Cubic spline interpolation with examples in Python

Name: Cubic spline interpolation with examples in Python
Rating: 4.4 (45 reviews)

Learn the math and get the code for constructing cubic interpolating splines

Created byDr. Thomas Maindl

Last updated 9/2017

English

What you'll learn

Construct one-dimensional cubic splines from scratch
Apply spline interpolation to their projects
Use spline library functions with confidence
Explain how to approach interpolation

Course content

4 sections • 15 lectures • 1h 33m total length

Introduction0:52
Course prerequisites3:48
Description of needed knowledge to get the most out of this course.
Polynomial interpolation3:22
Learn about polynomial interpolation and its side effects.
Polynomial interpolation example in Python (library function)11:48
This lecture walks you through using and visualizing polynomial interpolation using a SciPy library function and matplotlib.

The downloadable zip file contains the Python example as a Jupyter Notebook (Polynomial.ipynb) and as a pdf (Polynomial-ipynb.pdf).
Note that because of Udemy platform requirements the Notebook is inside the zip file and needs to be unzipped before use.
Run and modify the polynomial interpolation Python code

The spline concept3:45
This lecture introduces interpolating splines and some of their different types.
Linear splines4:50
Learn how to construct a linear interpolating spline.
Cubic splines11:18
Here the concept of cubic interpolating splines is introduced. The lecture also discusses the degrees of freedom when constructing such a spline interpolant (the boundary conditions) and outlines how to construct a cubic spline.
The downloadable zip file contains the Python example as a Jupyter Notebook (CubicSpline.ipynb) and as a pdf (CubicSpline-ipynb.pdf). This example shows how to use a SciPy library function to construct a cubic interpolating spline, which was used to create figures for the presentation and is included for reference only. The next section will deal with how actually to construct the splines.

Note that because of Udemy platform requirements the Notebook is inside the zip file and needs to be unzipped before use.
The spline cook book - how to calculate the spline coefficients0:01
This article lecture explains in detail how to calculate a cubic interpolating spline's coefficients for the different boundary conditions discussed in the previous lecture.
What is a spline?

The rocket project1:28
Answering the rocket example's questions will serve as a demonstration on how to construct, evaluate, and analyze a cubic interpolating spline. The example involves (generalized) natural, clamped, and not-a-knot splines that will be constructed, evaluated, differentiated, and integrated.
The Python code is attached to the next lecture, "The rocket example in Python I: preliminaries".
The rocket project in Python I: preliminaries4:26
Introduce the Jupyter Notebook Rocket.ipynb.
The downloadable zip file contains the Python example as a Jupyter Notebook (Rocket.ipynb) and as a pdf (Rocket-ipynb.pdf).

Note that because of Udemy platform requirements the Notebook is inside the zip file and needs to be unzipped before use.
The rocket project in Python II: data and helper functions14:02
Define input data and helper functions (spline coefficients, evaluate spline and its derivatives, evaluate spline integral).
The rocket project in Python III: splines with different boundary conditions12:47
Given the input data, calculate splines for different boundary conditions.
The rocket project in Python IV: visualization and solution8:58
Visualize the resulting splines and their derivatives; answer the example questions.
Apply the rocket example code
A Jupyter Notebook for periodic cubic spline interpolation8:09
This lecture demonstrates cubic spline interpolation with periodic boundary conditions with the Jupyter Notebook Periodic.ipynb.
The downloadable zip file contains the Python example as a Jupyter Notebook (Periodic.ipynb) and as a pdf (Periodic-ipynb.pdf).

Note that because of Udemy platform requirements the Notebook is inside the zip file and needs to be unzipped before use.
Implementing spline interpolation

Requirements

You should have calculus and linear algebra knowledge at a beginner level (continuous functions, derivatives of functions, systems of linear algebraic equations and their matrix representation)
You should have some coding experience in any programming language
You should be able to view and use IPython / Jupyter Notebooks

Description

This is a technical course designed for students and practitioners.

This course gets you

an introduction to spline interpolation
an understanding of what splines are
a detailed description of how to construct linear and cubic splines
Python code to construct cubic splines with different boundary conditions
the confidence of knowing what library functions for spline interpolation actually do

Who this course is for:

Engineering and science students
Computer graphics and game development students and professionals
People who always wanted to know what those splines are
Anyone interested in interpolation

Cubic spline interpolation with examples in Python

What you'll learn

Explore related topics

Course content

Introduction4 lectures • 20min

Linear and cubic splines4 lectures • 20min

Implementing cubic splines6 lectures • 50min

Closing1 lecture • 1min

Requirements

Description

Who this course is for: