# How do I determine/control the number of spans in a curve?

In viewing the latest excellent tutorials on “Better Living Through CNC” on YouTube, the topic of curve degree and curve spans has come up. The Alias Golden Rules was mentioned as a good reference for this and its rule #3 discusses curve span. I can’t figure out how, in Rhino, how to determine and control how many spans a curve has. Can someone enlighten me?

Thanks,
Dennis

A single-span curve has degree+1 control points. Any more than that, the curve is multi-span. So a degree 3 single-span curve will have 4 control points and a degree 5 single-span curve 6 control points.

Thanks. See the attached. Same curve drawn 2 ways. Have I interpreted these correctly?

Curves Spans.3dm (67.7 KB)

The first curve looks like two degree=3 curves that are joined.

See if this helps:
https://www.rhino3d.com/nurbs

The WHAT command on the top curve returns this:
curve

Object name: (not named)
Layer name: Default
Render Material:
source = from layer
index = -1
Active visual analysis modes:
Curvature graph analysis

Geometry:
Valid curve.
Open NURBS curve
start = (-1’-8 1/4",8 1/8",0")
end = (2 11/16",1’-2 1/4",0")
degree = 5
control points: non-rational, count=9
knots: non-uniform, domain = 0" to 3’-0 1/16"
clamped at start and end

How do I know how many spans there are from this information?

it kind of doesn’t matter how many spans it has if it’s above single span (degree + 1 control point)

If it’s not single span, then it’s a multi span curve and the single span rules kind of go out the window.

I guess I’m having trouble determining when I’ve gone from a single span curve with a lot of CV’s to a multi-span curve.

If you are using degree 3 curves, more than 4 CV’s it’s multi-span…

Don’t forget the difference between two or more joined curves (a polycurve) and a single NURBS curve which may be single or multi-span…

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Greek to me but thanks anyway.

Sorry John, I didn’t mean to be flip earlier. The page you sent me to was way over my head I’m afraid.