Help regarding the "spline_math_curve.html" page

Translated by Google Traduction, from the french version : Help - Info, in french.

A few decades ago I learned about degree 3 spline functions and wrote programs that use them to pass a curve through given points in a plane.
I've been waiting for such curves to be implemented in software like Inkscape and FreeCAD for a long time.
I saw at the end of december 2022 on Youtube the excellent video of Freya Holmér called: "The continuity of Splines"

Unfortunately, the curve that I would call "Math-spline", based on spline functions and that I implemented in the web page: is not described by Freya Homér nor used in the software that I know of.

Here are some characteristics of this "Math-spline" curve:
° continuous
° of tangents varying continuously along the curve
° of radii of curvature varying continuously along the curve, it is G2
° pass through all given points
° does not require any additional points to define the curve
° can easily be closed
° can have break points, so where the tangent varies discontinuously
° the influence of the points is done practically on the 8 neighboring segments of the point
° is invariant under rotation, symmetry and homothety.
° is easy to calculate, quickly

Explanations of some features of the implementation page

This page is not used for anything other than to make tests on the generation of curves passing through given points and using the spline functions.
I would love that such curves could be generated in software like Inkscape and FreeCAD.
The illustration of generation of a curve passing through given points is done in 2 dimensions, in an 800x800 canvas.
Obviously, we can generalize the way to curves passing through points defined in a 3-dimensional space and even in a space of any dimensions.

For more information, in particular on mathematics and algorithms, see French version .pdf and .odt
Version automatically translated into English .pdf and .docx
with Google Translate.

In this Web page, Youtube videos in french on this subject.

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Page mise à jour le 20 janvier 2023 par Bernard Gisin     ( Envoyer un e-mail )
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