G2 B-spline interpolation to a closed mesh

This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh1 G2continuously using regular Coons B-spline surfaces, which are popular in industrial CAD/CAM systems. We first decompose all non-quadrangular facets into quadrilaterals. The tangential and second-order derivative vectors are then estimated on each vertex of the quads. A least-square adjustment algorithm based on the homogeneous form of G2 continuity condition is applied to achieve curvature continuity. Afterwards, the boundary curves, the firstand the second-order cross-boundary derivative curves are constructed fulfilling G2 continuity and compatibility conditions. Coons B-spline patches are finally generated using these curves as boundary conditions. In this paper, the upper bound of the rank of G2 continuity condition matrices is also strictly proved to be 2n − 3, and the method of tangentvector estimation is improved to avoid petal-shaped patches in interpolating solids of revolution. Several examples demonstrate its feasibility. © 2010 Elsevier Ltd. All rights reserved.