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# scipy.interpolate.insert¶

scipy.interpolate.insert(x, tck, m=1, per=0)[source]

Insert knots into a B-spline.

Given the knots and coefficients of a B-spline representation, create a new B-spline with a knot inserted m times at point x. This is a wrapper around the FORTRAN routine insert of FITPACK.

Parameters: x (u) : array_like A 1-D point at which to insert a new knot(s). If tck was returned from splprep, then the parameter values, u should be given. tck : a BSpline instance or a tuple If tuple, then it is expected to be a tuple (t,c,k) containing the vector of knots, the B-spline coefficients, and the degree of the spline. m : int, optional The number of times to insert the given knot (its multiplicity). Default is 1. per : int, optional If non-zero, the input spline is considered periodic. BSpline instance or a tuple A new B-spline with knots t, coefficients c, and degree k. t(k+1) <= x <= t(n-k), where k is the degree of the spline. In case of a periodic spline (per != 0) there must be either at least k interior knots t(j) satisfying t(k+1)

Notes

Based on algorithms from [R73] and [R74].

Manipulating the tck-tuples directly is not recommended. In new code, prefer using the BSpline` objects.

References

 [R73] (1, 2) W. Boehm, “Inserting new knots into b-spline curves.”, Computer Aided Design, 12, p.199-201, 1980.
 [R74] (1, 2) P. Dierckx, “Curve and surface fitting with splines, Monographs on Numerical Analysis”, Oxford University Press, 1993.