Conformal maps on photography

I just found a Flickr set with some cool examples of applying conformal maps to photography.


  1. 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

    ( 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.

  2. ok, upon investigation ... this actually works