Providing local interpolation, tension and normal control in the manipulation of Loop subdivision surfaces

Abstract

Recursive subdivision surfaces allow a lot of freedom in designing surfaces of arbitrary topology. Tools to manipulate them however are still not as powerful as existing tools for longer established modeling paradigms such as for example B-spline surfaces. Furthermore the most well behaved and most widen, used schemes are approximating schemes, not interpolating their initial control points. In this paper, we describe a new modeling paradigm providing local interpolation together with interactive normal and tension control to the approximating Loop scheme, without interfering with its uniform subdivision rules. These tools are investigated for vertices both at the interior and at the border.