Ribbon trail Curve interpolate Help

hello. i’m Artist and i want Change trail curve Design.
i find “http://www.cemyuksel.com/research/catmullrom_param/catmullrom.pdf” and
I looked to find relevant code (I do not know whether it is the right code)
i change the code’s number but It was hard to fix

pictures of the white line, want to be interpolate red line.
Is there a way? please Help me!!!