Transform: Conformal Mapping Algorithms

From MIPAV
Revision as of 13:23, 17 August 2012 by Olga Vovk (Talk | contribs)

Jump to: navigation, search

The methods described in this document use conformal mapping to transform points in a circular sector, circle, ellipse, or nearly circular region to points in a circle or rectangle.

Background

A conformal mapping, is a transformation w=f(z) that preserves local angles. An analytic function is conformal at any point where it has a nonzero first derivative. A complex function is analytic on a region R if it is complex differentiable at every point in R. In a conformal mapping, in any small neighborhood the relative angle and shape are preserved.

Circular Sector to Rectangle

Transformation: Circle to Rectangle

Transformation: Ellipse to Circle

Transformation: Nearly Circular Region to Circle

Applying the algorithms

Circular Sector to Rectangle

Circle to Rectangle

Ellipse to Circle

Nearly Circle to Circle

References

See also:

For the time being, please refer to the MIPAV HTML help Algorithms/TransformConformalMapping.html