A mathematical representation of curves and surfaces using control points and weight values, enabling precise definition of complex smooth shapes.
NURBS (Non-Uniform Rational B-Splines) define curves and surfaces mathematically using a set of control points, knot vectors, and weights. Unlike polygon meshes, NURBS surfaces have infinite resolution: the math describes the exact surface geometry, not an approximation. Changing a control point smoothly modifies the nearby surface region. NURBS are the backbone of professional CAD tools (Rhino, CATIA, SolidWorks) and industrial surface design.
Use NURBS modeling for aerodynamic surfaces, consumer product casings, and any geometry requiring precise curvature continuity (G0, G1, G2). Rhino 3D is the most accessible NURBS tool for 3D printing designers. Before printing, NURBS must be tessellated (converted to a mesh): the tessellation tolerance directly controls surface smoothness in the final print.
NURBS surfaces must be converted to meshes for slicing, and overly coarse tessellation produces faceted surfaces. G2 continuity (curvature-continuous) patches are much harder to achieve than G1 (tangent-continuous) and require careful knot placement. NURBS files (IGES, STEP) may import with surface gaps or tolerance mismatches: always check surface join status after import.
Related terms: B-rep, Tessellation, Parametric Modeling
| Field | 3D design, engineering |
|---|---|
| Also called | Non-Uniform Rational B-Spline |
Engineer, author of The Big Book of 3D Printing and additive manufacturing expert