Get a mathematical expression of any curve

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Permalink Reply by David Rutten on December 12, 2016 at 8:28am

What do you mean by mathematical expression? f(x)→y?  f(t)→x; g(t)→y?  f(x,y)=c?

Either way I'm not sure it's possible and I am sure it is difficult. 

Permalink Reply by Raqib Karimi on December 12, 2016 at 1:32pm

For instance, a straight line in 2D has the parametric equation p:=[t,0,0] (The function f(x)=ax+b) This is very simple. 

If I draw a random interpolate curve in Rhino, is there any options to get the parametric equation of this line? For example: ax^4+bx^3+cx^2+d etc etc. 

Permalink Reply by David Rutten on December 12, 2016 at 2:47pm

For instance, a straight line in 2D has the parametric equation p:=[t,0,0] (The function f(x)=ax+b) This is very simple. 

Unless the line is vertical, in which case an explicit equation won't work.

No, there is typically no way to represent a bezier/nurbs curve using a polynomial of the form f(x) = ax^p + bx^(p-1) + cx^(p-2) + ... + fx + g

A nurbs curve consists of a collection of piece-wise polynomials for each spatial dimension it is defined in. The polynomials have a certain amount of continuity where they meet (this continuity is of a higher order when the curve degree is higher), but they completely separate entities.

Permalink Reply by franco ferreiro on March 27, 2017 at 3:49pm

Hi Raqib,

Just considering the title of your post you might want to take a look at Fourier Series if you already didn't

https://en.wikipedia.org/wiki/Fourier_series