Edit Profile (opens in new tab) Goldman, Ronald N. Co-Author Distance Author ID: goldman.ronald-n Published as: Goldman, Ron; Goldman, Ronald N.; Goldman, R. N.; Goldman, Ronald; Goldman, R.; Goldman, Ron N. more...less Homepage: https://rongoldman.rice.edu/ External Links: MGP Documents Indexed: 148 Publications since 1976, including 3 Books and 1 Additional arXiv Preprint 5 Contributions as Editor Co-Authors: 65 Co-Authors with 128 Joint Publications 1,652 Co-Co-Authors all top 5 Co-Authors 23 single-authored 16 Barry, Phillip J. 12 Simeonov, Plamen C. 8 Sederberg, Thomas W. 8 Wang, Xuhui 7 Jia, Xiaohong 7 Wang, Haohao 7 Zhang, Ming 6 Lodha, Suresh Kumar 6 Morin, Géraldine 5 Mann, Stephen 4 Dişibüyük, Çetin 4 Wang, Wenping 3 Alcazar, Juan Gerardo 3 Anderson, David C. 3 Brunnett, Guido H. 3 DeRose, Tony D. 3 Dyn, Nira 3 Farin, Gerald E. 3 Habib, Ayman W. 3 Hahmann, Stefanie 3 Micchelli, Charles A. 3 Shen, Liyong 3 Shi, Xiaoran 3 Vouga, Etienne 3 Xu, Xiaowei 2 Ait-Haddou, Rachid 2 Barsky, Brian A. 2 Budakçı, Gülter 2 Du, Juan 2 Joe, Barry 2 Krasauskas, Rimvydas 2 Lyche, Tom 2 Oruç, Halil 2 Song, Ning 2 Zafiris, Vasilis G. 2 Zeng, Xiaoming 1 Barry, Phil 1 Busé, Laurent 1 Chen, Falai 1 Cox, David A. 1 Du, Hang 1 Feng, Yifei 1 Filip, Daniel J. 1 Hagen, Hans-Juergen 1 Heath, David C. 1 Hoffman, Jerome William 1 Khetan, Arnit 1 Levin, David N. 1 Li, Meng 1 Mazure, Marie-Laurence 1 Miller, James R. 1 Ning, Song 1 Othman, Wan Ainun Mior 1 Pérez-Díaz, Sonia 1 Ramshaw, Lyle 1 Sederberg, Tom 1 Simsek, Yilmaz 1 Stefanus, Lim Yohanes 1 Tsianos, Konstantinos I. 1 Tu, Changhe 1 Walz, Guido 1 Wang, Liqun 1 Warren, Joe D. 1 Winkler, Joab R. 1 Zürnacı, Fatma all top 5 Serials 46 Computer Aided Geometric Design 7 Journal of Approximation Theory 7 Journal of Symbolic Computation 6 CAD. Computer-Aided Design 4 ACM Transactions on Graphics 4 International Journal of Computational Geometry & Applications 3 Calcolo 3 Computing 3 Journal of Computational and Applied Mathematics 3 Constructive Approximation 3 Numerical Algorithms 3 Advances in Applied Clifford Algebras 2 Applied Numerical Mathematics 2 Computer Vision, Graphics, and Image Processing 2 Annals of Numerical Mathematics 1 Discrete Mathematics 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 Journal of Differential Geometry 1 Journal of Geometry 1 Results in Mathematics 1 SIAM Journal on Algebraic and Discrete Methods 1 The Visual Computer 1 SIAM Journal on Discrete Mathematics 1 Aequationes Mathematicae 1 CVGIP: Graphical Models and Image Processing 1 Fractals 1 Filomat 1 Advances in Computational Mathematics 1 Graphical Models 1 Foundations of Computational Mathematics 1 Contemporary Mathematics 1 Mathematics in Computer Science 1 European Journal of Pure and Applied Mathematics 1 Synthesis Lectures on Computer Graphics and Animation 1 SIAM Journal on Applied Algebra and Geometry all top 5 Fields 98 Numerical analysis (65-XX) 39 Approximations and expansions (41-XX) 39 Computer science (68-XX) 17 Algebraic geometry (14-XX) 14 Differential geometry (53-XX) 11 Commutative algebra (13-XX) 8 Linear and multilinear algebra; matrix theory (15-XX) 5 General and overarching topics; collections (00-XX) 5 Functions of a complex variable (30-XX) 5 Special functions (33-XX) 4 Combinatorics (05-XX) 4 Field theory and polynomials (12-XX) 4 Geometry (51-XX) 4 Probability theory and stochastic processes (60-XX) 3 Number theory (11-XX) 3 Associative rings and algebras (16-XX) 3 Real functions (26-XX) 3 Quantum theory (81-XX) 1 Operator theory (47-XX) 1 Convex and discrete geometry (52-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 127 Publications have been cited 1,107 times in 671 Documents Cited by ▼ Year ▼ Curvature formulas for implicit curves and surfaces. Zbl 1084.53004 Goldman, Ron 84 2005 Implicit representation of parametric curves and surfaces. Zbl 0601.65008 Sederberg, T. W.; Anderson, D. C.; Goldman, R. N. 64 1984 On the validity of implicitization by moving quadrics for rational surfaces with no base points. Zbl 0959.68124 Cox, David; Goldman, Ronald; Zhang, Ming 43 2000 Implicitizing rational curves by the method of moving algebraic curves. Zbl 0872.68193 Sederberg, Tom; Goldman, Ron; Du, Hang 34 1997 Polya’s urn model and computer aided geometric design. Zbl 0602.68103 Goldman, Ronald N. 32 1985 Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves. Zbl 0571.65114 Goldman, R. N.; Sederberg, T. W.; Anderson, D. C. 31 1984 \(q\)-blossoming: A new approach to algorithms and identities for \(q\)-Bernstein bases and \(q\)-Bézier curves. Zbl 1242.65036 Simeonov, Plamen; Zafiris, Vasilis; Goldman, Ron 26 2012 Functional composition algorithms via blossoming. Zbl 0771.68100 Derose, Tony D.; Goldman, Ronald N.; Hagen, Hans; Mann, Stephen 23 1993 Nonlinear subdivision through nonlinear averaging. Zbl 1172.65347 Schaefer, S.; Vouga, E.; Goldman, R. 21 2008 \(h\)-blossoming: A new approach to algorithms and identities for \(h\)-Bernstein bases and \(h\)-Bézier curves. Zbl 1246.65034 Simeonov, Plamen; Zafiris, Vasilis; Goldman, Ron 20 2011 Shape parameter deletion for Pólya curves. Zbl 0749.41009 Barry, Phillip J.; Goldman, Ronald N. 19 1991 \(\mu \)-bases for polynomial systems in one variable. Zbl 1205.65043 Song, Ning; Goldman, Ron 18 2009 Axial moving lines and singularities of rational planar curves. Zbl 1171.65352 Song, Ning; Chen, Falai; Goldman, Ron 18 2007 Knot insertion and deletion algorithms for B-spline curves and surfaces. Zbl 0772.00011 17 1993 Computing quadric surface intersections based on an analysis of plane cubic curves. Zbl 1055.68133 Wang, Wenping; Joe, Barry; Goldman, Ronald 17 2002 Non-uniform subdivision for B-splines of arbitrary degree. Zbl 1205.65054 Schaefer, S.; Goldman, R. 16 2009 \(\mu \)-bases and singularities of rational planar curves. Zbl 1205.14033 Jia, Xiaohong; Goldman, Ron 16 2009 Degree, multiplicity, and inversion formulas for rational surfaces using \(u\)-resultants. Zbl 0756.65011 Chionh, Eng-Wee; Goldman, Ronald N. 16 1992 Implicitizing rational surfaces of revolution using \(\mu \)-bases. Zbl 1256.65016 Shi, Xiaoran; Goldman, Ron 15 2012 An integrated introduction to computer graphics and geometric modeling. Zbl 1175.65001 Goldman, Ronald 15 2009 Fast computation of the Bézout and Dixon resultant matrices. Zbl 0996.65046 Chionh, Eng-Wee; Zhang, Ming; Goldman, Ronald N. 14 2002 \(R(4, 4)\) as a computational framework for 3-dimensional computer graphics. Zbl 1312.65020 Goldman, Ron; Mann, Stephen 14 2015 Enhancing Levin’s method for computing quadric-surface intersections. Zbl 1069.65570 Wang, Wenping; Goldman, Ronald; Tu, Changhe 13 2003 Generating functions for the \(q\)-Bernstein bases. Zbl 1304.65264 Goldman, Ron; Simeonov, Plamen; Simsek, Yilmaz 13 2014 Quantum B-splines. Zbl 1275.65011 Simeonov, Plamen; Goldman, Ron 13 2013 Conversion from Bézier rectangles to Bézier triangles. Zbl 0655.65023 Goldman, Ronald N.; Filip, Daniel J. 12 1987 Rethinking quaternions. Theory and computation. Zbl 1243.68003 Goldman, Ron 12 2010 Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves. Zbl 1298.65028 Jia, Xiaohong; Goldman, Ron 12 2012 Dual polynomial bases. Zbl 0824.41007 Goldman, Ronald N. 12 1994 The dual basis functions for the generalized Ball basis of odd degree. Zbl 0896.65019 Othman, W. A. M.; Goldman, R. N. 11 1997 Implicitization, inversion, and intersection of planar rational cubic curves. Zbl 0623.68079 Sederberg, T. W.; Anderson, D. C.; Goldman, R. N. 11 1985 On a relationship between the moving line and moving conic coefficient matrices. Zbl 0997.65019 Zhang, Ming; Chionh, Eng-Wee; Goldman, Ronald N. 11 1999 Using a bihomogeneous resultant to find the singularities of rational space curves. Zbl 1268.14053 Shi, Xiaoran; Jia, Xiaohong; Goldman, Ron 11 2013 The Sylvester resultant matrix for Bernstein polynomials. Zbl 1043.41004 Winkler, Joab R.; Goldman, Ronald N. 10 2003 Blossoming and knot insertion algorithms for B-spline curves. Zbl 0713.65006 Goldman, Ronald N. 10 1990 Identities for piecewise polynomial spaces determined by connection matrices. Zbl 0769.41007 Barry, Phillip J.; Dyn, Nira; Goldman, Ronald N.; Micchelli, Charles A. 10 1991 Quantum Bernstein bases and quantum Bézier curves. Zbl 1320.65028 Goldman, Ron; Simeonov, Plamen 10 2015 The rational Bernstein bases and the multirational blossoms. Zbl 0997.65021 Goldman, Ron 10 1999 Algebraic aspects of geometric continuity. Zbl 0679.65006 Goldman, R. N.; Micchelli, C. A. 9 1989 Recursive polynomial curve schemes and computer-aided geometric design. Zbl 0682.41016 Barry, Philip J.; Goldman, Ronald N. 9 1990 Algorithms for progressive curves: Extending B-spline and blossoming techniques to the monomial, power, and Newton dual bases. Zbl 0797.41011 Barry, Phillip J.; Goldman, Ronald N. 9 1993 Urn models and B-splines. Zbl 0645.60012 Goldman, Ronald N. 8 1988 Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices. Zbl 1256.65017 Shi, Xiaoran; Wang, Xuhui; Goldman, Ron 8 2012 Axial moving planes and singularities of rational space curves. Zbl 1205.14077 Wang, Haohao; Jia, Xiaohong; Goldman, Ron 8 2009 A subdivision scheme for Poisson curves and surfaces. Zbl 0948.68185 Morin, G.; Goldman, R. 8 2000 Division algorithms for Bernstein polynomials. Zbl 1172.33304 Busé, Laurent; Goldman, Ron 8 2008 Markov chains and computer-aided geometric design. I. Problems and constraints. Zbl 0592.68081 Goldman, Ronald N. 8 1984 Shape preserving properties of univariate Lototsky-Bernstein operators. Zbl 1376.41010 Xu, Xiao-Wei; Zeng, Xiao-Ming; Goldman, Ron 8 2017 Modeling 3D geometry in the Clifford algebra \(\mathbb R(4,4)\). Zbl 1386.15045 Du, Juan; Goldman, Ron; Mann, Stephen 8 2017 Strong \(\mu\)-bases for rational tensor product surfaces and extraneous factors associated to bad base points and anomalies at infinity. Zbl 1371.68300 Shen, Li-Yong; Goldman, Ron 8 2017 Two essential properties of \((q, h)\)-Bernstein-Bézier curves. Zbl 1321.65023 Goldman, Ron; Simeonov, Plamen 8 2015 Rectangular corner cutting and Sylvester \(\mathcal{A}\)-resultants. Zbl 1326.68370 Zhang, Ming; Goldman, Ron 7 2000 On beta-continuous functions and their application to the construction of geometrically continuous curves and surfaces. Zbl 0692.41018 Goldman, R. N.; Barsky, B. A. 7 1989 On the smooth convergence of subdivision and degree elevation for Bézier curves. Zbl 0983.68217 Morin, G.; Goldman, R. 7 2001 Using multivariate resultants to find the intersection of three quadric surfaces. Zbl 0736.68074 Chionh, Eng-Wee; Goldman, Ronald N.; Miller, James R. 7 1991 Convergence and smoothness of nonlinear Lane-Riesenfeld algorithms in the functional setting. Zbl 1217.65035 Dyn, Nira; Goldman, Ron 6 2011 Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices. Zbl 0824.65005 Barry, Phillip J.; Goldman, Ronald N.; Micchelli, Charles A. 6 1993 Rational quadratic parameterizations of quadrics. Zbl 0887.68109 Wang, Wenping; Joe, Barry; Goldman, Ronald 6 1997 What is the natural generalization of a Bézier curve? Zbl 0714.41033 Barry, P. J.; Goldman, R. N. 6 1989 Knot insertion algorithms. Zbl 0797.41012 Barry, Phillip J.; Goldman, Ronald N. 6 1993 A recursive proof of a B-spline identity for degree elevation. Zbl 0644.41006 Barry, Philip J.; Goldman, Ronald N. 5 1988 Hybrid Dixon resultants. Zbl 0960.65056 Zhang, M.; Chionh, E.; Goldman, R. N. 5 1998 Set-theoretic generators of rational space curves. Zbl 1184.14052 Jia, Xiaohong; Wang, Haohao; Goldman, Ron 5 2010 A unified approach to evaluation algorithms for multivariate polynomials. Zbl 0886.65005 Lodha, Suresh K.; Goldman, Ron 5 1997 The analytic blossom. Zbl 0989.65026 Morin, Géraldine; Goldman, Ron 5 2001 The method of resolvents: A technique for the implicitization, inversion, and intersection of non-planar, parametric, rational cubic curves. Zbl 0583.65009 Goldman, Ronald N. 5 1985 Linear subdivision is strictly a polynomial phenomenon. Zbl 0587.68091 Goldman, R. N.; Heath, D. C. 5 1984 Factored knot insertion. Zbl 0795.41006 Barry, Phillip J.; Goldman, Ronald N. 5 1993 Extending fundamental formulas from classical B-splines to quantum B-splines. Zbl 1309.65018 Budakçı, Gülter; Dişibüyük, Çetin; Goldman, Ron; Oruç, Halil 5 2015 A unifying structure for polar forms and for Bernstein Bézier curves. Zbl 1307.65023 Dişibüyük, Çetin; Goldman, Ron 5 2015 Generalized quantum splines. Zbl 1418.41007 Goldman, Ron; Simeonov, Plamen 5 2016 De Casteljau-type subdivision is peculiar to Bézier curves. Zbl 0658.65012 Barry, P. J.; Goldman, R. N. 4 1988 On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging. Zbl 1205.65081 Goldman, R.; Vouga, E.; Schaefer, S. 4 2009 Bézier and B-spline curves with knots in the complex plane. Zbl 1215.65030 Tsianos, Konstantinos I.; Goldman, Ron 4 2011 Applications of the Shorgin identity to Bernstein type operators. Zbl 1390.41005 Goldman, Ron; Xu, Xiao-Wei; Zeng, Xiao-Ming 4 2018 A multivariate generalization of the de Boor-Fix formula. Zbl 0814.65005 Lodha, Suresh; Goldman, Ron 4 1994 Markov chains and computer aided geometric design. II. Examples and subdivision matrices. Zbl 0614.68080 Goldman, Ronald N. 4 1985 Using invariants to extract geometric characteristics of conic sections from rational quadratic parameterizations. Zbl 1061.68167 Goldman, Ron; Wang, Wenping 4 2004 Sylvester \(A\)-resultants for bivariate polynomials with planar Newton polygons. Zbl 1134.13312 Khetan, Arnit; Ning, Song; Goldman, Ron 4 2004 Interpolation and approximation of curves and surfaces using Pólya polynomials. Zbl 0829.41004 Barry, Phillip J.; Goldman, Ronald N. 4 1991 Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces. Zbl 1366.65033 Shen, Li-Yong; Goldman, Ron 4 2017 Best polynomial degree reduction on \(q\)-lattices with applications to \(q\)-orthogonal polynomials. Zbl 1410.65043 Ait-Haddou, Rachid; Goldman, Ron 4 2015 \(\mu\)-bases for complex rational curves. Zbl 1286.65027 Wang, Xuhui; Goldman, Ron 4 2013 Urn models, approximations, and splines. Zbl 0656.41006 Goldman, Ronald N. 3 1988 Recursive proof of Boehm’s knot insertion technique. Zbl 0656.65008 Barry, Phillip J.; Goldman, Ronald N. 3 1988 Two blossoming proofs of the Lane-Riesenfeld algorithm. Zbl 1125.65015 Vouga, E.; Goldman, R. 3 2007 Multisided arrays of control points for multisided Bézier patches. Zbl 1069.65519 Goldman, Ron 3 2004 Polar forms in geometric modeling and algebraic geometry. Zbl 1039.65013 Goldman, Ron 3 2003 Toric Bézier patches with depth. Zbl 1039.65014 Krasauskas, Rimvydas; Goldman, Ron 3 2003 The holonomy ring on the leaves of foliated manifolds. Zbl 0356.57016 Goldman, Ronald 3 1976 B-splines, Pólya curves, and duality. Zbl 0725.41011 Barry, Phillip J.; Goldman, Ronald N.; DeRose, Tony D. 3 1991 A recursive algorithm for Hermite interpolation over a triangular grid. Zbl 0859.65005 Habib, A. W.; Goldman, R. N.; Lyche, T. 3 1996 Change of basis algorithms for surfaces in CAGD. Zbl 0875.68922 Lodha, Suresh; Goldman, Ron 3 1995 Computing perspective projections in 3-dimensions using rotors in the homogeneous and conformal models of Clifford algebra. Zbl 1335.65030 Goldman, Ron; Mann, Stephen; Jia, Xiaohong 3 2014 Blossoming with cancellation. Zbl 0997.65020 Goldman, Ron 3 1999 On Lototsky-Bernstein operators and Lototsky-Bernstein bases. Zbl 1505.41018 Xu, Xiao-Wei; Goldman, Ron 3 2019 Birational 2D free-form deformation of degree \(1\times n\). Zbl 1418.65035 Sederberg, Thomas W.; Goldman, Ronald N.; Wang, Xuhui 3 2016 Algebraic geometry and geometric modeling: insight and computation. Zbl 1110.14308 Goldman, Ron 2 2006 Minimal generators for the Rees algebra of rational space curves of type \((1,1,d-2)\). Zbl 1209.14049 Wang, Haohao; Hoffman, J. William; Jia, Xiaohong; Goldman, Ron 2 2010 Syzygies for translational surfaces. Zbl 1404.14069 Wang, Haohao; Goldman, Ron 2 2018 Ruled surfaces of revolution with moving axes and angles. Zbl 1505.65102 Wang, Haohao; Goldman, Ron 1 2021 Recognizing algebraic affine rotation surfaces. Zbl 1505.65043 Alcázar, Juan G.; Goldman, Ron 1 2020 Limits of sums for binomial and Eulerian numbers and their associated distributions. Zbl 1477.05014 Li, Meng; Goldman, Ron 1 2020 On Lototsky-Bernstein operators and Lototsky-Bernstein bases. Zbl 1505.41018 Xu, Xiao-Wei; Goldman, Ron 3 2019 Algebraic affine rotation surfaces of parabolic type. Zbl 1430.53010 Alcázar, Juan G.; Goldman, Ron 2 2019 High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting. Zbl 1505.65053 Dyn, Nira; Goldman, Ron; Levin, David 1 2019 A polynomial blossom for the Askey-Wilson operator. Zbl 1428.33036 Simeonov, Plamen; Goldman, Ron 1 2019 \(q\)-blossoming for analytic functions. Zbl 1425.30002 Goldman, Ron; Simeonov, Plamen 1 2019 Applications of the Shorgin identity to Bernstein type operators. Zbl 1390.41005 Goldman, Ron; Xu, Xiao-Wei; Zeng, Xiao-Ming 4 2018 Syzygies for translational surfaces. Zbl 1404.14069 Wang, Haohao; Goldman, Ron 2 2018 Implicitizing ruled translational surfaces. Zbl 1381.65017 Wang, Haohao; Goldman, Ron 2 2018 Shape preserving properties of univariate Lototsky-Bernstein operators. Zbl 1376.41010 Xu, Xiao-Wei; Zeng, Xiao-Ming; Goldman, Ron 8 2017 Modeling 3D geometry in the Clifford algebra \(\mathbb R(4,4)\). Zbl 1386.15045 Du, Juan; Goldman, Ron; Mann, Stephen 8 2017 Strong \(\mu\)-bases for rational tensor product surfaces and extraneous factors associated to bad base points and anomalies at infinity. Zbl 1371.68300 Shen, Li-Yong; Goldman, Ron 8 2017 Algorithms for computing strong \(\mu\)-bases for rational tensor product surfaces. Zbl 1366.65033 Shen, Li-Yong; Goldman, Ron 4 2017 Generalized quantum splines. Zbl 1418.41007 Goldman, Ron; Simeonov, Plamen 5 2016 Birational 2D free-form deformation of degree \(1\times n\). Zbl 1418.65035 Sederberg, Thomas W.; Goldman, Ronald N.; Wang, Xuhui 3 2016 A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form. Zbl 1377.65018 Dişibüyük, Çetin; Goldman, Ron 2 2016 Novel polynomial Bernstein bases and Bézier curves based on a general notion of polynomial blossoming. Zbl 1344.65022 Goldman, Ron; Simeonov, Plamen 2 2016 \(R(4, 4)\) as a computational framework for 3-dimensional computer graphics. Zbl 1312.65020 Goldman, Ron; Mann, Stephen 14 2015 Quantum Bernstein bases and quantum Bézier curves. Zbl 1320.65028 Goldman, Ron; Simeonov, Plamen 10 2015 Two essential properties of \((q, h)\)-Bernstein-Bézier curves. Zbl 1321.65023 Goldman, Ron; Simeonov, Plamen 8 2015 Extending fundamental formulas from classical B-splines to quantum B-splines. Zbl 1309.65018 Budakçı, Gülter; Dişibüyük, Çetin; Goldman, Ron; Oruç, Halil 5 2015 A unifying structure for polar forms and for Bernstein Bézier curves. Zbl 1307.65023 Dişibüyük, Çetin; Goldman, Ron 5 2015 Best polynomial degree reduction on \(q\)-lattices with applications to \(q\)-orthogonal polynomials. Zbl 1410.65043 Ait-Haddou, Rachid; Goldman, Ron 4 2015 Generating functions for the \(q\)-Bernstein bases. Zbl 1304.65264 Goldman, Ron; Simeonov, Plamen; Simsek, Yilmaz 13 2014 Computing perspective projections in 3-dimensions using rotors in the homogeneous and conformal models of Clifford algebra. Zbl 1335.65030 Goldman, Ron; Mann, Stephen; Jia, Xiaohong 3 2014 Generating functions for B-splines with knots in geometric or affine progression. Zbl 1316.65020 Dişibüyük, Çetin; Budakçı, Gülter; Goldman, Ron; Oruç, Halil 2 2014 Generating functions for uniform B-splines. Zbl 1356.65034 Goldman, Ron 2 2014 Quantum B-splines. Zbl 1275.65011 Simeonov, Plamen; Goldman, Ron 13 2013 Using a bihomogeneous resultant to find the singularities of rational space curves. Zbl 1268.14053 Shi, Xiaoran; Jia, Xiaohong; Goldman, Ron 11 2013 \(\mu\)-bases for complex rational curves. Zbl 1286.65027 Wang, Xuhui; Goldman, Ron 4 2013 \(q\)-blossoming: A new approach to algorithms and identities for \(q\)-Bernstein bases and \(q\)-Bézier curves. Zbl 1242.65036 Simeonov, Plamen; Zafiris, Vasilis; Goldman, Ron 26 2012 Implicitizing rational surfaces of revolution using \(\mu \)-bases. Zbl 1256.65016 Shi, Xiaoran; Goldman, Ron 15 2012 Using Smith normal forms and \(\mu\)-bases to compute all the singularities of rational planar curves. Zbl 1298.65028 Jia, Xiaohong; Goldman, Ron 12 2012 Using \(\mu \)-bases to implicitize rational surfaces with a pair of orthogonal directrices. Zbl 1256.65017 Shi, Xiaoran; Wang, Xuhui; Goldman, Ron 8 2012 \(h\)-blossoming: A new approach to algorithms and identities for \(h\)-Bernstein bases and \(h\)-Bézier curves. Zbl 1246.65034 Simeonov, Plamen; Zafiris, Vasilis; Goldman, Ron 20 2011 Convergence and smoothness of nonlinear Lane-Riesenfeld algorithms in the functional setting. Zbl 1217.65035 Dyn, Nira; Goldman, Ron 6 2011 Bézier and B-spline curves with knots in the complex plane. Zbl 1215.65030 Tsianos, Konstantinos I.; Goldman, Ron 4 2011 A homogeneous model for three-dimensional computer graphics based on the Clifford algebra for \(\mathbb{R}^{3}\). Zbl 1290.68124 Goldman, Ron 1 2011 Rethinking quaternions. Theory and computation. Zbl 1243.68003 Goldman, Ron 12 2010 Set-theoretic generators of rational space curves. Zbl 1184.14052 Jia, Xiaohong; Wang, Haohao; Goldman, Ron 5 2010 Minimal generators for the Rees algebra of rational space curves of type \((1,1,d-2)\). Zbl 1209.14049 Wang, Haohao; Hoffman, J. William; Jia, Xiaohong; Goldman, Ron 2 2010 \(\mu \)-bases for polynomial systems in one variable. Zbl 1205.65043 Song, Ning; Goldman, Ron 18 2009 Non-uniform subdivision for B-splines of arbitrary degree. Zbl 1205.65054 Schaefer, S.; Goldman, R. 16 2009 \(\mu \)-bases and singularities of rational planar curves. Zbl 1205.14033 Jia, Xiaohong; Goldman, Ron 16 2009 An integrated introduction to computer graphics and geometric modeling. Zbl 1175.65001 Goldman, Ronald 15 2009 Axial moving planes and singularities of rational space curves. Zbl 1205.14077 Wang, Haohao; Jia, Xiaohong; Goldman, Ron 8 2009 On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging. Zbl 1205.65081 Goldman, R.; Vouga, E.; Schaefer, S. 4 2009 Nonlinear subdivision through nonlinear averaging. Zbl 1172.65347 Schaefer, S.; Vouga, E.; Goldman, R. 21 2008 Division algorithms for Bernstein polynomials. Zbl 1172.33304 Busé, Laurent; Goldman, Ron 8 2008 Axial moving lines and singularities of rational planar curves. Zbl 1171.65352 Song, Ning; Chen, Falai; Goldman, Ron 18 2007 Two blossoming proofs of the Lane-Riesenfeld algorithm. Zbl 1125.65015 Vouga, E.; Goldman, R. 3 2007 Algebraic geometry and geometric modeling: insight and computation. Zbl 1110.14308 Goldman, Ron 2 2006 Bézier subdivision for inverse molecular kinematics. Zbl 1108.92021 Zhang, Ming; Wang, Liqun; Goldman, Ronald 1 2006 Curvature formulas for implicit curves and surfaces. Zbl 1084.53004 Goldman, Ron 84 2005 Using invariants to extract geometric characteristics of conic sections from rational quadratic parameterizations. Zbl 1061.68167 Goldman, Ron; Wang, Wenping 4 2004 Sylvester \(A\)-resultants for bivariate polynomials with planar Newton polygons. Zbl 1134.13312 Khetan, Arnit; Ning, Song; Goldman, Ron 4 2004 Multisided arrays of control points for multisided Bézier patches. Zbl 1069.65519 Goldman, Ron 3 2004 Enhancing Levin’s method for computing quadric-surface intersections. Zbl 1069.65570 Wang, Wenping; Goldman, Ronald; Tu, Changhe 13 2003 The Sylvester resultant matrix for Bernstein polynomials. Zbl 1043.41004 Winkler, Joab R.; Goldman, Ronald N. 10 2003 Polar forms in geometric modeling and algebraic geometry. Zbl 1039.65013 Goldman, Ron 3 2003 Toric Bézier patches with depth. Zbl 1039.65014 Krasauskas, Rimvydas; Goldman, Ron 3 2003 Computing quadric surface intersections based on an analysis of plane cubic curves. Zbl 1055.68133 Wang, Wenping; Joe, Barry; Goldman, Ronald 17 2002 Fast computation of the Bézout and Dixon resultant matrices. Zbl 0996.65046 Chionh, Eng-Wee; Zhang, Ming; Goldman, Ronald N. 14 2002 The affine invariant analytic blossom. Zbl 1043.41006 Goldman, Ron; Morin, Géraldine 2 2002 On the smooth convergence of subdivision and degree elevation for Bézier curves. Zbl 0983.68217 Morin, G.; Goldman, R. 7 2001 The analytic blossom. Zbl 0989.65026 Morin, Géraldine; Goldman, Ron 5 2001 Blossoming and divided difference. Zbl 0990.65018 Goldman, R. 2 2001 Trimming analytic functions using right sided Poisson subdivision. Zbl 1206.65127 Morin, Géraldine; Goldman, Ron 1 2001 On the validity of implicitization by moving quadrics for rational surfaces with no base points. Zbl 0959.68124 Cox, David; Goldman, Ronald; Zhang, Ming 43 2000 A subdivision scheme for Poisson curves and surfaces. Zbl 0948.68185 Morin, G.; Goldman, R. 8 2000 Rectangular corner cutting and Sylvester \(\mathcal{A}\)-resultants. Zbl 1326.68370 Zhang, Ming; Goldman, Ron 7 2000 Efficient implicitization of rational surfaces by moving planes. Zbl 0981.65021 Zhang, Ming; Goldman, Ron; Chionh, Eng Wee 2 2000 On a relationship between the moving line and moving conic coefficient matrices. Zbl 0997.65019 Zhang, Ming; Chionh, Eng-Wee; Goldman, Ronald N. 11 1999 The rational Bernstein bases and the multirational blossoms. Zbl 0997.65021 Goldman, Ron 10 1999 Blossoming with cancellation. Zbl 0997.65020 Goldman, Ron 3 1999 Hybrid Dixon resultants. Zbl 0960.65056 Zhang, M.; Chionh, E.; Goldman, R. N. 5 1998 Lattices and algorithms for bivariate Bernstein, Lagrange, Newton, and other related polynomial bases based on duality between \(L\)-bases and \(B\)-bases. Zbl 0901.68207 Lodha, Suresh Kumar; Goldman, Ron 1 1998 Implicitizing rational curves by the method of moving algebraic curves. Zbl 0872.68193 Sederberg, Tom; Goldman, Ron; Du, Hang 34 1997 The dual basis functions for the generalized Ball basis of odd degree. Zbl 0896.65019 Othman, W. A. M.; Goldman, R. N. 11 1997 Rational quadratic parameterizations of quadrics. Zbl 0887.68109 Wang, Wenping; Joe, Barry; Goldman, Ronald 6 1997 A unified approach to evaluation algorithms for multivariate polynomials. Zbl 0886.65005 Lodha, Suresh K.; Goldman, Ron 5 1997 A recursive algorithm for Hermite interpolation over a triangular grid. Zbl 0859.65005 Habib, A. W.; Goldman, R. N.; Lyche, T. 3 1996 A ladder recurrence algorithm for the evaluation of L-patches. Zbl 0849.65010 Lodha, Suresh; Goldman, Ron; Warren, Joe 1 1996 Theories of contact specified by connection matrices. Zbl 0875.68888 Habib, Ayman W.; Goldman, Ron N. 1 1996 Change of basis algorithms for surfaces in CAGD. Zbl 0875.68922 Lodha, Suresh; Goldman, Ron 3 1995 Duality between degree elevation and differentiation for B-bases and L- bases. Zbl 0835.65030 Lodha, Suresh; Goldman, Ron 1 1995 Dual polynomial bases. Zbl 0824.41007 Goldman, Ronald N. 12 1994 A multivariate generalization of the de Boor-Fix formula. Zbl 0814.65005 Lodha, Suresh; Goldman, Ron 4 1994 Functional composition algorithms via blossoming. Zbl 0771.68100 Derose, Tony D.; Goldman, Ronald N.; Hagen, Hans; Mann, Stephen 23 1993 Knot insertion and deletion algorithms for B-spline curves and surfaces. Zbl 0772.00011 17 1993 Algorithms for progressive curves: Extending B-spline and blossoming techniques to the monomial, power, and Newton dual bases. Zbl 0797.41011 Barry, Phillip J.; Goldman, Ronald N. 9 1993 Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices. Zbl 0824.65005 Barry, Phillip J.; Goldman, Ronald N.; Micchelli, Charles A. 6 1993 Knot insertion algorithms. Zbl 0797.41012 Barry, Phillip J.; Goldman, Ronald N. 6 1993 Factored knot insertion. Zbl 0795.41006 Barry, Phillip J.; Goldman, Ronald N. 5 1993 Degree, multiplicity, and inversion formulas for rational surfaces using \(u\)-resultants. Zbl 0756.65011 Chionh, Eng-Wee; Goldman, Ronald N. 16 1992 Unimodal properties of B-spline and Bernstein-basis functions. Zbl 0765.41012 Barry, P. J.; Beatty, J. C.; Goldman, R. N. 1 1992 Shape parameter deletion for Pólya curves. Zbl 0749.41009 Barry, Phillip J.; Goldman, Ronald N. 19 1991 Identities for piecewise polynomial spaces determined by connection matrices. Zbl 0769.41007 Barry, Phillip J.; Dyn, Nira; Goldman, Ronald N.; Micchelli, Charles A. 10 1991 ...and 27 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 906 Authors 75 Goldman, Ronald N. 19 Chen, Falai 18 Sederberg, Thomas W. 16 Pérez-Díaz, Sonia 15 Busé, Laurent 12 Wang, Haohao 11 D’Andrea, Carlos 11 Jia, Xiaohong 11 Shen, Liyong 11 Simeonov, Plamen C. 10 Alcazar, Juan Gerardo 9 Barry, Phillip J. 9 Cox, David A. 9 Wang, Xuhui 9 Winkler, Joab R. 8 Dişibüyük, Çetin 8 Peña, Juan Manuel 7 Ait-Haddou, Rachid 7 Düldül, Mustafa 7 Farouki, Rida T. 7 Hughes, Thomas J. R. 7 Marco García, Ana 7 Wang, Wenping 6 Dyn, Nira 6 Gao, Xiaoshan 6 Martínez, José-Javier 6 Sendra, Juan Rafael 6 Shi, Xiaoran 6 Simsek, Yilmaz 6 Zhang, Yongjie Jessica 5 Aléssio, Osmar 5 Breuils, Stéphane 5 Cortadellas Benítez, Teresa 5 Hermoso Ortiz, Carlos 5 Hoffman, Jerome William 5 Jüttler, Bert 5 Kustin, Andrew R. 5 Mainar, Esmeralda 5 Mann, Stephen 5 Mazure, Marie-Laurence 5 Sánchez-Reyes, Javier 5 Tan, Jieqing 5 Zeng, Xiaoming 5 Zhang, Li 5 Zhu, Chungang 4 Abdel-All, Nassar Hassan 4 Badr, Sayed Abdel-Naeim 4 Bourne, Martin 4 Chardin, Marc 4 Delgado, Jorge F. M. 4 Dickenstein, Alicia M. 4 Elber, Gershon 4 Gonzalez-Vega, Laureano 4 Hitzer, Eckhard 4 Lai, Yisheng 4 Lamnii, Mohamed 4 Lávička, Miroslav 4 Li, Jinggai 4 Manocha, Dinesh 4 Micchelli, Charles A. 4 Mourrain, Bernard 4 Nozick, Vincent 4 Patterson, Richard R. 4 Peters, Jorg 4 Schicho, Josef 4 Seidel, Hans-Peter 4 Su, Yi 4 Tijini, Ahmed 4 Tu, Changhe 4 Vršek, Jan 4 Xu, Xiaowei 4 Zheng, Jianmin 3 Botbol, Nicolás 3 Canny, John F. 3 Casciola, Giulio 3 Chtcherba, Arthur D. 3 Deng, Chongyang 3 Deng, Jiansong 3 Duarte, Eliana 3 Duchamp, Thomas E. 3 Düldül, Bahar Uyar 3 Elkadi, Mohamed 3 Emiris, Ioannis Z. 3 Evans, John A. 3 Feng, Jieqing 3 Fuchs, Laurent 3 Kapur, Deepak 3 Kozak, Jernej 3 Lamnii, Abdellah 3 Lee, E. T. Y. 3 Li, Ji 3 Lodha, Suresh Kumar 3 Morin, Géraldine 3 Mühlbach, Günter W. 3 Muntingh, Georg 3 Peltier, Samuel 3 Peters, Thomas J. 3 Polini, Claudia 3 Pottmann, Helmut 3 Qin, Xiaolin ...and 806 more Authors all top 5 Cited in 156 Serials 186 Computer Aided Geometric Design 53 Journal of Symbolic Computation 39 Journal of Computational and Applied Mathematics 21 Computer Methods in Applied Mechanics and Engineering 20 Applied Mathematics and Computation 15 Advances in Applied Clifford Algebras 14 Numerical Algorithms 11 Journal of Computational Physics 10 Journal of Algebra 10 Linear Algebra and its Applications 9 Journal of Approximation Theory 9 Constructive Approximation 8 BIT 8 Journal of Systems Science and Complexity 7 Advances in Computational Mathematics 6 Mathematics of Computation 6 Mathematics and Computers in Simulation 6 International Journal of Computer Mathematics 5 Computers & Mathematics with Applications 5 Applied Numerical Mathematics 5 Journal of Inequalities and Applications 5 Foundations of Computational Mathematics 4 Calcolo 4 Computing 4 Computational Mechanics 4 Applicable Algebra in Engineering, Communication and Computing 4 Journal of Mathematical Imaging and Vision 4 SIAM Journal on Scientific Computing 4 Applied Mathematics. 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Serie II 1 Theoretical Computer Science 1 Optimization 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 Engineering with Computers ...and 56 more Serials all top 5 Cited in 49 Fields 411 Numerical analysis (65-XX) 145 Computer science (68-XX) 128 Approximations and expansions (41-XX) 114 Algebraic geometry (14-XX) 71 Commutative algebra (13-XX) 56 Differential geometry (53-XX) 36 Linear and multilinear algebra; matrix theory (15-XX) 28 Geometry (51-XX) 18 Fluid mechanics (76-XX) 17 Number theory (11-XX) 16 Special functions (33-XX) 16 Mechanics of deformable solids (74-XX) 15 Field theory and polynomials (12-XX) 15 Real functions (26-XX) 13 Combinatorics (05-XX) 13 Functions of a complex variable (30-XX) 11 Partial differential equations (35-XX) 8 Convex and discrete geometry (52-XX) 8 Probability theory and stochastic processes (60-XX) 7 Biology and other natural sciences (92-XX) 6 Ordinary differential equations (34-XX) 6 Information and communication theory, circuits (94-XX) 5 Topological groups, Lie groups (22-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Manifolds and cell complexes (57-XX) 4 Statistics (62-XX) 4 Mechanics of particles and systems (70-XX) 4 Operations research, mathematical programming (90-XX) 3 Associative rings and algebras (16-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Operator theory (47-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Quantum theory (81-XX) 3 Geophysics (86-XX) 2 Nonassociative rings and algebras (17-XX) 2 Difference and functional equations (39-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 Measure and integration (28-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX) Citations by Year