Parameterizing N-holed Tori

Published in Mathematics of Surfaces, 2003

Using hyperbolic geometry to parameterize n-holed objects. We define a parameterization for an n-holed tori based on the hyperbolic polygon. We model the domain using a manifold with 2n+2 charts, and linear fractional transformations for transition functions. We embed the manifold using standard spline techniques to produce a surface. parameterization, hyperbolic geometry, n-holed tori