Hi Everyone

We are working on a project and the goal is to find a curve's function. While working on Nurbs, I figured out that we can define it with Control points, weight and Knots. OK! So the question pops up! Is there any mathematical equation for Nurbs?? I Put the points, weights and knots in the equation and get the curve? Afterall Nurbs modeling is based on mathematics so perhaps we can have its equation for research.

I found this paper related to my question

https://www.cs.ubc.ca/~heidrich/Papers/CHAMONIX.96.pdf

Fitting Uncertain Data with NURBS

Fitting of uncertain data, that is, tting of data points

that are subject to some error, has important applications for example

in statistics and for the evaluation of results from physical experiments.

Fitting in these problem domains is usually achieved with polynomial

approximation, which involves the minimization of an error at discrete

data points. Norms typically used for this minimization include the l1, l2

and l1 norms, which are chosen depending on the problem domain and

the expected type of error on the data points.

In this paper we describe how the l1 and l1 norms can be applied

to integral and rational B-spline tting as a linear programming problem.

This allows for the use of B-splines and NURBS for the tting of uncertain

data.

Fitting Uncertain Data with NURBS