Can we fix some of the knot points and only optimize other points?

[HuangXiaoKai]

Often, I've encountered instances where fitting a closed curve didn't yield a closed outcome. There's a slight disparity between the first and last knot points. Alternatively, there are scenarios where certain points, such as extrema, should remain unchanged during the fitting process, with only the curve's slope being subject to alteration. How can we integrate specific knot points into the algorithm for fitting?