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Transformation of a Dynamic B-spline Curve Into Piecewise Power Basis Representation [chapter]

Joonghyun Ryu, Youngsong Cho, Deok-Soo Kim
2002 Lecture Notes in Computer Science  
In this paper, we present a new algorithm to convert Bspline curves into piecewise polynomials in power form.  ...  Then, algorithm computes the power form representation of B-spline basis functions and the required transformation of B-spline curve is obtained through the linear combination of B-splines in power form  ...  In this paper, we propose a faster algorithm for the evaluation of a B-spline curve based on the conversion of curve into a piecewise polynomial in a power form.  ... 
doi:10.1007/3-540-46080-2_9 fatcat:tayuvbu67fcndn5nj2mijfpora

The conversion of a dynamic B-spline curve into piecewise polynomials in power form

D.-S. Kim, J. Ryu, H.C. Lee, H. Shin
2002 Computer-Aided Design  
Presented in this paper is a new algorithm to convert a B-spline curve into a set of piecewise polynomial curves in power form.  ...  The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in power form is done either by a knot re®nement followed by basis conversions, or by applying a Taylor  ...  The ®rst author also thanks to A. Fischer, Technion-Israle Institute of Technology, for suggesting the possibility of applying the idea to dynamic B-spline curves and surfaces.  ... 
doi:10.1016/s0010-4485(01)00090-2 fatcat:z4cailyvcnhznd4pmzs77aksqi

PHYSICS BASED GEOMETRIC DESIGN

HONG QIN
1996 International journal of shape modeling  
In this paper, we s u r v ey the diversity of shape representations ranging from the primitive polynomial to the sophisticated Non-Uniform Rational B-Spline (NURBS).  ...  To o vercome the disadvantages of this indirect process, we summarize the prior work of physics-based modeling and review dynamic NURBS (D-NURBS) as a physics-based generalization of geometric NURBS for  ...  During 1973 and 1974, Riesenfeld and Gordon proposed B-splines as a powerful and proper generalization of Bernstein polynomials for free-form curve design 91, 4 8 ] .  ... 
doi:10.1142/s0218654396000099 fatcat:ctnoubb7vvaubpbxuiev5dpmpe

Sensors and Digital Signal Conditioning in Mechatronic Systems [chapter]

Dilşad Engin, Mustafa Engin
2017 Design, Control and Applications of Mechatronic Systems in Engineering  
In mechatronic systems, accurate measurement of the dynamic variables plays a vital role for the actuators to function properly.  ...  Piecewise and polynomial methods are used in linearization software, and the implemented embedded system for the linearization of a type K T/C is presented as a case study.  ...  We have a set of n data points fðx 1 , y 1 Þ, …ðx n , y n Þg with n residuals fðy 1 À b y 1 Þ, …ðy n À b y n Þg.  ... 
doi:10.5772/67986 fatcat:zds6pky7lvcvjdjqyjtz6i37nm

A Novel Classification Method with Cubic Spline Interpolation

Husam Ali Abdulmohsin, Hala Bahjat Abdul Wahab, Abdul Mohssen Jaber Abdul Hossen
2022 Intelligent Automation and Soft Computing  
This study proposes a statistical feature classification cubic spline interpolation (FC-CSI) algorithm to classify emotions in speech using a curve fitting technique.  ...  The proposed work shows fast classification and high accuracy of results.  ...  Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.  ... 
doi:10.32604/iasc.2022.018045 fatcat:k6nsmoz22re3fkhnlcb4webafe

Multiresolution curves

Adam Finkelstein, David H. Salesin
1994 Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94  
The next section discusses the theory of multiresolution analysis, and develops a multiresolution representation for B-spline curves.  ...  We describe a multiresolution curve representation, based on wavelets, that conveniently supports a variety of operations: smoothing a curve; editing the overall form of a curve while preserving its details  ...  B-spline surface editor.  ... 
doi:10.1145/192161.192223 dblp:conf/siggraph/FinkelsteinS94 fatcat:bsuzxgilrbbvbbypn2yljschfy

Mixed-Effects Regression Splines to Model Myopia Data

Nordhausen K Oja H
2015 Journal of Biometrics & Biostatistics  
We discuss alternative choices of the basis functions such as the truncated polynomial spline functions (2 types) and B-spline functions.  ...  Principal component functions may be used for an analysis of the variation of the curves in the population.  ...  The work of Klaus Nordhausen and Hannu Oja was supported by the Academy of Finland (grants 131929, 218327 and 268703).  ... 
doi:10.4172/2155-6180.1000239 fatcat:swczpjonybannnogly2g4svxmy

Splines in Biomedical Image Processing [chapter]

Slavica Jonic, Carlos Oscar Sanchez Sorzano
2011 Optical and Digital Image Processing  
The interpolation context Given a discrete set of measurements (xi, yi), interpolating is the art of "filling in the gaps" with a continuous function y = f (x) such that we meet the constraints imposed  ...  For instance, if ϕ1D(x) is a 1D spline, the 2D tensor product spline is defined as ϕ2D(x, y) = ϕ1D(x)ϕ1D(y).  ...  Let us assume that the set of coefficients of the polynomial p are written in vector form as p.  ... 
doi:10.1002/9783527635245.ch6 fatcat:bqb43ynll5fetnwycsssmtxmsy

Adaptive PI Controllers for Doubly Fed Induction Generator using B-spline Artificial Neural Networks

Rubén Tapia-O., Omar Aguilar M., Abel García-B., Omar J. Santos-S.
2013 International Journal of Computer Applications  
This paper presents the design and simulation of adaptive PI controllers for doubly fed induction generators using b-spline neural networks.  ...  The results show that the proposed controllers' tuning is comparable to that obtained by a conventional design, without requiring of a detailed model, which enable optimal speed tracking for maximum energy  ...  A B-spline neural network (BSNN) consists of the piecewise polynomials with a set of local basis functions to model an unknown function for which a finite set of process samples are available.  ... 
doi:10.5120/13956-1949 fatcat:leyupbmjbrhvhegqyv2nnoglya

Reviews and Descriptions of Tables and Books

1993 Mathematics of Computation  
Among them are two papers on minimal-energy splines, three on weighted splines, one on geometric-continuous B-splines, and one on the distance problem for pairs of parametric curves.  ...  This book provides a comprehensive and detailed treatment of best-constant problems for approximation of smooth functions by polynomials, trigonometric polynomials, and splines.  ... 
doi:10.1090/s0025-5718-93-99735-9 fatcat:k2c2nj25ezdppbrwzqkfz7uulq

A flexible model for estimating price dynamics in on-line auctions

Wolfgang Jank, Galit Shmueli, Shu Zhang
2010 Journal of the Royal Statistical Society, Series C: Applied Statistics  
We propose a flexible two-parameter beta model which adequately captures a wide range of auction price paths.  ...  Using bidding data from eBay auctions, we find that the beta model leads to fast and high accuracy price predictions. This behaviour is consistent across various forecasting models and data sets.  ...  Penalized smoothing splines Penalized smoothing splines (P-splines) (Simonoff, 1996) fit a polynomial of order p.  ... 
doi:10.1111/j.1467-9876.2010.00726.x fatcat:tihn7xah5rfohfxiu42tvemjzq

A Multilevel Modeling Approach towards Wind Farm Aggregated Power Curve

Mehrdad Mehrjoo, Mohammad Jafari Jozani, Miroslaw Pawlak, Bagen Bagen
2021 IEEE Transactions on Sustainable Energy  
To solve this issue, we propose a novel clustering feature set based on turbines' overall performance and utilize K-Means clustering to classify turbines into homogeneous groups accordingly.  ...  Another challenging issue in fitting empirical power curve which was investigated seldom in the literature is heteroscedasticity of the wind speed-power data set.  ...  In Jin and Tian (2010) , an analysis of wind energy production dynamics was investigated, and dynamic power curves were proposed.  ... 
doi:10.1109/tste.2021.3087018 fatcat:5m6mssvfszhgjcslcssforbph4

Integrative Density Forecast and Uncertainty Quantification of Wind Power Generation [article]

Jingxing Wang, Abdullah Alshelahi, Mingdi You, Eunshin Byon, Romesh Saigal
2020 arXiv   pre-print
Specifically, we model wind speed using the inhomogeneous Geometric Brownian Motion and convert the wind speed prediction density into the wind power density in a closed-form.  ...  Wind power forecasting usually depends on wind speed prediction and the wind-to-power conversion process. However, most current wind power prediction models only consider portions of the uncertainty.  ...  B. Modeling Wind-to-Power Conversion Process This section discusses how to convert the wind speed dynamics into the dynamics of wind power process.  ... 
arXiv:1808.07347v2 fatcat:vvd6opls5zetvkfj5upazkh55y

Reviews and Descriptions of Tables and Books

1994 Mathematics of Computation  
This task is performed with B-splines and rational spline curves. In Chapter 4, surfaces make their appearance, approximated first by tensor products of splines.  ...  This material is oriented toward the use of B-splines as basis splines. The chapters by Barry and Goldman use multiaffine and multilinear polar forms ("blossoms").  ... 
doi:10.1090/s0025-5718-94-99730-5 fatcat:6irn5lwunzcptjhtfjtjdhftd4

A snake-based approach to accurate determination of both contact points and contact angles

A.F. Stalder, G. Kulik, D. Sage, L. Barbieri, P. Hoffmann
2006 Colloids and Surfaces A: Physicochemical and Engineering Aspects  
In this approach, we avoid making physical assumptions by defining the contour of the drop as a versatile B-spline curve.  ...  We present a new method based on B-spline snakes (active contours) for measuring high-accuracy contact angles.  ...  B-spline snakes (B-snakes) are a particular category of snakes that use a parametric B-spline representation of the curve.  ... 
doi:10.1016/j.colsurfa.2006.03.008 fatcat:vc32ajsm6fexlatq6rxbvjf5le
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