Multi-resolution Mesh Fitting by B-spline Surfaces for Reverse Engineering

This paper presents a new multi-resolution mesh fitting algorithm, extending the adaptive patch-based fitting scheme where each underlying quadrilateral is recursively subdivided into four sub-patches. In this paper, the G¹ continuity constraints, which mainly consist of perpendicular constraints and twist compatibility constraints, are deduced for B-spline patches. In order to construct a unique B-spline patch for each quadrilateral, the mesh vertices are applied in a least-square approximation, and the energy functions associated with a patch are minimized. In contrast to the original algorithm, this paper fits the mesh into B-spline patches instead of Bezier patches with G¹ continuity. The B-spline patches make the algorithm have more free control points to be used for optimizing the shape of the quadrilateral patches to achieve higher flexible patch control and less recursive times.