Multi-level B-Spline Surface Fitting

Multi-level B-Spline surface fitting is a widely adopted algorithm in computer graphics primarily used for achieving smooth surface approximations. This algorithm utilizes uniformly distributed control points and generates surfaces with high smoothness and geometric approximation accuracy through hierarchical fitting of these points. The implementation typically involves multiple resolution levels where coarse control points provide initial approximation, followed by finer-level adjustments using residual error minimization techniques. Key computational steps include basis function evaluation, control point coefficient calculation through least-squares minimization, and hierarchical error compensation. The algorithm finds extensive applications across various industries including industrial design, automotive design, aerospace engineering, and medical imaging, particularly in scenarios requiring high-precision surface reconstruction from scattered data points.