ϵ→-G2 B-spline surface interpolation

This paper proposes a method to construct a B-spline surface that interpolates the specified four groups of boundary derivative curves in the B-spline form. The discontinuity can be bounded by an arbitrary geometric invariant ϵ→ as the tolerance. The method first handles the six types of the compatibility problems by continuity-preserving reparameterization, knot-insertion and local control-point tuning. The transformed boundary conditions are then parametrically compatible, so the Coons strategy can be applied to construct the final interpolant. Not only can it be used in the reliable geometric modeling, but the approach also can be applied to many other algorithms that require compatibility guarantee.

► An interpolation method is proposed to achieve ϵ  -G2G2 continuity. ► The boundary conditions and the generated surface are all in the B-spline form. ► The geometric invariant measures of the angular and the curvature tolerances are used. ► This paper focuses on the six types of G2G2 compatibility problems from the algebraic view.