Abstract
This chapter discusses the composite surfaces and spline interpolation. B-spline plays an important role in current surface design methods. For curves, triple end knots meant that the first and last two B-spline control points were also Bézier control points. The B-spline control points di for which i or j equal 0 or 1, are also control vertices of the piecewise Bézier net of the surface. Thus, they determine the boundary curves and the cross boundary derivatives. This corresponds to interpreting the B-spline control net row by row as univariate B-spline polygons and then converting them to piecewise Bézier form. The Bézier points thus obtained—column by column—may be interpreted as B-spline polygons, which one may again transform to Bézier form one by one. From the Bézier form, one may at present transform to any other piecewise polynomial form, such as the piecewise monomial or the piecewise Hermite form.
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