Conformal maps on photography
I just found a Flickr set with some cool examples of applying conformal maps to photography.
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ah, the change in area under a conformal mapping can be found from the jacobian. For a conformal map the jacobian matrix is a scalar times a rotation matrix. This means that its determinant is of the form
ReplyDelete( a cos t )( a cos t ) - ( a sin t )( - a sin t ) = a^2 ( cos^2 t + sin^2 t ) = a^2
I'm reasonable certain a^2 represents the change in area.
so, will it be possible to code in a representation of general conformal mappings as Taylor expansions, and also insert code that can compute this area differential algebraically ? this will increase the accuracy of the energy accumulation, and possibly remove all troubles from branches.
of course, this may also be nonsense.
ok, upon investigation ... this actually works
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