New in this edition: C-spheres

 


 

In general, a C-sphere is a surface in the boundary of hyperbolic space that is topologically a sphere and is foliated by chains (C-circles). One way to specify a C-circle is to give a path in homogeneous coordinates that provides vectors that are normal to the chains. The left picture is given by the path

\gamma(t) = ( -t^3, \sqrt{2}, t)

The points corresponding to t=\pm1 are (\pm 1, 0, 0). Taking them to (0,0,\pm 1) produces the picture on the right.

Note: the notebook ComplexHyperbolic0.5 did not draw correct C-spheres, so it's no longer available. The code for the images above will be in CH0.6.

Next >

Last Updated ( Monday, 20 July 2009 15:17 )