Modeling smooth shape using subdivision on differential coordinates
Traditional subdivision schemes are applied on Euclidean coordinates (the spatial geometry of the control mesh). Although the subdivision limit surfaces are almost everywhere C2 C 2 continuous, their mean-curvature normals are only C0 C 0 . In order to generate higher quality surfaces with better-distributed mean-curvature normals, we propose a novel framework to apply subdivision for shape modeling, which combines subdivision with differential shape processing. Our framework contains two parts: subdivision on differential coordinates (a kind of differential geometry of the control mesh), and mutual conversions between Euclidean coordinates and differential coordinates. Further discussions about various strategies in both parts include a special subdivision method for mean-curvature normals, additional surface editing options, and a version of our framework for curve design. Finally, we demonstrate the improvement on surface quality by comparing the results between our framework and traditional subdivision methods.
subdivision differential coordinates surface editing