Curves and Surfaces for Cagd: A Practical Guide

By G. Farin. 2001

1,794 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8830af1e277834dbda5f1b664418e068bc755f34

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Citations in the corpus

Integration by interpolation and look-up for Galerkin-based isogeometric analysis (2015, methodology): “For a more detailed introduction to spline theory and geometric modeling, the reader is referred to standard textbooks such as [17,16].”
Techniques and Applications of Digital Watermarking and Content Protection (2003, methodology): “in 1938 in which signal correlation and autocorrection were already present and the 1940 patent by Kotowski and Dannehl [51] describing an encryption device based on the combination of broadband noise with the payload signal [52].”
Isogeometric analysis using T-splines (2010, methodology): “The most widely used in engineering design is NURBS (non-uniform rational B-splines), the industry standard (see, e.g. [23,24,28,37,38,40]).”
ABC: A Big CAD Model Dataset for Geometric Deep Learning (2018, methodology): “In our dataset, each surface can represent a plane, cone, cylinder, sphere, torus, surface of revolution or extrusion or NURBS patch [24].”
Bayeswave: Bayesian inference for gravitational wave bursts and instrument glitches (2014, background): “It may be that higher dimensional quantities are needed, such as posterior distributions for Bezier curves [63] that track the development of the signal in time-frequency.”
Topology optimization in B-spline space (2013, unknown): “For details on B-splines, refer to [31, 32].”
Smooth Bézier Surfaces over Unstructured Quadrilateral Meshes (2014, methodology): “ned by dening, as coecients of these polynomials ,scalar, 2Dand 3Dcontrol points respectively. We deal with Bezier functions,(resp. plannar domains and surfaces) , following the CAGD conventions , [14], such objects will be dened as being of order n, (resp. (n;m) and (n;m;r) ), where n (resp. n;m, a”
Subdivision Methods for Geometric Design: A Constructive Approach (2001, background): “[59] Farin, G.: Curves and surfaces for CAGD: a practical guide, third edition.”
A geometrically exact isogeometric Kirchhoff plate: Feature‐preserving automatic meshing and C1 rational triangular Bézier spline discretizations (2018, background): “The displacement tensor is defined as u = [ u v d ]T = [−z ∂ ∂x −z ∂ ∂y 1 ]T d, (30) and the acceleration tensor is obtained from Equation (30) by differentiating twice in time.”
A BEM-isogeometric method for the ship wave-resistance problem (2013, methodology): “N: ð13Þ In order to ensure the solvability of the linear system (13), we select the collocation points to be the Greville abscissas of the associated NURBS bases; see, e.g., Farin (2001).”
Numerical method for shape optimization using T-spline based isogeometric method (2010, background): “Besides the properties mentioned earlier, B-spline curves have the affine covariance property and continuous derivatives of order p − 1 For details on the B-spline theory, readers are referred to Piegl and Tiller (1997), Rogers (2001), and Farin (2002). The B-spline surfaces and solids are defined a”
Polynomial splines over hierarchical T-meshes (2008, methodology): “j ðu; vÞ into these cells at level k þ 1 according to formula (14.15) in [ 4 ].”