Comments on: Reverse engineering Bezier curves

By: Mike

Mike — Thu, 29 Jul 2010 04:44:11 +0000

Man, you are awesome!!!!!! this article is fantastic. thanks!!!!!!!!!!!!!!!!!!!!!!!

By: Vincent Tan

Vincent Tan — Fri, 16 Oct 2009 13:18:40 +0000

Cardinal splines *do* look similar to my formulation. Thanks Bill.

By: Bill

Bill — Thu, 15 Oct 2009 21:13:26 +0000

You might want to look into cardinal splines. They are the typical way to solve a point interpolation problem:
http://en.wikipedia.org/wiki/Cardinal_spline#Cardinal_spline

It may be equivalent to your formulation… I confess that I just skimmed your equations. I ended up here by mistake when looking for something else.

By: A Polymath Programmer survey, because I can't read minds | Polymath Programmer

Thu, 01 Oct 2009 09:01:16 +0000

[...] Reverse engineering Bezier curves [...]

By: Those variables on Bezier curve equations are not fixed | Polymath Programmer

Thu, 09 Jul 2009 09:02:29 +0000

[...] wrote something on reverse engineering Bezier curves about… *goes to check* woah, 2 years ago! I don’t remember it being that long… [...]

By: Vincent Tan

Vincent Tan — Fri, 07 Nov 2008 16:31:53 +0000

Hey Guus, let me know how it turns out. I want to know if it can be scaled to higher degree Bezier curves too.

By: Guus

Guus — Thu, 06 Nov 2008 20:51:20 +0000

Vincent,

Thanks, I will put some effort in resolving this. There are a few mathematicians in my family, so I should be able to get help.

Ciao,
Guus.

By: Vincent Tan

Vincent Tan — Thu, 06 Nov 2008 13:03:47 +0000

Hi Guus, suppose that you want a Bezier curve passing through 10 points. Then you’re working with a degree 9 Bezier curve, and there are 8 unknowns (and not 2, as in u and v).

If you follow the logic I wrote, you’d have to solve an 8 by 8 matrix. I don’t know the required conditions to guarantee a solution.

This is why you’d need to do Gaussian elimination to iteratively compute a solution, if there’s one (instead of the quick and dirty method I used with a 2 by 2 inverse matrix multiplication).

You’re welcome to do research on how to solve 8 linear equations with 8 unknowns using Gaussian elimination. That’s how I would do it if I wanted.

By: Guus

Guus — Wed, 05 Nov 2008 21:31:01 +0000

Good work Vincent!

This is exactly what I need, only I typically have more than four points.

Have you any idea how to go about this? For segments to match, the angles must match. The only conclusion is that I need to vary u and v. It should be possible, I think, but the math eludes me.

Tia,
Guus.

By: Linear and cubic interpolation | Polymath Programmer

Linear and cubic interpolation | Polymath Programmer — Mon, 29 Sep 2008 09:02:27 +0000

[...] really want to write anything on the subject after I remember my Hermite splines… I love Bezier curves though, so I thought maybe I can write something with [...]