# B-Spline Relationship and Definition Degree CVs Spline Points

Question asked by Jens Hartwich on Oct 27, 2015

Hi

In SolidWorks:

B-Spline = Spline

Edit Point = Spline Point

Control Vertices = Control Polygon (Point)

There are a lot of people out there who think that a edit point aka spline point or the connection between two splines is a knot. But its not. A knot is show on http://www.pic-upload.de/view-28695397/KnotsBreakpts.jpg.html  . A knot is called P(u(i)). And all knots together are the knot vector. Am i right?

In SolidWorks: Every Splinepoint is also the Control Polygon Point, but if i am using the spline handel SW is adding more polyon points to the spline, without adding more spline points. The result is a higher degree spline.

If i want so caluclate the relationship between the degree of the B-spline and the number of CVs i need the number of knots? Am i right?

If i want to know the number of knots, i need the, like my source (http://www.pic-upload.de/view-28695397/KnotsBreakpts.jpg.html)  called "breakpoints". Is a "breakpoint" a vertex (apex)? And if so, how can i find out the number of breakpoints = knots?

I cant find any option in SW2014/15. So its impossible for me to find out the degree of the B-Spline. Am i right? I know that you will have the option for placing 3°,5°,7°-B-Spline with Style-Spline (confusing) in SW2016, but there wont be an option to find out the degree of a freeform B-Spline. Am i right?

Its also not possible to add weight on a control polygon or spline point. Neither with B-Spline (Spline) nor Bezier (Style-Spline). The only thing i can do is using the spline handels to add some kind of weight to the spline point. Am i right?

The formula for Bezier is the formula for NURBS, which is: Number of CVs = Degree + Number of Spans, while the number of spans for a Bezier Spline in SW is always 1. Am i right?

Formula can be found here: Link removed (you need to google for source)

B-Splines is SW are confusing for me . The 2016 B-Spline look like Bezier, which seems the CVs have weight now ^^ (2016 SOLIDWORKS Help - Style Spline Support for B-Splines )

Complex topic for me

Sry for my bad english, thanks 4 the help.