G² continuity for multiple surfaces fitting

Fitting 3D known data into sculptured surfaces has received extensive attention. However, most algorithms available are suitable only for an isolated surface. A part typically contains multiple surface regions that must be blended to a degree of continuity. The conventional approach based on blending, lofting, stitching, etc. cannot guarantee the quality of the surface near the jointed area. The purpose of this work is to present a surface-fitting algorithm for multiple sets of data, concentrating on G² continuity across the boundary of the fitted surfaces. The proposed surface-fitting algorithm essentially fits several sets of data simultaneously, and yields a B-spline surface for each set of data. The G⁰, G¹, and G² continuity conditions between B-spline surface patches were addressed. Based on these results, additional constraints were specified to achieve G² continuity across the surface boundary. A successful demonstration of the proposed strategy is provided also.