Streamline modeling with subdivision surfaces on the Gaussian sphere

Curvature and variation of curvature are the essential factors in determini ng the fairness of a surface. Unfortunately, most of the traditional surfac e representation schemes do not provide users with direct manipulation tech niques of these quantities. Streamline modeling, a recently proposed free-f orm surface design methodology, is aimed at overcoming this shortcoming by allowing a user to control tangent vectors (and, consequently, curvature an d variation of curvature) of the surface to be designed directly. A free-fo rm surface is regarded as a set of streamlines: iso-parametric lines define d by blending directions of tangent vectors instead of blending positions o f control points. This new surface design methodology can generate high qua lity smooth surfaces but requires much processing power for tangent vector blending. In this paper, we present subdivision based blending techniques o f tangent vectors. These techniques can be used to develop subdivision tech niques for curves and surfaces on the Gaussian sphere, such as Doo-Sabin, C atmull-Clark, and Kobbelt subdivisions. We also present new streamline mode ling techniques based on the new tangent vector blending techniques. The ne w techniques reduce the processing time for the integration process require d in streamline modeling. A prototype system based on the new techniques sh ows that free-form surface design using the streamline modeling methodology can achieve real-time performance. (C) 2001 Elsevier Science Ltd. All righ ts reserved.