How to Find Mathematical Function of Curves

Replies to This Discussion

Permalink Reply by Leonardo Nuevo Arenas on December 17, 2015 at 9:51am

Could you please post an example of the images you want to use?

Permalink Reply by Arend on December 17, 2015 at 9:53am

What do you mean by mathematical functions? What do you want to achieve?

Rhino supports different kind of definitions for curves (e.g. a circle, arc, rectangle, line, polyline), but most of them can be represented as a nurbs curve (ToNurbsCurve() method on any kind of curve).

The mathematical definition of nurbs curves is quite open an can be found in any geometry textbook.

https://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

Permalink Reply by MattM on December 17, 2015 at 10:01am

What I'm looking for is the exact curve's function of curves I draw in Rhino

For instance, I guess for a "S line" (photo attached) should be something like the following (whit numbers instead of a,b,c,d):

F(x)=y=a*X^3 - c*x^2+ bX + d

Thanks

Attachments:

• Capture.PNG, 18 KB

Permalink Reply by Ángel Linares on December 17, 2015 at 10:12am

Could this link help?

http://help.autodesk.com/view/MAYAUL/2016/ENU/?guid=GUID-84AD4364-9...

Permalink Reply by MattM on December 17, 2015 at 10:22am

Thanks,

I think this is interesting and useful for sure.

However, I would rather find a way to calculate the exact F(x)=y = ? of any curve I would draw in Rhino because my research will need to compare different kind of curves.

So, I would need the exact formula of each curve rather than the general formula ax ³ + by ² + 2cxy + 2dx +2ey + f = 0.

Basically, the output of the script would be the above or similar function with numbers instead of the parameters (a, b, c, d, e).

Permalink Reply by David Rutten on December 17, 2015 at 11:29am

It is not possible to represent any curve in Rhino as a one-dimensional polynomial. Nurbs curves are piece-wise curves where each piece is defined by three polynomials (one for x, one for y and one for z).

It is possible to fit a polynomial through a set of points, but there's absolutely no guarantee that the equation in between the points is anywhere near the original curve.

Permalink Reply by David Rutten on December 17, 2015 at 11:55am

There do exist good polynomial fitting algorithms. MathNet has several.

The attached file uses those to create a polynomial of a specific degree which resembles the sampled points as best as possible over a chosen domain.

Attachments:

• polynomialfinder.gh, 8 KB
• MathNet.Numerics.dll, 1.1 MB

Permalink Reply by MattM on December 21, 2015 at 6:56am

Thank you very much,

I will test some of these and let you know.

Matt

Permalink Reply by Hakam husam on March 5, 2017 at 12:59pm

David, I downloaded both files, and unblocked MathNet.Numerics.dll and kept it where I downloaded it in the C:/WINDOWS/DOWNLOADS folder, do I have to copy it somewhere? I am getting this error 

Permalink Reply by Hakam husam on March 5, 2017 at 1:11pm

ok sorry, I just had to close and open rhino, that error is gone, however I am receiving a new error regarding the matrix

Permalink Reply by Alice Emma Mariani on September 2, 2019 at 8:18am

Hi, i'm trying to find an equation of a curve i created from grasshopper.

 

I dowloaded your script, i closed and restarted rhino i also copied the .dll file in the libriaries grsshopper folder but it still says that it's not to be found.. were did i get it wrong ?

thank you for any help

Permalink Reply by Janice de Freitas Pires on June 30, 2017 at 6:33am

I'm using Geogebra software to find the exact formulas of the curves. I find it quite useful because you can insert an image and draw the curve points on top of this image and then create the curve from the points. The curve formula appears immediately in the expression window.