NURBS question


What is the purpose of these CVs which are there unless I draw the curves manually. They are also created when I rebuild the curves. And is there a name for these CVs?

Thank you.

How many degrees in that surface?

Typically you need N + 1 knots for a spline of degree N (so you need a minimum of 4 cvs for a degree 3 spline). The math interpolates between some number of points (Maya goes as high as 7, which is a very smooth spline that’s hard to edit by hand but useful for things like CAD where you must control the curvature very carefully).

it’s a 3 degree surface. I understand the N+1 rule. What I would like to know that, why the CV on that surface are in that weird distance/place. I can draw a curve, follow the N+1 rule and make the CVs equally apart. But the moment I rebuild it, even without changes, it still adds those CVs there.

it needs those extra one to specify the outgoing tangents. If you rebuild to a specified number of spans you’ll need to add an extra know at the ends to preserve the shape of the curve on its way out of each end. To put it another way, a span needs 3 knots to be defined in D3 spline. The spans in the middle share knots with the spans to either side, but the last span does not.

Doesn’t two knots (edit points) make a span?

Could you explain this a bit easier for me to understand? “The spans in the middle share knots with the spans to either side, but the last span does not.”

To evaluate a point on a d3 spline you need 4 knots. So the end segments gets (0,1,2,3) , the first non-end segment gets (1,2,3,4) and so on. So you’ll always have to have an extra know in the first and last segments; you can think of them as being the two middle ones you get in your most minimal 4-knot d3 curve being pushed out to the ends.

Draw a CV curve in maya and watch the hilighted sections as you go: you’ll see the latest added section always highlight the previous 3 knots as it goes along and the segment boundary always follows along:

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wow. at last I know what the highlight means.

Thanks for a thorough explanation.