In this context, you may want to compare the parametrizations that
were used
on some of the subdivision objects or evolver starting files that you
have seen before ...
A
genus-3 object with suitably aligned quadrilateral parametrization.
A sample collection of genus-4 objects ...
Some frequently encountered misconceptions:
Pr#4: Only 6 (u,v) knot value pairs in each direction affect the shape
of the patch (see also Quiz#1).
Pr#7: A "minimal surface" must have H=0 everywhere -- not just
minimize some arbitrary energy functional.
Pr#9: The extraordinary n-gons themselves do become more regular; they
shrink to affinely distorted regular n-gons.
Pr#13.3: even for the triangular subdivision schemes by Loop and Zorin
the vertex growth factor is 4!
Pr#16b: Refinement is not a "clean-up" operation for messed-up meshes.
Pr#18a: Surfels also typically carry color and shading information.