Difference between revisions of "Transform: Conformal Mapping Algorithms"
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| − | + | 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 == | == Background == | ||
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| + | 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 === | === Circular Sector to Rectangle === | ||
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=== Transformation: Nearly Circular Region 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 == | == References == | ||
Revision as of 13:23, 17 August 2012
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
