Bezier and B-Spline Techniques

By H. Prautzsch, W. Boehm, M. Paluszny. 2002

677 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/b6ccba8f7de05079b5a72c46049257aa38c826ed

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In Computational Mechanics

In Mechanical Engineering

Citations in the corpus

Smooth, second order, non‐negative meshfree approximants selected by maximum entropy (2009, methodology): “in Bézier, B-Spline techniques [13], natural neighbor approximations [14], and subdivision approximations [15].”
Local maximum‐entropy approximation schemes: a seamless bridge between finite elements and meshfree methods (2006, neutral): “in Bézier and B-Spline techniques [9].”
Shape restricted regression with random Bernstein polynomials (2007, neutral): “10 54 v1 [ m at h. ST ] 8 A ug”
The Bernstein polynomial basis: A centennial retrospective (2012, background): “Since there are several excellent sources for this material [28, 74, 103, 116, 157] this section will only highlight a few key concepts involved in generalizing the basic Bézier curve (9).”
Bounding the influence of domain parameterization and knot spacing on numerical stability in Isogeometric Analysis (2014, methodology): “We refer to [29–32] for more detailed information on properties and algorithms for B-splines and NURBS.”
Subdivision-stabilised immersed b-spline finite elements for moving boundary flows (2012, background): “where the bracket expression in the first term represents the usual binomial coefficient and S ik is the subdivision matrix [22, 23], which has been defined for convenience.”
Numerical simulation of multiple 3D fracture propagation using arbitrary meshes (2011, methodology): “A set of points can be approximated and trimmed by a NURBS curves or surface using standard B-Spline approximation techniques [46].”
Bayesian Survival Analysis Using Bernstein Polynomials (2005, methodology): “The former is seen in the constructive proof of the Bernstein–Weierstrass theorem, and the latter explains the popularity of Bernstein bases in the area of curve design (see e.g. Prautzsch et al., 2002).”
Modelling three‐dimensional trajectories by using Bézier curves with application to hand motion (2007, methodology): “The geometric construction for Bézier curves using the De Casteljau algorithm that motivates their use in graphic design can be found in many texts such as Prautzsch et al. (2002).”
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]).”
Discrete Differential Geometry (2008, background): “[ 9 ] C. R. Collins and K. Stephenson, A circle packing algorithm, Comput.”
Fast Interactive Object Annotation With Curve-GCN (2019, background): “The two most common splines, i.e . the cubic Bezier spline and the uniform B-Spline [27, 12], are deﬁned by control points which do not lie on the curve, which could potentially confuse an annotator that needs to make edits.”