The Experts below are selected from a list of 567 Experts worldwide ranked by ideXlab platform
Juan Manuel Peña - One of the best experts on this subject based on the ideXlab platform.
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Algorithm 960: POLYNOMIAL: An Object-Oriented Matlab Library of Fast and Efficient Algorithms for Polynomials
ACM Transactions on Mathematical Software, 2016Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:The Design and implementation of a Matlab object-oriented software library for working with polynomials is presented. The construction and evaluation of polynomials in Bernstein form are motivated and justified. Efficient constructions for the coefficients of a polynomial in Bernstein form when the polynomial is not given with this representation are proviDed. The presented adaptive evaluation Algorithm uses the VS (Volk and Schumaker) Algorithm, the De Casteljau Algorithm, and a compensated VS Algorithm. In addition, we have completed the library with other Algorithms to perform other usual operations with polynomials in Bernstein form.
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Corner cutting evaluation Algorithms for general rational curves
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas, 2014Co-Authors: E. Mainar, Juan Manuel PeñaAbstract:The rational De Casteljau Algorithm for the evaluation of rational Bezier curves is extenDed to very general rational spaces. Many examples are incluDed.
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On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
Advances in Computational Mathematics, 2013Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:An efficient evaluation Algorithm for rational triangular Bernstein–Bézier surfaces with any number of barycentric coordinates is presented and analyzed. In the case of three barycentric coordinates, it coinciDes with the usual rational triangular De Casteljau Algorithm. We perform its error analysis and prove the optimal stability of the basis. Comparisons with other evaluation Algorithms are incluDed, showing the better stability properties of the analyzed Algorithm.
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On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
Advances in Computational Mathematics, 2011Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:An efficient evaluation Algorithm for rational triangular Bernstein---Bezier surfaces with any number of barycentric coordinates is presented and analyzed. In the case of three barycentric coordinates, it coinciDes with the usual rational triangular De Casteljau Algorithm. We perform its error analysis and prove the optimal stability of the basis. Comparisons with other evaluation Algorithms are incluDed, showing the better stability properties of the analyzed Algorithm.
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Running Relative Error for the Evaluation of Polynomials
SIAM Journal on Scientific Computing, 2009Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:Running relative error for evaluating polynomials is analyzed and applied to different evaluation Algorithms: Horner, VS, De Casteljau, and Clenshaw Algorithms. Numerical experiments show that the Derived running relative error bounds are sharp and that the De Casteljau Algorithm presents better stability properties than the remaining Algorithms.
Jorge Delgado - One of the best experts on this subject based on the ideXlab platform.
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Algorithm 960: POLYNOMIAL: An Object-Oriented Matlab Library of Fast and Efficient Algorithms for Polynomials
ACM Transactions on Mathematical Software, 2016Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:The Design and implementation of a Matlab object-oriented software library for working with polynomials is presented. The construction and evaluation of polynomials in Bernstein form are motivated and justified. Efficient constructions for the coefficients of a polynomial in Bernstein form when the polynomial is not given with this representation are proviDed. The presented adaptive evaluation Algorithm uses the VS (Volk and Schumaker) Algorithm, the De Casteljau Algorithm, and a compensated VS Algorithm. In addition, we have completed the library with other Algorithms to perform other usual operations with polynomials in Bernstein form.
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On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
Advances in Computational Mathematics, 2013Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:An efficient evaluation Algorithm for rational triangular Bernstein–Bézier surfaces with any number of barycentric coordinates is presented and analyzed. In the case of three barycentric coordinates, it coinciDes with the usual rational triangular De Casteljau Algorithm. We perform its error analysis and prove the optimal stability of the basis. Comparisons with other evaluation Algorithms are incluDed, showing the better stability properties of the analyzed Algorithm.
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On the evaluation of rational triangular Bézier surfaces and the optimal stability of the basis
Advances in Computational Mathematics, 2011Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:An efficient evaluation Algorithm for rational triangular Bernstein---Bezier surfaces with any number of barycentric coordinates is presented and analyzed. In the case of three barycentric coordinates, it coinciDes with the usual rational triangular De Casteljau Algorithm. We perform its error analysis and prove the optimal stability of the basis. Comparisons with other evaluation Algorithms are incluDed, showing the better stability properties of the analyzed Algorithm.
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Running Relative Error for the Evaluation of Polynomials
SIAM Journal on Scientific Computing, 2009Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:Running relative error for evaluating polynomials is analyzed and applied to different evaluation Algorithms: Horner, VS, De Casteljau, and Clenshaw Algorithms. Numerical experiments show that the Derived running relative error bounds are sharp and that the De Casteljau Algorithm presents better stability properties than the remaining Algorithms.
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Monografías Del Seminario Matemático García De GalDeano 31, 111–120 (2004) 111 ON EFFICIENT AlgorithmS FOR POLYNOMIAL EVALUATION IN CAGD
2008Co-Authors: Jorge Delgado, Juan Manuel PeñaAbstract:Abstract. For evaluating polynomial curves in computer Design the usual Algorithm is the De Casteljau Algorithm. Although it is simple and stable, this Algorithm is not efficient, in the sense that it has not linear complexity. In this paper we discuss and compare the properties of four more efficient Algorithms used unDer some circumstances as alternative to the De Casteljau Algorithm
Xiaoming Zeng - One of the best experts on this subject based on the ideXlab platform.
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CSAE - Q-Baskakov Bases and q-Baskakov Curves and Surfaces
Proceedings of the 3rd International Conference on Computer Science and Application Engineering - CSAE 2019, 2019Co-Authors: Wenhui Zhang, Chong Zhao, Xiaoming ZengAbstract:In this paper, we discuss q-Baskakov bases and study some important geometric and analytic properties of these bases, such as non-negative, partition of unity, linear inDepenDence, Degree elevation, Degree reduction and end-point properties. Furthermore, we propose q-Baskakov-Bernstein bases, which are a new class of mix tensor product bases. By means of these bases, we construct a new class of curves and a new class of surfaces. We obtain some important geometric properties and geometric characterization, such as geometric and affine invariance, convexity preserving, end-point interpolation, Degree elevation and De Casteljau Algorithm, for these curves and surfaces.
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q-Poisson Bases and q-Poisson Curves
DEStech Transactions on Computer Science and Engineering, 2018Co-Authors: Xiaoming Zeng, Ying ZengAbstract:We construct a new class of bases (q-Poisson bases) with one shape parameter based on q-integers. The q-Poisson bases have lots of good properties, including non-negativity, partition of unity, linear inDepenDence, which are suitable for moDeling. Based on q-Poisson bases, we Define q-Poisson curves, which have some properties similar to classical Poisson curves. We also present a Degree elevation and De Casteljau Algorithm for q-Poisson curve. The effect of the parameter q on q-Poisson curves is also studied. The introduction of the parameter q makes Poisson curves convenient and flexible for shape moDeling.
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Mixed tensor product Be´zier-Poisson surfaces
2010 5th International Conference on Computer Science & Education, 2010Co-Authors: Xiang Long, Xiaoming ZengAbstract:A kind of mixed tensor product Bernstein-Poisson basis function is presented in this paper. Some important properties of this kind of basis function are discussed and mixed tensor product Bezier-Poisson surface is Defined based on it. The basic properties of the such surface are discussed. Via De Casteljau Algorithm, the evaluation Algorithm and subdivision Algorithm for mixed tensor product Bezier-Poisson surfaces are Derived as extensions of the Algorithms of Bezier curves and Poisson curves.
Ying Zeng - One of the best experts on this subject based on the ideXlab platform.
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q-Poisson Bases and q-Poisson Curves
DEStech Transactions on Computer Science and Engineering, 2018Co-Authors: Xiaoming Zeng, Ying ZengAbstract:We construct a new class of bases (q-Poisson bases) with one shape parameter based on q-integers. The q-Poisson bases have lots of good properties, including non-negativity, partition of unity, linear inDepenDence, which are suitable for moDeling. Based on q-Poisson bases, we Define q-Poisson curves, which have some properties similar to classical Poisson curves. We also present a Degree elevation and De Casteljau Algorithm for q-Poisson curve. The effect of the parameter q on q-Poisson curves is also studied. The introduction of the parameter q makes Poisson curves convenient and flexible for shape moDeling.
E. Mainar - One of the best experts on this subject based on the ideXlab platform.
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Corner cutting evaluation Algorithms for general rational curves
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas, 2015Co-Authors: E. Mainar, J. M. PeñaAbstract:The rational De Casteljau Algorithm for the evaluation of rational Bézier curves is extenDed to very general rational spaces. Many examples are incluDed.
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Corner cutting evaluation Algorithms for general rational curves
Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales. Serie A. Matematicas, 2014Co-Authors: E. Mainar, Juan Manuel PeñaAbstract:The rational De Casteljau Algorithm for the evaluation of rational Bezier curves is extenDed to very general rational spaces. Many examples are incluDed.
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Running Error Analysis of Evaluation Algorithms for Bivariate Polynomials in Barycentric Bernstein Form
Computing, 2006Co-Authors: E. Mainar, J. M. PeñaAbstract:Running error analysis for the bivariate De Casteljau Algorithm and the VS Algorithm is performed. Theoretical results joint with numerical experiments show the better stability properties of the De Casteljau Algorithm for the evaluation of bivariate polynomials Defined on a triangle in spite of the lower complexity of the VS Algorithm. The sharpness of our running error bounds is shown.
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Evaluation Algorithms for multivariate polynomials in Bernstein--Bézier form
Journal of Approximation Theory, 2006Co-Authors: E. Mainar, J. M. PeòaAbstract:The evaluation of multivariate polynomials of n variables in Bernstein-Bezier form is consiDered. A forward error analysis for the corresponding De Casteljau Algorithm and the VS Algorithm is performed. We also incluDe Algorithms that simultaneously evaluate the polynomial and proviDe ''a posteriori'' error bounds, without increasing significantly the computational cost. The sharpness of our running error bounds is shown in the case of trivariate polynomials.
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Factorizations of Normalized Totally Positive Systems
2000Co-Authors: J. M. Carnicer, E. MainarAbstract:Abstract : The De Casteljau Algorithm for evaluation of Bezier curves can he generalized to curves generated by any normalized totally positive basis. The construction of this Algorithm is based upon a factorization of the system as a product of bidiagonal stochastic matrices of functions. These factorizations Depend on a selection of a sequence of rectangular bidiagonal matrices of Decreasing dimensions.