NURBS (non-uniform rational B-splines)
Non-uniform rational B-splines, a mathematical way to describe precise curves and surfaces in CAD software such as Rhino.
Why jewelers use NURBS
A NURBS surface is defined by control points and weights rather than by triangles, so it is perfectly smooth at any zoom. That precision suits jewelry, where a prong seat or a shank profile must match measurements to a fraction of a millimetre.
NURBS versus meshes
Renderers, real-time viewers and 3D printers work with meshes, not NURBS. Before a NURBS model can be displayed, it is tessellated into triangles. The density of that render mesh decides how smooth curves look. Too coarse and a round shank shows flat facets, too fine and the file becomes heavy.
Exporting for rendering
When you export from Rhino or MatrixGold to GLB, OBJ or STL, the export settings control the mesh density. Increase density on curved metal surfaces that will be seen in close-up, and keep stones simple, since their facets are flat.
3DM files can carry NURBS geometry together with render meshes. If a 3DM is saved with the Save Small option, Rhino drops those render meshes and some viewers cannot display the surfaces, so save normally or export a mesh format before you upload.
Closed shapes
NURBS models built from separate surfaces may contain small gaps. Joining surfaces into closed polysurfaces in CAD gives cleaner meshes and fewer rendering artefacts. See watertight mesh.