Optimization of NURBS Fitting for Non-symmetric Acetabulum Bone Surface with Bending Energy

This paper presents a proposed method of fitting NURBS (Non- Uniform Rational B-Spline) surfaces for freeform surfaces to obtain both accuracy and smoothness. This proposed method has been applied to reconstruct human acetabulum surfaces from given grid of data points (m × n) that are obtained from the opened bone layer contours. Three parameters of the NURBS surface, namely weights, control points and knot vectors are optimized to minimize fitting error. In order to obtain smoothness surfaces, the bending energy that related to surface curvature is used as a constraint of this optimization problem. In the simulation result, the smooth acetabulum model is obtained with an acceptable fitting error from a given bone data of dimension 43 × 50 × 39 mm. This result shows that this proposed method can be applied to reconstruct freeform surfaces.