Adaptive Knot Placement in Non-uniform B-spline Surface Fitting

Knot placement of non-uniform B-spline is studied, and an iterative surface fitting scheme is proposed by exploring the degrees of freedom of knots to improve the fitting surface's quality. Our algorithm takes as input triangular meshes with parameterization. In the first iteration, the parametric domain is partitioned into several sub-regions with equally accumulated surface geometric information, and the coordinates of the centroids are chosen as the candidates of knots; in the following iteration steps, we partition the regions according to the fitting errors analogously while the centroids generated by previous steps remain unchanged. The fitting surface's quality is progressively improved as more control points are adaptively introduced into the region of the surface with more features or larger fitting error. Several experiments demonstrate the efficacy of our method in fitting surface with distinct geometric features.