Is it a Cubic B-Spline Function?

[swaraj1112]

I ran the code twice with 5 control points, in the second run I changed the fourth control point by a certain magnitude and observed that the global shape of the spline changed completely. I was hoping for more local control.

[ttk592]

I don't use b-splines as a basis internally, but the default spline (tk::spline::cspline) will create the same result as if the interpolation was done with cubic b-splines as basis. See examples/plot_bspline.cpp. However, why do you expect a local behaviour with b-splines? If you modify a single grid point (x_i, y_i) it will modify all the coefficients and the entire spline will change globally. For a more local behaviour you can use tk::spline s(X,Y,tk::spline::cspline_hermite) but this is only once cont differentiable and therefore not a b-spline.

Results for b-splines and tk::spline::cspline are indistinguishable:

$ ./plot_bspline.sh -b 1 -t cspline

$ ./plot_bspline.sh -b 1 0 0 0 1 0 0.5 -t cspline

[ttk592]

To illustrate, changing a single input grid point has the following impact:

C² spline (tk::spline::cspline): impacts the entire spline

C¹ Hermite spline (tk::spline::cspline_hermite): impacts two adjacent segments on each side