Points, Knots, and Segments

 
 
 

The shape of a NURBS is controlled by its points, sometimes also called control points or control vertices (CVs). The points define segments and the segments are joined at knots.

In a linear curve, the segments are straight lines between the control points and the control points and knots overlap exactly.

A

Points and knots are coincident.

B

Segments connect points.

In a cubic curve, the segments are interpolated between control points and the knots lie on the curve.

A

Points control the shape

B

Segments interpolate between points.

C

Knots are where the segments join.

In a surface, the segments form knot curves in two directions (knot curves are sometimes called isoparams or isoparms). The knot curves intersect at the knots, forming four-sided patches.

A

Points control the shape

B

Segments form knot curves.

C

Knots curves intersect at knots.

D

Patches are the visible surface.