Efficient and adaptive T-spline surface fairing using bilateral filter

The surface fairing is an essential procedure connecting computer-aided design (CAD) and computer-aided engineering (CAE), and it assists the designer in readjusting the surface to obtain a smoother visual effect in CAD and affects the simulation result in CAE which is the benchmark to redesign the models. The traditional energy minimization algorithm on fairing spline surfaces is time-consuming and has limited improvement. Inspired by mesh denoising methods, we generalize the bilateral filter to the continuous T-spline surface domain and propose efficient and adaptive bilateral filtering approaches for T-spline surface fairing. The filter measures the displacement of control points along their normal vectors, leveraging 1-ring neighboring angles/area/angle–area weight methods to approximate normal vectors when direct normals are unavailable. Our algorithm demonstrates remarkable performance in eliminating serrated points, which is challenging in parametric field fairing of spline surface, maintaining boundary geometries compared with other approaches, and suitable for unstructured T-spline.