G2G2 B-spline interpolation to a closed mesh

This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh 1G2G2-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 G2G2 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 G2G2 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 G2G2 continuity condition matrices is also strictly proved to be 2n−32n−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.

Research highlights
► A method is proposed to interpolate vertices/normals of a closed mesh G2G2-continuously.
► Only standard B  -spline Coons surfaces are used.
► The upper bound of the rank of the G2G2 condition matrix is strictly proved to be 2n−32n−3.
► A least-square adjustment based on homogeneous G2G2 continuity condition is proposed.
► The method of tangent-vector estimation is enhanced to avoid petal-shaped patches.