G2 G 2 B-spline interpolation to a closed mesh
This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh 1G2 G 2 -continuously 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 G 2 continuity condition is applied to achieve curvature continuity. Afterwards, the boundary curves, the first- and the second-order cross-boundary derivative curves are constructed fulfilling G2 G 2 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 G 2 continuity condition matrices is also strictly proved to be 2n?3 2 n ? 3 , and the method of tangent-vector estimation is improved to avoid petal-shaped patches in interpolating solids of revolution. Several examples demonstrate its feasibility.
smooth mesh interpolation coons b-spline surface g2 g 2 -continuity g2 g 2 g2 g 2 g 2