Transform: Conformal Mapping Algorithms
From MIPAV
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