On calculating with B-splines

Boor, Carl de

doi:10.1016/0021-9045(72)90080-9

Cited by 1,485 publications

(613 citation statements)

References 6 publications

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“…This approach has the advantage over Note to Note Alignment that small variations between tunes are not penalized strongly when the melodic contour is roughly the same. This concept is used by Urbano (2013), who developed a global sequence alignment algorithm using B-Splines (De Boor, 1972) to model the melodic shape of a song. This Melodic Shape Alignment method has been the best-performing approach for the Symbolic Melodic Similarity MIREX task 3 over five years (2010)(2011)(2012)(2013)(2014).…”

Section: Similarity Calculationmentioning

confidence: 99%

Evaluating the Role of Repeated Patterns in Folk Song Classification and Compression

Boot

Volk

Haas

2016

Journal of New Music Research

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According to musicological studies on oral transmission, repeated patterns are considered important for determining musical similarity in folk songs. In this paper, we study the relevance of repeated patterns for modelling similarity and compression in a retrieval setting. Using a dataset of 360 Dutch folk songs, we compare the classification accuracy of both humanly annotated patterns and automatically retrieved patterns by means of a pattern discovery algorithm. A framework is proposed to use these patterns for compression and classification in tune families. The annotated patterns allow us to compress the songs by 60% at the expense of a 3 percentage points decrease in classification accuracy. However, none of the automatic pattern discovery algorithms is able to reach a similar combination of compression ratio and retrieval accuracy. We conclude that repeated patterns are relevant for similarity estimation and compression, but that the state of the art in automatic pattern discovery cannot compete with expert annotations in this retrieval setting.

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Section: Similarity Calculationmentioning

confidence: 99%

Evaluating the Role of Repeated Patterns in Folk Song Classification and Compression

Boot

Volk

Haas

2016

Journal of New Music Research

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“…Since NURBS are a generalization of B-Splines the latter are explained first. B-Spline basis functions N i,p depend on the knot vector , which is defined by a set of non-descending parameters, and a polynomial degree p. The basis functions can be evaluated by the Cox-de Boor [14,15] recursion formula.…”

Section: Nurbs Basis Functions For Curves and Surfacesmentioning

confidence: 99%

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

Teschemacher

Bauer

Oberbichler

et al. 2018

Adv. Model. and Simul. in Eng. Sci.

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An entire design-through-analysis workflow solution for isogeometric B-Rep analysis (IBRA), including both the interface to existing CADs and the analysis procedure, is presented. Possible approaches are elaborated for the full scope of structural analysis solvers ranging from low to high isogeometric simulation fidelity. This is based on a systematic investigation of solver designs suitable for IBRA. A theoretically ideal IBRA solver has all CAD capabilities and information accessible at any point, however, realistic scenarios typically do not allow this level of information. Even a classical FE solver can be included in the CAD-integrated workflow, which is achieved by a newly proposed meshless approach. This simple solution eases the implementation of the solver backend. The interface to the CAD is modularized by defining a database, which provides IO capabilities on the base of a standardized data exchange format. Such database is designed to store not only geometrical quantities but also all the numerical information needed to realize the computations. This feature allows its use also in codes which do not provide full isogeometric geometrical handling capabilities. The rough geometry information for computation is enhanced with the boundary topology information which implies trimming and coupling of NURBS-based entities. This direct use of multi-patch trimmed CAD geometries follows the principle of embedding objects into a background parametrization. Consequently, redefinition and meshing of geometry is avoided. Several examples from illustrative cases to industrial problems are provided to demonstrate the application of the proposed approach and to explain in detail the proposed exchange formats.

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“…The article was actually published nearly 20 years later, in 1966, see [2]. B-splines became more accessible to practical use when Cox-de'Boor recursion formula was introduced in 1972, see [3]. B-splines (the basis functions) is notated in two ways: b d,i (t) = b(t; t i , ..., t i+d+1 ), where d is the polynomial degree.…”

Section: B-splinesmentioning

confidence: 99%

Pre-evaluation and interactive editing of B-spline and GERBS curves and surfaces

Lakså¹

2017

AIP Conference Proceedings

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Abstract. Interactive computer based geometry editing is very useful for designers and artists. Our goal has been to develop useful tools for geometry editing in a way that increases the ability for creative design.When we interactively editing geometry, we want to see the change happening gradually and smoothly on the screen. Preevaluation is a tool for increasing the speed of the graphics when doing interactive affine operation on control points and control surfaces. It is then possible to add details on surfaces, and change shape in a smooth and continuous way.We use pre-evaluation on basis functions, on blending functions and on local surfaces. Pre-evaluation can be made hierarchically and is thus useful for local refinements. Sampling and plotting of curves, surfaces and volumes can today be handled by the GPU and it is therefore important to have a structured organization and updating system to be able to make interactive editing as smooth and user friendly as possible. In the following, we will show a structure for pre-evaluation and an optimal organisation of the computation and we will show the effect of implementing both of these techniques.

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On calculating with B-splines

Cited by 1,485 publications

References 6 publications

Evaluating the Role of Repeated Patterns in Folk Song Classification and Compression

Evaluating the Role of Repeated Patterns in Folk Song Classification and Compression

Realization of CAD-integrated shell simulation based on isogeometric B-Rep analysis

Pre-evaluation and interactive editing of B-spline and GERBS curves and surfaces

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