The NURBS Book

By L. Piegl, W. Tiller. 1995

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Citations in the corpus

SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017, background): “The definition range of gl is the interval in which the partition of unity property of the B-spline bases holds [19].”
Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates (2014, background): “weighted average of the B-spline basis functions [29]:”
Mathematical analysis of variational isogeometric methods* (2014, methodology): “The refinement algorithms of knot insertion and degree elevation, to recompute the control points in finer spaces, can be generalized to multivariate splines and NURBS (Piegl and Tiller 1997).”
OpenAlea: a visual programming and component-based software platform for plant modelling. (2008, unknown): “The midrib curve and the variation of the leaf width are approximated, in the parametric model, with NURBS curves using the least square fitting algorithm (Piegl and Tiller 1997), available in the Python scientific library, SciPy (Oliphant 2007).”
Evolutionary algorithm based offline/online path planner for UAV navigation (2003, background): “B-Spline curves are parametric curves, with their construction based on blending functions [11], [12].”
Generalized kinematics of five-axis serial machines with non-singular tool path generation (2013, methodology): “Here, a C continuous interpolating B-spline curve is constructed on the 4D sphere in quaternion space as described in Piegl and Tiller [32].”
Challenges and Present Fields of Action at Laser Scanner Based Deformation Analyses (2016, background): “However, NURBS do not yet permit to relate individual parameters to individual areal deformations.”
Curve Modeling via Interpolation Base on Multidimensional Reduced Data (2004, unknown): “[2], [5], [12], [17], [20], [21], [33], [48] or [56], approximation and complexity theory e.”
Isogeometric Analysis for Topology Optimization with a Phase Field Model (2012, methodology): “We represent the design domain Ω by means of a NURBS basis of degree 2 [80] for which, by using Isogeometric Analysis, the exact representation of the geometry is maintained through the analysis and the topology optimization procedure.”
Image interpolation and resampling (2000, unknown): “Numerous candidates have been proposed: Appledorn [21], B-spline [22], Dodgson [23], Gauss, Hermite, Keys [24, 25], Lagrange, linear, Newton, NURBS [ 26 ], o-Moms [27], Rom-Catmull,”