Rudimentary implementations of Newton and Halley’s methods have been added to the Singularity library. Due to the availability of a cheap second derivative, Halley’s method will most likely be used in the upcoming Bezier y-at-x development. Download Singularity here.

## 5 thoughts on “Newton and Halley’s Methods”

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Excellent stuff, Jim. I was wondering how could we use the Newton method to find the closest point on a BezierSpline.

I finally found some time to play with your library and I’m really enjoying it.

Carlos – if memory serves, this was covered in Graphic Gems – a quick Google search uncovered a link – http://tog.acm.org/GraphicsGems/gems/NearestPoint.c

If time permits, I’ll dust the cobwebs off my memory and add this to Singularity after the y-at-x development.

thanks!

– jim

Hello. Do you know any resource that explains what you mean by this? 🙂 I kind of understand it, but then when it would come to programing it I get completely lost.

What is this cheap second derivative you mention? I’ve just always had a hard time taking math equations and performing them in Flash so any guidence you could provide would be very helpful.

Thanks for the tip Jim. It would be great if we could get Singularity from svn like googlecode. I’m using it more and more.

Carlos – I’ve been thinking about that; probably something that will happen when I get a chance to finish off the rigging classes and perhaps refactor some of the library. It started out as a code repository meant simply to illustrate algorithms. Now, it’s growing into something completely different.

regards,

– jim