Periodic Splines [toc]

Demos

These demos illustrate some uses of the splinekit.PeriodicSpline1D class.

The demos rely on the Jupyter Lab deployment of Python. They run in-browser and do not necessitate anything to be installed beforehand. Edits to the notebooks will persist for a time in the cache of your browser. This duration is ephemeral and uncontrolled; dot not rely on it for persistent storage.

Hint

• To discard your modifications and revert to the notebooks as distributed, choose the entry <   ⃠ Clear Browser Data> from the menu <Help>.

• To run code, click on a notebook cell and hit the <SHIFT-CR> keys ⇧⏎.

Contents:

• Plots of Periodic One-Dimensional Splines
  • Periodic One-Dimensional Spline Objects
  • Plots
• Random One-Dimensional Splines
  • Spline Real Functions
• Random Two-Dimensional Spline Curves
  • 2D Curve with 1D Spline Cartesian Components
  • About Smoothness
    • Kinks
• Constructors of Periodic One-Dimensional Splines
  • Periodic One-Dimensional Splines
    • Defining Parameters
    • Regularizations
      • From Noiseless Samples
      • From Noisy Samples
• Simple Operations on Periodic Splines
  • Purpose
    • Additional Delay
    • Addition of a Constant
    • Multiplication by a Constant
    • Negation
    • Mirroring
• Spline Statistics
  • Average vs Mean
  • Variance
  • Bounds
  • Illustration
• Polynomial Pieces of Splines
  • Roadmap
  • Construction of the B-Spline
    • Polynomial Simple Element
      • Derivative of a Polynomial Simple Element
    • B-Spline
  • Construction of a Spline
    • Evaluation of Splines
      • Evaluation Matrix
      • Ancillary Variables
      • Vector of Spline Coefficients
      • Vandermonde Vector
    • Spline Pieces
• Evaluation of Splines
  • Linear-Algebra Formulation
  • Evaluation at a Single Argument
  • Evaluation at Multiple Arguments
  • Experimental Performance
    • Results
    • Discussion
• Upper and Lower Bounds of Splines
  • Upper Bound
  • Upper Bound over a Unit Interval
    • Bound of Higher Degree
    • Bound of Same Degree
    • Bound of Smaller Degree
    • Global Bound
  • Generalizations