@J.M. Hello, J.M. I have a question about the B-spline least-square fitting.
In this paper, (1996)Smooth surface approximation to serial cross-sections, the author used a parameter value resetting method to reduce error
However, when I implemented that formula in Mathematica, I discoved that some parameter values will become negative. Namely, which exceeds the normlized domain [0,1]
I would like to know your opinion when [email protected]. have time:)
@ShutaoTANG I actually haven't experimented with that method, but as a reminder: don't do it as $(\mathbf N^\top \mathbf N)^{-1}$ ("normal equations"); either use the LeastSquares[] function (LeastSquares[n, p]) or either of QRDecomposition[] or SingularValueDecomposition[] for the purpose.
In any case, I think this question of yours should be asked on main, as it is sufficiently complicated.
@J.M. OK, thanks a lot:) In fact, I didn't use $(\mathbf N^\top \mathbf N)^{-1}$. Alterlatively, I applied LinearSolve[]. My main confusion is the following formula:
Here, I using CocDeBoor[] to compute P(uj) and calcTangent[] to calculate the Cu(uj). However, the parameter that with the help of the above formula exceeds the domain [0,1]. Very strange.
