Explaining B-spline and NURBS

I kinda understand b-splines and NURBS. What I don’t understand is how they represent triangles and rectangles, or cubes and pyramids. Unless the latter are composed of 3 or 4 separate 2-pt b-splines, and similarly separate number of flat NURBS.

A degree 1 NURBS is made up of straight line segment. A multi-span degree 1 NURBS has position continuity, referred to as G0 continuity, between spans. A rectangle can be a 4 span degree 1 NURBS. A triangle can be a 3 span degree 1 NURBS.

An alternative to a multi-span degree 1 NURBS is a polyline which is a series of individual lines joined together. For many purposes the differences between a multi-span degree 1 NURBS and a polyline are not important. (The differences between a polycurve and multi-span higher degree NURBS curves are frequently significant.)

Closed volumes in Rhino are represented by a set of surfaces joined at the edges. A cube can be 6 single span degree 1 surfaces.


I would strongly suggest to read this all time classic:

This is brilliant. Many thanks, David.

Many thanks, Peter. But I didn’t want a long treatise but a short explanation. Which David has done. I do appreciate to link, though.