Continuity Transition with a Single Regular Curved-Knot Spline Surface

We propose a specialized form of the curved-knot B-spline surface of Hayes [1982] that we call regular curved-knot spline surface. Unlike the original formulation where the knots of the first parametric coordinate can evolve arbitrarily with respect to the second coordinate, our formulation designs the knot functions as special curves that guarantee a monotonic blending of the knots corresponding to opposite surface boundaries. Furthermore, we demonstrate that local derivatives on the boundary can be described as an ordinary B-spline surface. The latter property allows for constructing smooth transitions between B-spline boundaries with different knot vectors.