Chaikin Curves in C#: An alternative curve generation algorithm

A chaikin curve, increasing in order each frame.

A little while ago I was curious to know if there were any other ways to generate a smooth curve other than with a Bezier Curve. Turns out the answer is yes, and it comes in the form of a Chaikin Curve, which was invented in 1974 by a lecturer in America by the name of George Chaikin. A few days (and a lot of debugging) later, I found myself with a Chaikin curve generator written in pure C♯ (I seem to have this fascination with implementing algorithms :P), so I thought I'd share it here.

Before I do though, I should briefly explain how Chaikin's algorithm actually works. It's actually quite simple. If you have a list of control points, and you were to draw a line through them all, you'd get this:

Some lines before the chaikin algorithm has been run.

The magic of the algorithm happens when you interpolate between your control points. If you build a new list of points that contains points that are ¼ and ¾ along each of the lines between the current control points and draw a line though them instead, then the line suddenly gets a lot smoother. This process can be repeated multiple times to further refine the curve, as is evidenced in the animation above.

This page is very helpful in understanding the algorithm if you're having trouble getting your head around it.

My implementation makes use of the PointF class in the System.Drawing namespace, and also has the ability to generate an SVG version of any generated curve, so that it can be inspected and debugged.

You can find my implementation here: Chaikin Generator - comments and improvements are welcome!

Instructions on how to use to use it are available in the README, and the class is fully documented with Intellisense comments, so it should feel fairly intuitive to use. I've tried to use patterns that are present in the rest of the .NET framework too, so you can probably even guess how to use it correctly.

Additionally, I 'm going to try put it up as a Nuget package, but currently I can't get Nuget to pack it currently on linux (when I do, you can expect a tutorial on here!)

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Art by Mythdael