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| 2009
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1
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Keynote lecture 1: four open mathematical problems related to computer graphics and geometric modeling
Ron Goldman
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April 2009
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AMATH'09: Proceedings of the 15th american conference on Applied mathematics
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Publisher: World Scientific and Engineering Academy and Society (WSEAS)
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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Four unsolved problems that originate from research in Computer Graphics and Geometric Modeling will be presented. The first problem involves understanding the notion oscillation for Bezier surfaces, the freeform polynomial surfaces most common in Computer ...
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2
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Keynote lecture 1: four open mathematical problems related to computer graphics and geometric modeling
Ron Goldman
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April 2009
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CIS'09: Proceedings of the international conference on Computational and information science 2009
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Publisher: World Scientific and Engineering Academy and Society (WSEAS)
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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Four unsolved problems that originate from research in Computer Graphics and Geometric Modeling will be presented. The first problem involves understanding the notion oscillation for Bezier surfaces, the freeform polynomial surfaces most common in Computer ...
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3
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Axial moving planes and singularities of rational space curves
Haohao Wang, Xiaohong Jia, Ron Goldman
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March 2009
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Computer Aided Geometric Design
, Volume 26 Issue 3
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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Relationships between the singularities of rational space curves and the moving planes that follow these curves are investigated. Given a space curve C with a generic 1-1 rational parametrization F(s,t) of homogeneous degree d, we show that if P and ...
Keywords: μ-basis, Axial moving planes, Rational space curve, Singularity
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4
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μ-bases for polynomial systems in one variable
Ning Song, Ron Goldman
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February 2009
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Computer Aided Geometric Design
, Volume 26 Issue 2
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 1 |
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The notion of a @m-basis for an arbitrary number of polynomials in one variable is defined. The basic properties of these @m-bases are derived, and an algorithm is presented based on Gaussian Elimination to calculate a @m-basis for any collection of ...
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5
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On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging
R. Goldman, E. Vouga, S. Schaefer
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February 2009
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Computer Aided Geometric Design
, Volume 26 Issue 2
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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Our main result is that two point interpolatory subdivision schemes using C^k nonlinear averaging rules on pairs of real numbers generate real-valued functions that are also C^k. The significance of this result is the following consequence: Suppose that ...
Keywords: CCScat{I.3.5}, Computer graphics, Curve, surface, and solid representations
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6
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Non-uniform subdivision for B-splines of arbitrary degree
S. Schaefer, R. Goldman
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January 2009
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Computer Aided Geometric Design
, Volume 26 Issue 1
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 3 |
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We present an efficient algorithm for subdividing non-uniform B-splines of arbitrary degree in a manner similar to the Lane-Riesenfeld subdivision algorithm for uniform B-splines of arbitrary degree. Our algorithm consists of doubling the control points ...
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| 2008
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7
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Division algorithms for Bernstein polynomials
Laurent Busé, Ron Goldman
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December 2008
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Computer Aided Geometric Design
, Volume 25 Issue 9
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 0 |
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Three division algorithms are presented for univariate Bernstein polynomials: an algorithm for finding the quotient and remainder of two univariate polynomials, an algorithm for calculating the GCD of an arbitrary collection of univariate polynomials, ...
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9
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Nonlinear subdivision through nonlinear averaging
S. Schaefer, E. Vouga, R. Goldman
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March 2008
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Computer Aided Geometric Design
, Volume 25 Issue 3
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 1 |
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We investigate a general class of nonlinear subdivision algorithms for functions of a real or complex variable built from linear subdivision algorithms by replacing binary linear averages such as the arithmetic mean by binary nonlinear averages such ...
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| 2007
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10
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Axial moving lines and singularities of rational planar curves
Ning Song, Falai Chen, Ron Goldman
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May 2007
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Computer Aided Geometric Design
, Volume 24 Issue 4
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Publisher: Elsevier Science Publishers B. V.
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| Bibliometrics: Downloads (6 Weeks): n/a, Downloads (12 Months): n/a, Citation Count: 3 |
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A natural one to one correspondence is derived between the singular points of rational planar curves and the axial moving lines that follow these curves. This correspondence is applied to compute and to analyze all the singular points of low degree rational ...
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