have parameters that you will need to determine for your particular problem.

Good luck!

jason

- #6

- 11

- 0

Basically my question is:

I have a circle an every point in the circle as (x,y). I need a transformation that changes every point in the circle to a point in a rectangle (x',y') so I could write x' in terms of x and y' in terms of y.

If you look in the attachement you can see what I mean :)

ps. I am not that concern about the base of the rectangle it could be circular so that y=y' but I am stuck with the x'

Thank you!!

I have a circle an every point in the circle as (x,y). I need a transformation that changes every point in the circle to a point in a rectangle (x',y') so I could write x' in terms of x and y' in terms of y.

If you look in the attachement you can see what I mean :)

ps. I am not that concern about the base of the rectangle it could be circular so that y=y' but I am stuck with the x'

Thank you!!

- #7

jasonRF

Science Advisor

Gold Member

- 1,465

- 525

Basically my question is:

I have a circle an every point in the circle as (x,y). I need a transformation that changes every point in the circle to a point in a rectangle (x',y') so I could write x' in terms of x and y' in terms of y.

If you look in the attachement you can see what I mean :)

ps. I am not that concern about the base of the rectangle it could be circular so that y=y' but I am stuck with the x'

Thank you!!

If your mapping needs to be conformal, as indicated by your post title, then my previous post should give you the words you need to search for either in Google or a complex analysis book; this should point you in the right direction so that you can figure out your mapping. By the way, the Mobius transformation is the same as the "linear fractional" transformation, which may help in your search.

- #8

- 11

- 0

It certainly needs to be conformal... Thank you for your great answer I will look into this direction, and sorry I posted my reply with the attached figure before reading yours.

Share: