Geometry & modeling
NURBS
Non-uniform rational B-splines
Definition
NURBS are mathematical curves and surfaces that can represent both simple shapes, such as lines, arcs, and circles, and complex freeform surfaces exactly. CAD kernels use them for the faces and edges of B-Rep solids that are not simple planes or cylinders.
Also known as: non-uniform rational B-splines, NURBS surface, B-spline
Updated
Why they matter#
Rhino's explanation describes NURBS as mathematical representations of 3D geometry that can accurately describe anything from a 2D line or circle to a complex organic free-form surface or solid.
In mechanical CAD, many faces are simpler analytic surfaces such as planes, cylinders, and cones. NURBS cover the rest: blends, lofts, sweeps, and styled surfaces. Because they are exact, a NURBS surface can be evaluated at any resolution, unlike a mesh that is fixed at the resolution it was exported with.
Sources
Related terms
B-Rep
B-Rep is the way professional CAD kernels describe a solid: by its boundary, made of exact surfaces (faces), the curves where they meet (edges), and the points where edges end (vertices). Because the geometry is exact and the topology is explicit, B-Rep models can be measured, filleted, dimensioned, and manufactured precisely.
Mesh
A mesh represents a shape as a surface of small flat polygons, almost always triangles, joined at shared edges and vertices. Meshes work well for rendering, games, and 3D printing, but they have no true faces, edges, or exact curves, so they are hard to dimension or edit as engineering geometry.
IGES
IGES is an older neutral format for exchanging CAD geometry, developed in the United States. It still appears in legacy workflows and for surface data, but STEP has largely replaced it for solid models.