Formula omitted] B-spline interpolation to a closed mesh

Abstract

This paper focuses on interpolating vertices and normal vectors of a closed quad-dominant mesh 1 1 A mesh is quad-dominant if it contains quad facets as its majority. The quantity of quad facets is much more than the quantity of triangular and other multi-sided facets. 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 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 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 G 2 continuity condition matrices is also strictly proved to be 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.