Kinematically smoothing trajectories by NURBS reparameterization – an innovative approach

On the application of isogeometric finite volume method in numerical analysis of wet-steam flow through turbine cascades

“…NURBS formulation is considered as a universal class for geometry modeling in computer-aided design, manufacture and engineering (CAD/CAM/CAE). The trajectory of a robot [59], geometry of a curved structure [60][61][62][63], free surface of a fluid [64], a tool-path in multi-axis machining [65,66] and automotive body panels [67][68][69]…”

Studies on knot placement techniques for the geometry construction and the accurate simulation of isogeometric spatial curved beams

“…As one of typical curve fitting approaches, interpolation guarantees the curve passes through all data points by setting the number of control points equal to data points. The fitted curve, however, may fluctuate rather than being smooth, especially for a noisy set of data points (see, e.g., [44]). The problem of fluctuating can be overcome in curve approximation by relaxing the strict requirement that all data points must be crossed by the curve.…”

“…As we stated in §2.2, zero fitting error is guaranteed by setting the number of control points equal to data points, so that the curve approximation is converted to interpolation that is not always of interest in curve fitting problems (see, e.g. [38,44,48]).…”

Numerical investigation of wet inflow in steam turbine cascades using NURBS-based mesh generation method

“…Inasmuch as many real-world objects have been constructed by free-form curves and surfaces, the NURBS formulation appears to be a universal class for curve/surface modeling in computer-aided design, manufacture and engineering (CAD/CAM/CAE). The trajectory of a robot [28], geometry of a curved structure [29][30][31], and a multi-axis machining toolpath [32,33] are common examples modeled by NURBS formulation. In addition, NURBS has other advantages in comparison to polygonal meshing, e.g., faster generation, and lower processing load.…”