# Spline

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1. ## [Solved] 2D linear regression problem

I recommend lapack, or its C interface, lapacke. The function you are looking for is "LAPACK_dgels", http://www.netlib.org/lapack/lapacke.html
2. ## Upper and lower bound for NURBS length

Uh, you need to help me out here... how are these guys going to help me? Save asking them, I mean...? Perhaps I should re-state my intentions. What I currently do in order to determine the length of a nurbs curve is to split it into the non-empty intervals defined by the knot vectors and perform a piece-wise numerical integration (my special thanks go to Gauss & Legendre...). Now I split the intervals in half and perform another iteration. The difference between the larger and the sum of the two corresponding smaller intervals are my error estimates. Until the sum of error estimates is smaller than some ?, I recursively split the interval with the largest error estimate. For all curves I have tested so far this works well and all, however, I lack a (mathematically sound!) argument as to the "real" error bound. Or another approach that has such a guarantee - although my current method seems to give good results, an error bound would be rather large due to my derivate estimation alone. And while De Casteljau has defined a numerically sound algorithm to evaluate Bezier curves, and the NURBS basis can, for some degenerate cases, degenerate to Bernstein polynomials, I fail to see the connection to my problem and would appreciate any more concrete hints. Kind regards Spline