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Semi-structured \(B\)-spline for blending two \(B\)-spline surfaces. (English) Zbl 1362.65024

Summary: 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.

MSC:

65D07 Numerical computation using splines
65D17 Computer-aided design (modeling of curves and surfaces)
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