Geometric modeling with splines - an introduction

By E. Cohen, R. Riesenfeld, G. Elber. 2001

338 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/257be3289fb1fdb14dd8eca327a3ec71d0500167

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In Biomedical Engineering

In Computational Mechanics

In Industrial and Manufacturing Engineering

Citations in the corpus

Isogeometric shell analysis: The Reissner-Mindlin shell (2010, background): “, Piegl and Tiller [35], Rogers [36], and Cohen, Riesenfeld and Elber [18]).”
Forward and Inverse Transformations between Cartesian and Channel-fitted Coordinate Systems for Meandering Rivers (2007, background): “Recent applications of spline interpolation in the context of planform dynamics include Fagherazzi, Gabet, and Furbish (2004), Perucca, Camporeale, and Ridolfi (2005), and Camporeale and others (2005); Davis (1986), De Boor (2001), and Cohen, Riesenfeld, and Elber (2001) provide more general backg”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, background): “[80], Rogers [81] or Farin [82], who provide in-depth reviews of the underlying geometric concepts and algorithms.”
Isogeometric analysis of nearly incompressible large strain plasticity (2014, background): “[9], Rogers [12] and Piegl and Tiller [10], as well as Cottrell et al.”
Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes (2014, methodology): “. Both elds have extremely extensive bibliography that makes it impossible to present a full list of related works. Reviews and wide lists of references can be found, for example, in [20], [13], [?], [12] for CAGD methods) and in [7], [15], [43] (for Finite Element methods). The recent Isogeometric ”
Optimal control problems with Atangana‐Baleanu fractional derivative (2020, neutral): “(37) In view of Theorem 2 and the initial condition, we have x(t) ≃ XT RLγ t Φ(t) + a = (XTIγ + AT)Φ(t) = XT γ Φ(t).”
NURBS-based isogeometric analysis for the computation of flows about rotating components (2008, methodology): “(For background on NURBS the reader is referred to [ 13 , 16,25,26], while the basics of NURBS-based isogeometric analysis are outlined in the original papers [4,6,14,22].) We use the fact that NURBS, in contrast to standard finite elements, are capable of exactly representing all conic sections,inc”
The role of continuity in residual-based variational multiscale modeling of turbulence (2007, neutral): “see [16,36,37]).”
Mathematical analysis of variational isogeometric methods* (2014, neutral): “For readers interested in obtaining a better understanding of this field we recommend the books by Cohen et al. (2001), Piegl and Tiller (1997) and Rogers (2001).”