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Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .
SMS software is based on years of research and application of NURBS technology. Les Piegl and Wayne Tiller (a partner of Solid Modeling Solutions) wrote the definitive "The NURBS Book" on non-uniform rational B-splines, with aids to designing geometry for computer-aided environment applications. [2]
NURBS curve – polynomial curve defined in homogeneous coordinates (blue) and its projection on plane – rational curve (red) In computer aided design, computer aided manufacturing, and computer graphics, a powerful extension of B-splines is non-uniform rational B-splines (NURBS). NURBS are essentially B-splines in homogeneous coordinates ...
NURMS are used in commercial 3D packages such as Autodesk 3ds Max to perform mesh smoothing operations. The mesh smooth modifier in 3ds Max operates by applying this algorithm to a low-polygon mesh and creates a high-polygon smoothed mesh.
I'm not sure I like the identification "NURBS (Non Uniform Rational Basis, or Bézier Spline)" in the History section. A Bézier spline is a special case of a B-Spline; for example, a degree 3 Bézier spline on four control points is the same as a B-Spline with knot vector [0,0,0,0,1,1,1,1].
Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis (FEA) into conventional NURBS-based CAD design tools. . Currently, it is necessary to convert data between CAD and FEA packages to analyse new designs during development, a difficult task since the two computational geometric approaches are diffe
Rhinoceros (typically abbreviated Rhino or Rhino3D) is a commercial 3D computer graphics and computer-aided design (CAD) application software that was developed by TLM, Inc, dba Robert McNeel & Associates, an American, privately held, and employee-owned company that was founded in 1978.
A vector r = (r 1, …, r k–1) such that the spline has smoothness at t i for i = 1, …, k – 1 is called a smoothness vector for the spline. Given a knot vector t, a degree n, and a smoothness vector r for t, one can consider the set of all splines of degree ≤ n having knot vector t and smoothness vector r. Equipped with the operation of ...
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