An Introduction to NURBS: With Historical Perspective

By D. Rogers. 2011

747 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f453252e68ffec809ba4b9fc14d6f7cc61de5998

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Isogeometric analysis: An overview and computer implementation aspects (2012, background): “led into a vector R as follows R 1 = [N 1M 1;N 2M 1;N 1M 2;N 2M 2;N 1M 3;N 2M 3]: (67) These six basis functions are associated with six global basis indices given by (in MatlabR notation) IEN(:;1) = [1;2;3;4;5;6]: (68) Similarly, for element 2, the shape function vector is given by R 2 = [N 1M 2;N ”
Framework for the Buckling Optimization of Variable-Angle Tow Composite Plates (2015, methodology): “B-spline or nonuniform rational B-spline (NURBS) techniques that have been widely used in CAD systems [22] are able to represent complex geometries (variations) using relatively few design variables.”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, unknown): “The resulting p+1 knot spans contain piecewise polynomials of degree p, which join smoothly up to a continuous differentiability of C [53,54].”
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction (2010, methodology): “Explicit representation methods such as NURBS [39] rely on a parametrization of the surface, which requires a signiﬁcant amount of a priori knowledge of the surface topology.”
Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials (2015, methodology): “The basics on IGA have been presented in detail in numerous papers and we do not repeat them here again, but refer to [55, 56] for an introduction to NURBS, to [17, 24] for details on IGA, and to [27, 57] for its application to geometrically nonlinear Kirchhoff–Love shell analysis.”
An unconditionally energy-stable method for the phase field crystal equation (2012, methodology): “NURBS are generated from B-Splines using projective transformations, while B-Splines are simply piecewise polynomials [41,43].”
Mathematical analysis of variational isogeometric methods* (2014, background): “D. F. Rogers (2001), An Introduction to NURBS: With Historical Perspective, Morgan Kaufmann.”
The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches (2010, unknown): “, [39, 40]).”
Isogeometric analysis of nearly incompressible large strain plasticity (2014, background): “[9], Rogers [12] and Piegl and Tiller [10], as well as Cottrell et al.”
Isogeometric Collocation: Cost Comparison with Galerkin Methods and Extension to Adaptive Hierarchical NURBS Discretizations (2013, background): “Beyond the essential property of smoothness, IGA basis functions come with an apparatus of optimized algorithms that allow for a highly formalized and efficient implementation and can handle very complex geometries [79,81,82].”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “We can generate any mesh size with any polynomial degree p by simply using standard knot insertion with subsequent degre e elevation on the original NURBS surface [36, 123, 135].”