When creating a new curve of a certain degree from the scratch, you have basically two options:
- Create the curve by specifying the Control Vertices (CVs)
=> Use "Curves" / "New Curves" / "New CV Curve"
- Create the curve by specifying some Edit Points (EPs) the curve should run through
=> Use "Curves" / "New Curves" / "New Edit Point Curve"
(Both tools have an option dialog where the intended degree can be specified. For now, I assume this degree been set to 3.)
In the attached screen shot, you will find two planar curves (z = 0) to the top, both using four input points at almost identical positions (mirrored by y-axis). In the left curve these four points are interpreted a CVs, while for the curve to the right the giving point are taken as EPs.
- The curve has degree d = 3 (of course) and consists of a single span (as degree 3 Bezier curve is defined by 4 CVs).
Addition: If the user would have used (d + s) many input CVs the yielded curve would consist of s spans.
- This curve has also d = 3 (see above) and runs through the specified 4 points. It has 6 CVs (which are needed / implied as to meet the requirement to run through these EPs); consequently, it has 3 spans.
Please note that EP curves should be considered to be CV curves too, and vice versa. Actually, from the math point of view there is no difference: all NURBS curves are defined by their knot vector (which defines degree and parametrization) and their CVs.
To illustrate this, please have a look at curve 3 in the attached screen shot. It's a degree 3 curve again having 6 CVs. At first glance, one might think it has been defined as an EP curve running through the four points on that curve (similiar to curve 2). Actually, I have defined this curve using "New CV Curve" tool. Hence, the displayed points on all three curves (which each curve passes through) are EPs and they are available even if one introduces the curves as "CV curve" (remember: every curve is a CV curve!)
- curve 1 has two EPs: start and end point
- curve 2 and 3 has four each: start and end point, and two in the middle
curve 2 and 3 both have 3 spans; the transition points between spans are exactly those EPs.
Hth
Thomas
Thomas Rausch
Software Development Manager