bspline | zju cg homework bspline | Machine Learning library

I have a sequence of knots of a cubic spline in the NumPy array knots, and I would like to efficiently evaluate an entire cubic BSpline basis which is represented by the array of knots at a certain point x. What I am currently doing is constructing the basis using the SciPy scipy.interpolate.BSpline class:

I'm generating some data for bsplines in R and I've encountered some weird behavior! If I plot the function without specifying line type, the curve looks okay. When I specify the line type, I get a plot where each point is connected with other points and I haven't been able to figure out why. Here is some reproducible code and the subsequent plots. Any explanation is much appreciated!

I'm working on saturate B-spline basis using standard roughness penalty.

I'd like to have plots like below:

But my plot looks like this:

I don't know why my plot() function cannot change the color of lines. Here is my code below and could you please tell me the reason with solution? Thank you in advance!

I have two solutions to this problem actually, they are both applied below to a test case. The thing is that none of them is perfect: first one only take into account the two end points, the other one can't be made "arbitrarily smooth": there is a limit in the amount of smoothness one can achieve (the one I am showing). I am sure there is a better solution, that kind-of go from the first solution to the other and all the way to no smoothing at all. It may already be implemented somewhere. Maybe solving a minimization problem with an arbitrary number of splines equidistributed?

Thank you very much for your help

Ps: the seed used is a challenging one

Using the fda package I have created the fd object called "curve":

I'm trying to create a PyPi package for my graphics framework Goopylib (https://github.com/BhavyeMathur/goopylib), and it is working for the most part.

All the package files are being created when I try to pip install my package - the only problem is that these package files are not being created in a directory of their own, rather just in the site-packages directory.

In these 2 screenshots, you can see that package files like the 'math' folder or the GraphWin.py file are being created in the site-packages folder and not a folder of their own.

Here what I would want my code to be organized like with the goopylib folder being inside the site-packages folder:

Here is my setup file:

Once again I am in over my head so please bear with me.

I have a B-spline (imported from Solidworks) that I can analyze with geomdl in python.
From geomdl I can extract the first and second derivatives as well as the tangent, normal, and binormal vectors for any given point on the spline.

From there I can calculate the curvature at that point from the first and second derivatives.

However I am not able to determine which way the curve is turning.

I would like to find the point that is at the center of curvature of current point of interest on the bspline.

I 'think' that the tangent vector and the normal vector both lie on the osculating plane of interest. The cross product would then give me the normal to the osculating plane. However I can not make this work.

At a minimum I need to know which way the curve is bending. i.e. CW or CCW.

But if I have the point at the center of curvature I would know pretty much everything about that point.

Is this correct?

To restate the question:

Given a point, the derivatives of the curve at that point, and and the Tangent, Normal, and BiNormal vectors, how do I find the center of curvature?

I'm trying to reproduce a function from a paper, which is specified only in terms of spline knots and coefficients. After finding this on stackoverflow, given a scipy interpolation object, from its knots and coefficients, I can recreate the scipy interpolation. However, the approach fails for the function specified in the paper. To reproduce a scipy interpolation I can do this: