Jupyter Labs [toc]

Jupyter Labs

Jupyter Lab notebooks with examples of use of the splinekit library.

The notebooks below are distributed in compressed format. Their execution relies on the availability of a workable Jupyter Lab environment and of an installed version of the splinekit library, along with its dependencies. To install everything in one shot, launch a terminal and issue the command:

pip install numpy scipy sympy matplotlib jupyterlab ipywidgets splinekit

Module bsplines

bspline_bases Illustration of the cardinal B-spline basis \(\eta,\) the dual B-spline basis \(\mathring{\beta},\) and the orthonormal B-spline basis \(\phi.\)

bspline_interactive_shape Illustration of the B-spline basis \(\beta\) and its variational forms \(\dot{\beta}\) and \(\int\beta,\) one degree at a time.

bspline_inverse_sequence Illustration of the B-spline inverse sequence \(\left(b^{-1}\right)\) and its periodized version.

bspline_m_scale Illustration of the multiresolution embedding of the B-spline bases \(\beta.\)

bspline_numeric_stability Four approaches to the computation of the B-spline basis \(\beta,\) and discussion of their relative merits in terms of speed and numerical accuracy.

bspline_poles Visualization of the so-called B-spline poles and their relation to the annihilating sequences for B-splines.

bspline_random1d Discussion of how splines differ from B-splines and display of a random one-dimensional spline that evolves dynamically.

bspline_random2d A random two-dimensional spline curve that evolves dynamically.

bspline_static_shape Illustration of the B-spline basis \(\beta\) and its variational forms \(\dot{\beta}\) and \(\int\beta,\) several degrees jointly.

bspline_vs_exponentials Relation of the B-spline basis \(\beta\) to the \(\exp,\) the \({\mathrm{Erf}},\) and the Gaussian functions.

bspline_vs_pi How B-splines \(\beta\) lead to the mathematical constant \(\pi.\)

bspline_vs_polynomials How to build a monomial out of B-splines; which polynomial results from the sum of monomial-weighted integer-shifted B-splines; and convolution of a monomial with a B-spline.

bspline_vs_trigonometry Relation of the B-spline basis \(\beta\) to the \(\sin\) and \(\cos\) functions.

Module spline_padding

padding How to extend a finite-length vector of data to a virtually infinite-length sequence.

Class PeriodicSpline1D

periodicspline1d_bounds How to obtain a periodic one-dimensional spline of arbitrary degree that bounds another spline, by above or by below.

periodicspline1d_creator How to create a periodic one-dimensional spline that interpolates data samples.

periodicspline1d_evaluate How to evaluate a periodic one-dimensional spline at just one argument or at a series of arguments.

periodicspline1d_polynomials How to access the polynomial pieces of a piecewise-polynomial periodic one-dimensional spline.