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B-spline Curves: Important Properties

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B-spline curves share many important properties with Bézier curves, because the former is a generalization of the later. Moreover, B-spline curves have more desired properties than Bézier curves. This page lists some of the most important properties of B-spline. We shall only concentrate on clamped B-spline curves here. In the following we shall assume a B-spline curve p(u) of degree p is defined by n + 1 control points, knot vector U = { u0, u1, ...., um } with the first p+1 and last p+1 knots "clamped" (i.e., u0 = u1 = ... = up and um-p = um-p+1 = ... = um). This nice property allows us to design very complicated shapes with lower degree polynomials. For example, the right figure below shows a Bézier curve with the same set of control points. It still cannot follow the control polygon nicely even though its degree is 10! In general, the lower the degree, the closer a B-spline curve follows its control polyline. The following figures all use the same control polyline and knots are cla

B-spline Curves: Important Properties B-spline Curves: Important Properties B-spline curves share many important properties with Bézier curves, because the former is a generalization of the later. Moreover, B-spline curves have more desired properties than Bézier curves. This page lists some of the most important properties of B-spline. We shall only concentrate on clamped B-spline curves here. In the following we shall assume a B-spline curve p ( u ) of degree p is defined by n + 1 control points, knot vector U = { u 0 , u 1 , ...., u m } with the first p +1 and last p +1 knots

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