How to plot the b_spline curve in x-y plane?

[xiaobrnbrn]

Hello, I want to know how to draw the red b-spline as shown in the above picture? Now I can get the bottom point coordinate traversed by the green dotted line through sampling, how to get the above one?

[xiaobrnbrn]

Also, how to display the complete b-spline generated from control points, rather than drawing it by sampling?