Cubic Spline Interpolation Tutorial

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Discussion Overview

The discussion revolves around cubic spline interpolation, including both classic and parametric formulations. Participants share tutorials, seek help with implementation issues, and discuss specific examples and potential errors in calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • Some participants express appreciation for the tutorials on cubic splines, noting their clarity and usefulness.
  • One participant shares their attempt to replicate results for cubic interpolation of a circle but encounters discrepancies in the plotted results, seeking advice on potential errors in their MATLAB code.
  • Another participant suggests that the method of fitting a circle with cubic polynomials may not be optimal, proposing the use of a single parametric cubic instead.
  • A participant identifies a potential error in one of the tutorial examples regarding the second derivative, leading to a discussion about the correct values and continuity of the polynomials.
  • There are multiple claims about the correctness of coefficient calculations, with some participants correcting each other and refining their expressions.
  • Several participants discuss the interpolation error associated with cubic spline methods and compare them to Hermitian cubic splines.
  • One participant raises concerns about discrepancies between their results and those from a cubic spline utility, prompting a discussion on boundary conditions and different interpolation methods.
  • Another participant identifies that the utility may use a 'not-a-knot' boundary condition, leading to further exploration of how this affects the results.

Areas of Agreement / Disagreement

Participants generally express appreciation for the tutorials, but there are competing views on specific implementations, potential errors, and the best methods for fitting curves. The discussion remains unresolved regarding the optimal approach to cubic spline interpolation and the implications of different boundary conditions.

Contextual Notes

Some discussions involve assumptions about boundary conditions and the specific algorithms used in different utilities, which may affect the results. There are also unresolved mathematical steps in some participants' calculations.

Who May Find This Useful

This discussion may be useful for individuals interested in cubic spline interpolation, particularly those seeking practical implementation advice, exploring different methods, or troubleshooting their own calculations.

  • #31
I was just browsing for related blog posts for my project research and I happened to

discover yours. Thanks for the excellent information!
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  • #32
Hello,
Thank you for this excellent tutorial!

I've now implemented cubic splines in C++ and shared the result on my website should anyone want a reference C++ implementation...

http://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html"

Marcus
 
Last edited by a moderator:
  • #33
toastedcrumpets said:
Hello,
Thank you for this excellent tutorial!

I've now implemented cubic splines in C++ and shared the result on my website should anyone want a reference C++ implementation...

http://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html"

Marcus

Thanks for the acknowledgment on your website!
 
Last edited by a moderator:
  • #34
Excellent tutorial.

Somebody knows the formula to calulate the 95%CI for the spline?
Thank you for your help.
 
  • #35
Hi,
I want the verilog or VHDL coding for performing cubic spline interpolation used in biomedical EMD processor
 
  • #36
I have a project:
The goal is to create a curve interpolation tool that functions the same as the spline sketch
tool in Pro/E. The input is a set of data points. The output is a cubic C2 B-spline curve.
I have to do it in MATLAB. I am very new to this subject and do not have much idea about it.
Can anyone help me with this project. Like suggesting me how and where I should start? I have only 15 days to complete this project.
Thanks.
 

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