Non-uniform rational B-spline

Non-uniform rational basis spline (NURBS) is a mathematical model using <a href="/facts/B-spline/MLTCWCEd">basis splines</a> (B-splines) that is commonly used in <a href="/facts/Computer_graphics/lapBE8wv">computer graphics</a> for representing curves and <a href="/facts/Surface_(mathematics)/whF08jvy">surfaces</a>. It offers great flexibility and precision for handling both analytic (defined by common mathematical <a href="/facts/Formula/BosTcKnv">formulae</a>) and <a href="/facts/3D_modeling/6V3Ry9AJ">modeled shapes</a>. It is a type of <a href="/facts/3D_modeling/6V3Ry9AJ">curve modeling</a>, as opposed to <a href="/facts/Polygonal_modeling/lhEsjXWc">polygonal modeling</a> or <a href="/facts/Digital_sculpting/Kt8Dvjyv">digital sculpting</a>. NURBS curves are commonly used in <a href="/facts/Computer-aided_design/5gSXrmmN">computer-aided design</a> (CAD), <a href="/facts/Computer-aided_manufacturing/gqYHXcK9">manufacturing</a> (CAM), and <a href="/facts/Computer-aided_engineering/dAsPLr5Y">engineering</a> (CAE). They are part of numerous industry-wide standards, such as <a href="/facts/IGES/TtKwR0eF">IGES</a>, <a href="/facts/ISO_10303/1sUvrP4t">STEP</a>, <a href="/facts/ACIS/245HIIx2">ACIS</a>, and <a href="/facts/PHIGS/dwR9wpv6">PHIGS</a>. Tools for creating and editing NURBS surfaces are found in various <a href="/facts/3D_computer_graphics_software/zlWW6eaF">3D graphics</a>, <a href="/facts/Rendering_(computer_graphics)/YYxfnmAq">rendering</a>, and <a href="/facts/3D_Animation/093f9nUg">animation</a> software packages.
They can be efficiently handled by computer programs yet allow for easy human interaction. NURBS surfaces are functions of two <a href="/facts/Parameter/zFvVFMv9">parameters</a> mapping to a surface in <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a>. The shape of the surface is determined by <a href="/facts/Control_point_(mathematics)/v9L1j4vz">control points</a>. In a compact form, NURBS surfaces can represent simple <a href="/facts/Geometric_shape/nww0x85d">geometrical shapes</a>. For complex organic shapes, <a href="/facts/T-Spline_(mathematics)/g5IVWYwp">T-splines</a> and <a href="/facts/Subdivision_surfaces/9AKT4pfM">subdivision surfaces</a> are more suitable because they halve the number of control points in comparison with the NURBS surfaces.
In general, editing NURBS curves and surfaces is intuitive and predictable. Control points are always either connected directly to the curve or surface, or else act as if they were connected by a rubber band. Depending on the type of user interface, the editing of NURBS curves and surfaces can be via their control points (similar to <a href="/facts/B%25C3%25A9zier_curve/zJx3Uj60">Bézier curves</a>) or via higher level tools such as spline modeling and hierarchical editing.

Non-uniform rational B-spline open-in-new

Non-uniform rational B-spline