Surface reconstruction using simplex splines on feature-sensitive configurations

Recently, new non-tensor product splines, called as triangle configuration B-splines (TCB-splines), have been proposed, which generalize the Delaunay configuration B-splines (DCB-splines) by introducing more flexibility in knot geometry while preserving the most attractive properties of univariate B-splines (Liu and Snoeyink, 2007). In this paper, we present a surface reconstruction framework that explores the flexibility of this spline for its use in shape modeling. Starting from a carefully designed feature-sensitive triangulation, we apply the so-call link triangulation procedure to obtain a feature-sensitive configuration family and then construct simplex spline bases as well as spline surface on it. The approximation quality of the surface is then progressively improved by adaptively adding more knots onto the parametric domain according to the fitting errors obtained in the previous fit procedure and updating the feature-sensitive configurations. Conditions to ensure the C1 continuity of the whole result surface are also provided. Our framework is tested on several models to demonstrate its efficacy and ability in preserving geometric features. Compared with DCB-splines, our splines can generate visually pleasant surfaces with smaller fitting errors by using the same number of knots and iterations. With almost the same number of control points, our framework produces more accurate and visually pleasant results than the classical B-spline surface fitting method based on adaptive knot placement strategy (Park, 2011). In addition, the resultant surface provides a control net, which enables an intuitive user interactive design.