Ron Goldman

Orcid: 0000-0001-8720-3860

Affiliations:
  • Rice University, Houston, TX, USA


According to our database1, Ron Goldman authored at least 150 papers between 1983 and 2024.

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Bibliography

2024
Subdivision algorithms with modular arithmetic.
Comput. Aided Geom. Des., 2024

2023
On the uniqueness of the multirational blossom.
Comput. Aided Geom. Des., December, 2023

2021
Ruled Surfaces of Revolution with Moving Axes and Angles.
Int. J. Comput. Geom. Appl., 2021

2020
Limits of sums for binomial and Eulerian numbers and their associated distributions.
Discret. Math., 2020

Recognizing algebraic affine rotation surfaces.
Comput. Aided Geom. Des., 2020

2019
q-Blossoming for analytic functions.
Numer. Algorithms, 2019

Rational curves over generalized complex numbers.
J. Symb. Comput., 2019

Surfaces of revolution with moving axes and angles.
Graph. Model., 2019

Limits of Sums for Binomial and Eulerian Numbers and their Associated Distributions.
CoRR, 2019

On Lototsky-Bernstein operators and Lototsky-Bernstein bases.
Comput. Aided Geom. Des., 2019

Representing rational curve segments and surface patches using semi-algebraic sets.
Comput. Aided Geom. Des., 2019

High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting.
Comput. Aided Geom. Des., 2019

2018
Using Dual Quaternion to Study Translational Surfaces.
Math. Comput. Sci., 2018

Syzygies for translational surfaces.
J. Symb. Comput., 2018

de Boor-suitable (DS) T-splines.
Graph. Model., 2018

Implicitizing ruled translational surfaces.
Comput. Aided Geom. Des., 2018

Combining complementary methods for implicitizing rational tensor product surfaces.
Comput. Aided Des., 2018

2017
Detecting When an Implicit Equation or a Rational Parametrization Defines a Conical or Cylindrical Surface, or a Surface of Revolution.
IEEE Trans. Vis. Comput. Graph., 2017

Implicitizing Rational Tensor Product Surfaces Using the Resultant of Three Moving Planes.
ACM Trans. Graph., 2017

Strong μ-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity.
SIAM J. Appl. Algebra Geom., 2017

An Asymmetric Distributed Method for Sorting a Robot Swarm.
IEEE Robotics Autom. Lett., 2017

Shape preserving properties of univariate Lototsky-Bernstein operators.
J. Approx. Theory, 2017

Algorithms for computing strong μ-bases for rational tensor product surfaces.
Comput. Aided Geom. Des., 2017

Building Fractals with a Robot Swarm.
Proceedings of the Advances in Swarm Intelligence - 8th International Conference, 2017

2016
Finding the Axis of Revolution of an Algebraic Surface of Revolution.
IEEE Trans. Vis. Comput. Graph., 2016

Novel polynomial Bernstein bases and Bézier curves based on a general notion of polynomial blossoming.
Numer. Algorithms, 2016

Algebraic surfaces invariant under scissor shears.
Graph. Model., 2016

Explicit μ-bases for conic sections and planar rational cubic curves.
Comput. Aided Geom. Des., 2016

Birational 2D Free-Form Deformation of degree 1 × n.
Comput. Aided Geom. Des., 2016

Two additional advantages of complex μ-bases for non-ruled real quadric surfaces.
Comput. Aided Geom. Des., 2016

Generalized quantum splines.
Comput. Aided Geom. Des., 2016

Generating a 3D Normative Infant Cranial Model.
Proceedings of the International Conference on Computational Science 2016, 2016

2015
Extending fundamental formulas from classical B-splines to quantum B-splines.
J. Comput. Appl. Math., 2015

Quantum Bernstein bases and quantum Bézier curves.
J. Comput. Appl. Math., 2015

A unifying structure for polar forms and for Bernstein Bézier curves.
J. Approx. Theory, 2015

Quaternion rational surfaces: Rational surfaces generated from the quaternion product of two rational space curves.
Graph. Model., 2015

Complex μ-bases for real quadric surfaces.
Comput. Aided Geom. Des., 2015

Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials.
Appl. Math. Comput., 2015

2014
Generating Functions for the q-Bernstein Bases.
SIAM J. Discret. Math., 2014

Corrigendum to Example 4 in "μ-Bases for complex rational curves" [Computer Aided Geometric Design 30 (2013), 623-635].
Comput. Aided Geom. Des., 2014

2013
Using a bihomogeneous resultant to find the singularities of rational space curves.
J. Symb. Comput., 2013

Modeling perspective projections in 3-dimensions by rotations in 4-dimensions.
Graph. Model., 2013

μ-Bases for complex rational curves.
Comput. Aided Geom. Des., 2013

2012
q-Blossoming: A new approach to algorithms and identities for q-Bernstein bases and q-Bézier curves.
J. Approx. Theory, 2012

Formulas and algorithms for quantum differentiation of quantum Bernstein bases and quantum Bézier curves based on quantum blossoming.
Graph. Model., 2012

Using μ-bases to implicitize rational surfaces with a pair of orthogonal directrices.
Comput. Aided Geom. Des., 2012

Implicitizing rational surfaces of revolution using μ-bases.
Comput. Aided Geom. Des., 2012

Using Smith normal forms and μ-bases to compute all the singularities of rational planar curves.
Comput. Aided Geom. Des., 2012

Generating Functions for Uniform B-Splines.
Proceedings of the Mathematical Methods for Curves and Surfaces, 2012

2011
Convergence and Smoothness of Nonlinear Lane-Riesenfeld Algorithms in the Functional Setting.
Found. Comput. Math., 2011

Understanding quaternions.
Graph. Model., 2011

h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves.
Comput. Aided Geom. Des., 2011

A Homogeneous Model for Three-Dimensional Computer Graphics Based on the Clifford Algebra for ℝ<sup>3</sup>.
Proceedings of the Guide to Geometric Algebra in Practice., 2011

2010
Rethinking Quaternions
Synthesis Lectures on Computer Graphics and Animation, Morgan & Claypool Publishers, ISBN: 978-3-031-79549-7, 2010

Set-theoretic generators of rational space curves.
J. Symb. Comput., 2010

Using Smith Normal Forms and mu-Bases to Compute all the Singularities of Rational Planar Curves
CoRR, 2010

2009
Axial moving planes and singularities of rational space curves.
Comput. Aided Geom. Des., 2009

mu-bases for polynomial systems in one variable.
Comput. Aided Geom. Des., 2009

Non-uniform subdivision for B-splines of arbitrary degree.
Comput. Aided Geom. Des., 2009

µ-Bases and singularities of rational planar curves.
Comput. Aided Geom. Des., 2009

On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging.
Comput. Aided Geom. Des., 2009

2008
Nonlinear subdivision through nonlinear averaging.
Comput. Aided Geom. Des., 2008

Division algorithms for Bernstein polynomials.
Comput. Aided Geom. Des., 2008

After the revolution: Geometric algebra for Computer Scientists in the twenty-first century.
Comput. Aided Des., 2008

2007
Two blossoming proofs of the Lane-Riesenfeld algorithm.
Computing, 2007

Editorial: Special issue on Geometric Modeling (Dagstuhl 2005).
Computing, 2007

Axial moving lines and singularities of rational planar curves.
Comput. Aided Geom. Des., 2007

2006
Bézier Subdivision for Inverse Molecular Kinematics.
Int. J. Comput. Geom. Appl., 2006

Algebraic geometry and geometric modeling: insight and computation.
Proceedings of the Algebraic Geometry and Geometric Modeling, 2006

2005
Curvature formulas for implicit curves and surfaces.
Comput. Aided Geom. Des., 2005

Improving conformational searches by geometric screening.
Bioinform., 2005

Subdivision Schemes and Attractors.
Proceedings of the Third Eurographics Symposium on Geometry Processing, 2005

05221 Report of the Dagstuhl seminar on - Geometric Modelling.
Proceedings of the Geometric Modeling, 29.05. - 03.06.2005, 2005

2004
Using Invariants To Extract Geometric Characteristics Of Conic Sections From Rational Quadratic Parameterizations.
Int. J. Comput. Geom. Appl., 2004

Recursive turtle programs and iterated affine transformations.
Comput. Graph., 2004

Multisided arrays of control points for multisided Bezier patches.
Comput. Aided Geom. Des., 2004

Turtle geometry in computer graphics and computer-aided design.
Comput. Aided Des., 2004

Sylvester-resultants for bivariate polynomials with planar newton polygons.
Proceedings of the Symbolic and Algebraic Computation, 2004

The Fractal Nature of Bezier Curves.
Proceedings of the 2004 Geometric Modeling and Processing (GMP 2004), 2004

2003
Deriving Linear Transformations in Three Dimensions.
IEEE Computer Graphics and Applications, 2003

Enhancing Levin's method for computing quadric-surface intersections.
Comput. Aided Geom. Des., 2003

Computer Graphics in its Fifth Decade: Ferment at the Foundations.
Proceedings of the 11th Pacific Conference on Computer Graphics and Applications, 2003

Morphing Rational B-spline Curves and Surfaces Using Mass Distributions.
Proceedings of the 24th Annual Conference of the European Association for Computer Graphics, 2003

Pyramid algorithms - a dynamic programming approach to curves and surfaces for geometric modeling.
Morgan Kaufmann series in computer graphics and geometric modeling, Morgan Kaufmann, ISBN: 978-1-55860-354-7, 2003

2002
On the algebraic and geometric foundations of computer graphics.
ACM Trans. Graph., 2002

Fast Computation of the Bezout and Dixon Resultant Matrices.
J. Symb. Comput., 2002

Computing quadric surface intersections based on an analysis of plane cubic curves.
Graph. Model., 2002

The affine invariant analytic blossom.
Comput. Aided Geom. Des., 2002

2001
Baseball Arithmetic and the Laws of Pseudoperspective.
IEEE Computer Graphics and Applications, 2001

On the smooth convergence of subdivision and degree elevation for Bézier curves.
Comput. Aided Geom. Des., 2001

Trimming analytic functions using right sided Poisson subdivision.
Comput. Aided Des., 2001

2000
On the Validity of Implicitization by Moving Quadrics for Rational Surfaces with No Base Points.
J. Symb. Comput., 2000

The Ambient Spaces of Computer Graphics and Geometric Modeling.
IEEE Computer Graphics and Applications, 2000

A subdivision scheme for Poisson curves and surfaces.
Comput. Aided Geom. Des., 2000

Rectangular corner cutting and Sylvester A-resultants.
Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation, 2000

Poisson Approximation.
Proceedings of the Geometric Modeling and Processing 2000, 2000

Implicitization by Dixon A-Resultants.
Proceedings of the Geometric Modeling and Processing 2000, 2000

1999
On a relationship between the moving line and moving conic coefficient matrices.
Comput. Aided Geom. Des., 1999

The rational Bernstein bases and the multirational blossoms.
Comput. Aided Geom. Des., 1999

Blossoming with cancellation.
Comput. Aided Geom. Des., 1999

Blossoming and Divided Difference.
Proceedings of the Geometric Modelling, Dagstuhl, 1999

1998
On the Linear Independence of the Bivariate Discrete Convolution Blending Functions.
Proceedings of Computing: The Fourth Australasian Theory Symposium (CATS'98), 1998

1997
A unified approach to evaluation algorithms for multivariate polynomials.
Math. Comput., 1997

Implicitizing Rational Curves by the Method of Moving Algebraic Curves.
J. Symb. Comput., 1997

Rational Quadratic Parameterizations of Quadrics.
Int. J. Comput. Geom. Appl., 1997

The dual basis functions for the generalized Ball basis of odd degree.
Comput. Aided Geom. Des., 1997

1996
Theories of contact specified by connection matrices.
Comput. Aided Geom. Des., 1996

1995
Geometric Algorithms for Detecting and Calculating All Conic Sections in the Intersection of Any 2 Natural Quadric Surfaces.
CVGIP Graph. Model. Image Process., 1995

Elimination and resultants.2. Multivariate resultants.
IEEE Computer Graphics and Applications, 1995

Elimination and resultants. 1. Elimination and bivariate resultants.
IEEE Computer Graphics and Applications, 1995

Change of basis algorithms for surfaces in CAGD.
Comput. Aided Geom. Des., 1995

1994
On the Existence and the Coefficients of the Implicit Equation of Rational Surfaces.
CVGIP Graph. Model. Image Process., 1994

Knot Insertion Using Forward Differences.
Proceedings of the Graphics Gems, 1994

1993
Functional Composition Algorithms via Blossoming.
ACM Trans. Graph., 1993

Erratum: Volume 55, Number 1 (1993) in the article "An Extension of Chaiken's Algorithm to B-Spline Curves with Knots in Geometric Progression," by Ron Goldman and Joe Warren, pages 58-62.
CVGIP Graph. Model. Image Process., 1993

An Extension of Chaiken's Algorithm to B-Spline Curves with Knots in Geometric Progression.
CVGIP Graph. Model. Image Process., 1993

Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices.
Adv. Comput. Math., 1993

Unimodal Properties of Generalized Ball Bases.
Proceedings of the Geometric Modelling, Dagstuhl, 1993

1992
Using multivariate resultants to find the implicit equation of a rational surface.
Vis. Comput., 1992

Using tangent balls to find plane sections of natural quadrics.
IEEE Computer Graphics and Applications, 1992

Blossoming Marsden's identity.
Comput. Aided Geom. Des., 1992

Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants.
Comput. Aided Geom. Des., 1992

Unimodal properties of B-spline and Bernstein-basis functions.
Comput. Aided Des., 1992

Chapter 4: Knot Insertion Algorithms.
Proceedings of the Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces, 1992

Chapter 3: Factored Knot Insertion.
Proceedings of the Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces, 1992

Chapter 2: Algorithms for Progressive Curves: Extending B-Spline and Blossoming Techniques to the Monomial, Power, and Newton Dual Bases.
Proceedings of the Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces, 1992

Decomposing linear and Affine Transformations.
Proceedings of the Graphics Gems III (IBM Version), 1992

Decomposing Projective Transformations.
Proceedings of the Graphics Gems III (IBM Version), 1992

Cross Product in Four Dimensions and beyond.
Proceedings of the Graphics Gems III (IBM Version), 1992

1991
Using Multivariate Resultants to Find the Intersection of Three Quadric Surfaces.
ACM Trans. Graph., 1991

Shape parameter deletion for Pólya curves.
Numer. Algorithms, 1991

Interpolation and approximation of curves and surfaces using Pólya polynomials.
CVGIP Graph. Model. Image Process., 1991

Combining algebraic rigor with geometric robustness for the detection and calculation of conic sections in the intersection of two natural quadric surfaces.
Proceedings of the first ACM Symposium on Solid Modeling Foundations and CAD/CAM Applications, 1991

1990
Blossoming and knot insertion algorithms for B-spline curves.
Comput. Aided Geom. Des., 1990

Geometric continuity.
Comput. Aided Des., 1990

1988
A recursive proof of a B-spline identity for degree elevation.
Comput. Aided Geom. Des., 1988

A recursive evaluation algorithm for a class of Catmull-Rom splines.
Proceedings of the 15th Annual Conference on Computer Graphics and Interactive Techniques, 1988

1986
Algebraic Geometry for Computer-Aided Geometric Design.
IEEE Computer Graphics and Applications, 1986

Urn Models and Beta-Splines.
IEEE Computer Graphics and Applications, 1986

Recursive subdivision without the convex hull property.
Comput. Aided Geom. Des., 1986

1985
Some applications of resultants to problems in computational geometry.
Vis. Comput., 1985

Illicit Expressions in Vector Algebra.
ACM Trans. Graph., 1985

Markov Chains and Computer Aided Geometric Design II - Examples and Subdivision Matrices.
ACM Trans. Graph., 1985

Implicitization, inversion, and intersection of planar rational cubic curves.
Comput. Vis. Graph. Image Process., 1985

The method of resolvents: A technique for the implicitization, inversion, and intersection of non-planar, parametric, rational cubic curves.
Comput. Aided Geom. Des., 1985

1984
Markov Chains and Computer-Aided Geometric Design: Part I - Problems and Constraints.
ACM Trans. Graph., 1984

Implicit representation of parametric curves and surfaces.
Comput. Vis. Graph. Image Process., 1984

Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves.
Comput. Aided Geom. Des., 1984

Linear subdivision is strictly a polynomial phenomenon.
Comput. Aided Geom. Des., 1984

1983
Solid modeling(Panel Session).
Proceedings of the 10th Annual Conference on Computer Graphics and Interactive Techniques, 1983


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