BSpline
A B-spline curve of degree p with controlPoints and a non-decreasing knots vector of length controlPoints.size + p + 1, after Piegl and Tiller, "The NURBS Book" (Springer, 1997). The curve is defined on the domain from knot p to knot controlPoints.size, is C^(p-k) where a knot has multiplicity k, and stays inside the convex hull of every p + 1 consecutive control points.
Create one with BSpline.clamped, BSpline.periodic or by interpolation with interpolatingBSpline.
Parameters
whether the curve is closed, as a periodic spline is; drawn as a closed contour or path
Constructors
Properties
Functions
The control points of the Bézier pieces of the curve, one list of p + 1 points per non-empty knot span of the domain: every knot in the domain, its ends included, is inserted until it has multiplicity p.
The derivative at parameter u.
The derivative B-spline of degree p - 1, with control points p·(Pᵢ₊₁ - Pᵢ) / (uᵢ₊ₚ₊₁ - uᵢ₊₁) and the inner knots; null for degree 1, whose derivative is piecewise constant.
The spline with knot u inserted once, by Boehm's algorithm (Piegl and Tiller, algorithm A5.1); it describes the same curve. With k the last knot index at or before u and s the multiplicity of u, the control points k - p + 1 to k - s are replaced by points on the edges of the control polygon.