Computers and Mathematics with Applications Semi-structured B-spline for Blending Two B-spline Surfaces

Surface blending is a useful operation in geometric design for rounding sharp edges or corners. Meanwhile, NURBS has already become the de facto industrial standard in existing CAD/CAM systems. Therefore, it is required to study how to blend two B -spline surfaces. However, two arbitrary B -spline surfaces (called base surfaces) are hard to be blended with a B -spline surface (called blending surface) because the knot vectors of the two base surfaces are usually mismatched. In this paper, we proposed a curve-based spline representation, i.e., the semi-structured B-spline surface, which is generated by skinning a series of B -spline curves with different knot vectors. By assigning suitable knot vectors to the head and tail skinned curves, the semi-structured B -spline surface can blend two B -spline surfaces smoothly without disturbing them at all. We formulated the B -spline surface blending problem as an optimization problem with continuity constraints, and the continuity between the base and blending surfaces can reach G 2 or C 2 . Examples illustrated in this paper validate the effectiveness and efficiency of our method.

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