The parametric equations for Dini's Surface are:
f(u,v) = (cos(u)sin(v),sin(u)sin(v),cos(v)+log(tan(v/2))+a*u),
0 <= u <= 2*pi, 0 < v < pi.
Notice that when v goes to zero and to pi, the z coordinate of Dini's surface goes to negative infinity and to positive infinity respectively. In the picture, c <= v <= pi/2 , where c is chosen arbitrarily. This parameter "c" cuts off the peak of Dini's surface.
With this parameterization we got:
Notice that the mesh is compressed in the top, therefore we did a reparameterization in order to get a more uniform mesh.
The new parameterization is:
d = atan(-m) + pi/2Where "m" controls how much the mesh is compressed or stretched.
w = atan(2m*v/pi - m) + pi/2
v1 = (pi-2c)(w-d)/(pi-2d) + c
f(u,v1) = (cos(u)sin(v1),sin(u)sin(v1),cos(v1)+log(tan(v1/2))+a*u)
After this parameterization we got:
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Created: Mar 6 1996 ---- Last modified: Mon May 13 12:45:41 1996
Copyright © 1996 by The Geometry Center, all rights reserved