NURBSmallinnusta

NURBSmallinnusta, or NURBS modeling, is the mathematical representation used to create and edit curves and surfaces in computer-aided design and computer graphics. NURBS stands for Non-Uniform Rational B-Splines. They extend B-splines by incorporating weights and non-uniform knot vectors, enabling exact representation of common shapes such as circles and ellipses and offering flexible control over sharp and smooth features.

A NURBS object consists of control points, weights, a degree, and a knot vector. A curve is formed as a weighted sum of basis functions, yielding a smooth, adjustable path whose shape responds locally to changes in the control points. Surfaces are built as tensor products of NURBS curves, using a grid of control points and two parametric directions. Refinement is possible through knot insertion, degree elevation, or patching, allowing increased detail without altering the overall form.

Advantages include local control, exact representation of many analytic shapes, smoothness, and well-defined mathematical properties that support precise CAD operations. NURBS are widely used in CAD/CAM/CAE, automotive and aerospace design, shipbuilding, product development, and digital content creation for animation. They facilitate operations such as lofting, sweeping, revolving, and trimming, and support complex surface modeling and interoperability between software packages.

Historically, NURBS synthesize ideas from Bezier curves and B-splines and were standardized and popularized in the late 20th century to support robust data exchange in the industry. Today, many major CAD and graphics packages—such as Rhino, CATIA, Autodesk tools, and Blender to varying degrees—provide NURBS modeling capabilities.