Mapping in complex plane

From: Brad Cooper (Brad.Cooper_17_at_bigpond.com)
Date: 10/22/04 

Date: Fri, 22 Oct 2004 11:14:19 GMT

Hi,

At http://homes.jcu.edu.au/~ccbsc/

is a conformal mapping that "looks" a bit like one I am actually
trying to produce. It is tan(z)/tan(1) - seen when you scroll
down on the Web page.

I would like to have the "tall" rectangle one unit wide map onto
a shape that approaches a quarter circle with unit radius.

Specifically, the right hand edge of the rectangle should fold
over to tend to form a quarter circle as this mapping "appears"
to nearly do so.

The top edge of the rectangle is required to bunch up and tend
towards a point on the y-axis, again as "appears". Finally,
points on the x-axis and y-axis should remain on those axes.

The mapping shown is not what I am after (it just looks kinda close
to it), but if anyone knows how to produce the quarter circle mapping
I would appreciate the help.

Cheers,
Brad

Relevant Pages

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  • Mapping in complex plane
    ... is a conformal mapping that "looks" a bit like one I am actually ... I would like to have the "tall" rectangle one unit wide map onto ... a shape that approaches a quarter circle with unit radius. ... points on the x-axis and y-axis should remain on those axes. ...
    (sci.math)
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    ... Taking a hint from Robert Israel's enlightening posts, I'd consider a composition of the following: A mapping from the real line to a circle in the complex plane, a rotation of the circle by 2 pi / 5, and an inverse mapping from the circle back to the real line. ...
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