NURBS Face Trimming

A nurbs surface is a two dimensional sheet in the three dimensional space and is defined by a geometrical function mapping a rectangle to the space. The geometry of a nurbs face is always a part of a nurbs surface but may be more complex than that. This is made possible by trims.

A trim defines a cut on the domain rectangle of the surface, a cut with a two dimensional nurbs curve. This implies a cut on the three dimensional sheet of the surface. This cut lies along the bounding nurbs edge of the face and the geometry of the cut along the surface sheet must be consistent with the geometry of the nurbs edge.

A nurbs face has contours just like a traditional PGON, but the contours are not lists of nurbs edges but nurbs trims because the trims have the information needed to cut the face properly. (The 2d curve of trims may be computed from the 3d curve of the edge but it may be inaccurate or even ambiguous in case of surfaces with self-intersection or singularities or in case of erroneous data.)