Mark Halstead, Michael Kass, Tony D. DeRose
Abstract:
We describe an efficient method for constructing a smooth surface
that interpolates the vertices of a mesh of arbitrary topological
type. Normal vectors can also be interpolated at an arbitrary subset
of the vertices. The method improves on existing interpolation
techniques in that it is fast, robust and general. Our approach is to
compute a control mesh whose Catmull-Clark subdivision surface
interpolates the given data and minimizes a smoothness or
"fairness" measure of the surface. Following Celniker and
Gossard, the norm we use is based on a linear combination of
thin-plate and membrane energies. Even though Catmull-Clark surfaces
do not possess closed-form parametrizations, we show that the
relevant properties of the surfaces can be computed efficiently and
without approximation. In particular, we show that (1) simple, exact
interpolation conditions can be derived, and (2) the fairness norm
and its derivatives can be computed exactly, without resort to
numerical integration.
Available in the Proceedings of SIGGRAPH 1993.