Ron Goldman

Q: What Schools Are Affiliated With Ron Goldman

Ron Goldman is affiliated with the following schools: Rice University, Princeton University, Stanford University, Massachusetts Institute of Technology, Johns Hopkins University

Ron Goldman 's AcademicInfluence.com Rankings

Ron Goldman

Mathematics

#6119

World Rank

#8536

Historical Rank

#1896

USA Rank

Measure Theory

#2364

World Rank

#2827

Historical Rank

#670

USA Rank

mathematics Degrees

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Mathematics

Ron Goldman 's Degrees

Masters Mathematics Stanford University

Why Is Ron Goldman Influential?

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According to Wikipedia, Ronald Neil Goldman is a Professor of Computer Science at Rice University in Houston, Texas. Professor Goldman received his B.S. in Mathematics from the Massachusetts Institute of Technology in 1968 and his M.A. and Ph.D. in Mathematics from Johns Hopkins University in 1973.

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Ron Goldman 's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Curvature formulas for implicit curves and surfaces (2005) (382)
Poisson approximation (2000) (380)
Implicit representation of parametric curves and surfaces (1984) (329)
Pyramid algorithms - a dynamic programming approach to curves and surfaces for geometric modeling (2002) (150)
Topics in Algebraic Geometry and Geometric Modeling (2003) (105)
On the Validity of Implicitization by Moving Quadrics for Rational Surfaces with No Base Points (2000) (102)
Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves (1984) (99)
Functional composition algorithms via blossoming (1993) (98)
Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces (1992) (93)
Implicitizing Rational Curves by the Method of Moving Algebraic Curves (1997) (92)
Understanding quaternions (2011) (87)
An Integrated Introduction to Computer Graphics and Geometric Modeling (2009) (87)
A recursive evaluation algorithm for a class of Catmull-Rom splines (1988) (67)
Polya’s Urn Model and Computer Aided Geometric Design (1985) (62)
Geometric Algorithms for Detecting and Calculating All Conic Sections in the Intersection of Any 2 Natural Quadric Surfaces (1995) (61)
Enhancing Levin's method for computing quadric-surface intersections (2003) (61)
AREA OF PLANAR POLYGONS AND VOLUME OF POLYHEDRA (1991) (57)
Subdivision algorithms for Bézier triangles (1983) (57)
Computing quadric surface intersections based on an analysis of plane cubic curves (2002) (56)
Fast Computation of the Bezout and Dixon Resultant Matrices (2002) (50)
q-Blossoming: A new approach to algorithms and identities for q-Bernstein bases and q-Bézier curves (2012) (45)
Degree, multiplicity, and inversion formulas for rational surfaces using u-resultants (1992) (45)
Elimination and resultants. 1. Elimination and bivariate resultants (1995) (44)
Blossoming and knot insertion algorithms for B-spline curves (1990) (44)
Algebraic Geometry for Computer-Aided Geometric Design (1986) (43)
Conversion from Be´zier rectangles to Be´zier triangles (1987) (42)
Implicitization, inversion, and intersection of planar rational cubic curves (1985) (42)
Nonlinear subdivision through nonlinear averaging (2008) (41)
Using multivariate resultants to find the intersection of three quadric surfaces (1991) (36)
Non-uniform subdivision for B-splines of arbitrary degree (2009) (36)
Intersection of two lines in three-space (1990) (35)
Illicit expressions in vector algebra (1985) (35)
On the algebraic and geometric foundations of computer graphics (2002) (34)
Mu-bases for Polynomial Systems in One Variable (2009) (34)
Identities for the Univariate and Bivariate Bernstein Basis Functions (1995) (33)
Elimination and resultants.2. Multivariate resultants (1995) (32)
On the smooth convergence of subdivision and degree elevation for Bézier curves (2001) (30)
h-Blossoming: A new approach to algorithms and identities for h-Bernstein bases and h-Bézier curves (2011) (30)
The method of resolvents: A technique for the implicitization, inversion, and intersection of non-planar, parametric, rational cubic curves (1985) (30)
Rethinking Quaternions: Theory and Computation (2010) (29)
R(4, 4) As a Computational Framework for 3-Dimensional Computer Graphics (2015) (29)
µ-Bases and singularities of rational planar curves (2009) (28)
Generating Functions for the q-Bernstein Bases (2014) (28)
Quantum B-splines (2013) (28)
Dual Polynomial Bases (1994) (27)
Improving conformational searches by geometric screening (2005) (26)
Axial moving lines and singularities of rational planar curves (2007) (26)
Using tangent balls to find plane sections of natural quadrics (1992) (26)
Turtle geometry in computer graphics and computer-aided design (2004) (25)
Implicitizing rational surfaces of revolution using μ-bases (2012) (25)
Using degenerate Bézier triangles and tetrahedra to subdivide Bézier curves (1982) (24)
Subdivision schemes and attractors (2005) (23)
Combining algebraic rigor with geometric robustness for the detection and calculation of conic sections in the intersection of two natural quadric surfaces (1991) (23)
Axial moving planes and singularities of rational space curves (2009) (22)
A subdivision scheme for Poisson curves and surfaces (2000) (22)
On beta-continuous functions and their application to the construction of geometrically continuous curves and surfaces (1989) (22)
Markov chains and computer-aided geometric design: part I - problems and constraints (1984) (22)
On a relationship between the moving line and moving conic coefficient matrices (1999) (22)
Rectangular corner cutting and Sylvester A-resultants (2000) (21)
Modeling 3D Geometry in the Clifford Algebra R(4, 4) (2017) (21)
A unified approach to evaluation algorithms for multivariate polynomials (1995) (21)
Shape parameter deletion for Pólya curves (1991) (20)
Division algorithms for Bernstein polynomials (2008) (20)
Rethinking Quaternions (2010) (20)
The dual basis functions for the generalized Ball basis of odd degree (1997) (19)
Using a bihomogeneous resultant to find the singularities of rational space curves (2013) (18)
The rational Bernstein bases and the multirational blossoms (1999) (18)
Algebraic aspects of geometric continuity (1989) (18)
The Ambient Spaces of Computer Graphics and Geometric Modeling (2000) (18)
Extending fundamental formulas from classical B-splines to quantum B-splines (2015) (18)
Recursive subdivision without the convex hull property (1986) (18)
Using Smith normal forms and μ-bases to compute all the singularities of rational planar curves (2010) (17)
Implicitizing Rational Tensor Product Surfaces Using the Resultant of Three Moving Planes (2017) (17)
De Casteljau-type subdivision is peculiar to Be´zier curves (1988) (16)
Using multivariate resultants to find the implicit equation of a rational surface (1992) (16)
Urn models and B-splines (1988) (16)
Implicitization by Dixon A-resultants (2000) (16)
Topics in resultants and implicitization (2000) (15)
Markov chains and computer aided geometric design: Part II—examples and subdivision matrices (1985) (15)
Interpolation and approximation of curves and surfaces using Pólya polynomials (1991) (15)
The fractal nature of Bezier curves (2004) (15)
Quantum Bernstein bases and quantum Bézier curves (2015) (15)
Urn models, approximations, and splines (1988) (15)
Set-theoretic generators of rational space curves (2010) (14)
Finding the Axis of Revolution of an Algebraic Surface of Revolution (2016) (14)
Urn Models and Beta-Splines (1986) (14)
Recursive turtle programs and iterated affine transformations (2004) (13)
Strong μ-Bases for Rational Tensor Product Surfaces and Extraneous Factors Associated to Bad Base Points and Anomalies at Infinity (2017) (13)
Wonderful triangle: a simple, unified, algorithmic approach to change of basis procedures in computer aided geometric design (1992) (13)
Chapter 2: Algorithms for Progressive Curves: Extending B-Spline and Blossoming Techniques to the Monomial, Power, and Newton Dual Bases (1992) (13)
A Tutorial Introduction to Blossoming (1991) (13)
Implicitizing rational surfaces with base points by applying perturbations and the factors of zero theorem (1992) (13)
Using μ-bases to implicitize rational surfaces with a pair of orthogonal directrices (2012) (13)
Rational Quadratic Parameterizations of Quadrics (1997) (12)
Blossoming Marsden's identity (1992) (12)
Transformations and Transitions from the Sylvester to the Bezout Resultant (1999) (11)
Analytic approach to intersection of all piecewise parametric rational cubic curves (1987) (11)
Two essential properties of ( q , h ) -Bernstein-Bézier curves (2015) (11)
What is the natural generalization of a Be´zier curve? (1989) (11)
Formulas and algorithms for quantum differentiation of quantum Bernstein bases and quantum Bézier curves based on quantum blossoming (2012) (11)
Linear subdivision is strictly a polynomial phenomenon (1984) (10)
Shape preserving properties of univariate Lototsky-Bernstein operators (2017) (10)
Convergence and Smoothness of Nonlinear Lane–Riesenfeld Algorithms in the Functional Setting (2011) (10)
Knot insertion algorithms for piecewise polynomial spaces determined by connection matrices (1993) (10)
Multisided arrays of control points for multisided Bezier patches (2004) (10)
A recursive proof of a B-spline identity for degree elevation (1988) (9)
Generalized quantum splines (2016) (9)
Beta Continuity and Its Application to Rational Beta-splines (1988) (9)
An Extension of Chaiken's Algorithm to B-Spline Curves with Knots in Geometric Progression (1993) (9)
MORE MATRICES AND TRANSFORMATIONS: SHEAR AND PSEUDO-PERSPECTIVE (1991) (9)
Deriving Linear Transformations in Three Dimensions (2003) (9)
Applications of the Shorgin Identity to Bernstein Type Operators (2018) (8)
The Block Structure of Three Dixon Resultants and Their Accompanying Transformation Matrices (1999) (8)
Detecting When an Implicit Equation or a Rational Parametrization Defines a Conical or Cylindrical Surface, or a Surface of Revolution (2017) (8)
Computing Perspective Projections in 3-Dimensions Using Rotors in the Homogeneous and Conformal Models of Clifford Algebra (2014) (8)
Algorithms for computing strong μ-bases for rational tensor product surfaces (2017) (8)
Sylvester-resultants for bivariate polynomials with planar newton polygons (2004) (8)
Change of basis algorithms for surfaces in CAGD (1995) (8)
An Asymmetric Distributed Method for Sorting a Robot Swarm (2017) (8)
RECOVERING THE DATA FROM THE TRANSFORMATION MATRIX (1991) (7)
Morphing Rational B-spline Curves and Surfaces Using Mass Distributions (2003) (7)
Birational 2D Free-Form Deformation of degree 1 × n (2016) (7)
A unifying structure for polar forms and for Bernstein Bézier curves (2015) (7)
A multivariate generalization of the de Boor-fix formula (1994) (7)
B-spline, Po´lya curves, and duality (1991) (7)
Using Invariants To Extract Geometric Characteristics Of Conic Sections From Rational Quadratic Parameterizations (2004) (7)
Recursive proof of Boehm's knot insertion technique (1988) (7)
BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE (2011) (7)
Intersection of three planes (1990) (7)
Trimming analytic functions using right sided Poisson subdivision (2001) (7)
On the smoothness of real-valued functions generated by subdivision schemes using nonlinear binary averaging (2009) (7)
Algebraic surfaces invariant under scissor shears (2016) (6)
Modeling perspective projections in 3-dimensions by rotations in 4-dimensions (2013) (6)
Computer graphics in its fifth decade: ferment at the foundations (2003) (6)
A recursive algorithm for Hermite interpolation over a triangular grid (1996) (6)
μ-Bases for complex rational curves (2013) (6)
Two blossoming proofs of the Lane-Riesenfeld algorithm (2007) (6)
Discrete convolution schemes (1992) (6)
The holonomy ring on the leaves of foliated manifolds (1976) (6)
Syzygies for translational surfaces (2017) (5)
Blossoming with cancellation (1999) (5)
Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials (2015) (5)
EFFICIENT IMPLICITIZATION OF RATIONAL SURFACES BY MOVING PLANES (2000) (5)
The analytic blossom (2001) (5)
Matrices and transformations (1990) (4)
Combining complementary methods for implicitizing rational tensor product surfaces (2018) (4)
Cross Product in Four Dimensions and beyond (1992) (4)
Freeform Curves on Spheres of Arbitrary Dimension (2005) (4)
Generating Functions for Uniform B-Splines (2012) (4)
Three examples of dual properties of Be´zier curves (1989) (4)
CHAPTER 7 – B-Spline Approximation and the de Boor Algorithm (2003) (4)
CHAPTER 2 – Lagrange Interpolation and Neville's Algorithm (2003) (4)
Novel polynomial Bernstein bases and Bézier curves based on a general notion of polynomial blossoming (2016) (4)
Implicitizing ruled translational surfaces (2018) (4)
Surfaces of revolution with moving axes and angles (2019) (3)
R(4, 4) As a Computational Framework for 3-Dimensional Computer Graphics (2014) (3)
Implicitization Matrices in the Style of Sylvester with the Order of Bezout (2000) (3)
Chapter 4: Knot Insertion Algorithms (1992) (3)
Theories of contact specified by connection matrices (1996) (3)
Affine differential geometry and affine rotation surfaces: algebraic surfaces invariant under non-Euclidean affine rotations (2018) (3)
Generating functions for B-Splines with knots in geometric or affine progression (2014) (3)
On the Linear Independence of the Bivariate Discrete Convolution Blending Functions (1998) (3)
Analytic functions in computer-aided geometric design (2002) (3)
Unimodal properties of B-spline and Bernstein-basis functions (1992) (3)
Pruned Bezier curves (1990) (3)
Some applications of resultants to problems in computational geometry (1985) (3)
Algebraic geometry and geometric modeling: insight and computation (2006) (3)
A Homogeneous Model for Three-Dimensional Computer Graphics Based on the Clifford Algebra for ℝ3 (2011) (3)
On Lototsky-Bernstein operators and Lototsky-Bernstein bases (2019) (3)
Decomposing linear and Affine Transformations (1992) (3)
Blossoming and Divided Difference (1999) (3)
Quaternion rational surfaces: Rational surfaces generated from the quaternion product of two rational space curves (2015) (3)
Decomposing Projective Transformations (1992) (3)
Algebraic affine rotation surfaces of parabolic type (2019) (2)
TRANSFORMATIONS AS EXPONENTIALS (1991) (2)
Limits of Sums for Binomial and Eulerian Numbers and their Associated Distributions (2019) (2)
Baseball Arithmetic and the Laws of Pseudoperspective (2001) (2)
A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form (2016) (2)
High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting (2019) (2)
Recognizing algebraic affine rotation surfaces (2020) (2)
Lattices and Algorithms for Bivariate Bernstein, Lagrange, Newton, and Other Related Polynomial Bases Based on Duality betweenL-Bases andB-Bases (1998) (2)
SOME PROPERTIES OF BÉZIER CURVES (1990) (2)
After the revolution: Geometric algebra for Computer Scientists in the twenty-first century (2008) (2)
Bézier Subdivision for Inverse Molecular Kinematics (2006) (2)
The affine invariant analytic blossom (2002) (2)
Identities for the B-Spline Basis Functions (1995) (1)
Complex μ-bases for real quadric surfaces (2015) (1)
Chapter 3: Factored Knot Insertion (1992) (1)
Vector Geometry: A Coordinate-Free Approach (2009) (1)
Keynote lecture 1: four open mathematical problems related to computer graphics and geometric modeling (2009) (1)
Topics in algebraic geometry and geometric modeling : Workshop on Algebraic Geometry and Geometric Modeling, July 29-August 2, 2002, Vilnius University, Vilnius, Lithuania (2003) (1)
Tensor product slices (1992) (1)
de Boor-suitable (DS) T-splines (2018) (1)
Representing rational curve segments and surface patches using semi-algebraic sets (2019) (1)
Generating a 3D Normative Infant Cranial Model (2016) (1)
A Polynomial Blossom for the Askey–Wilson Operator (2018) (1)
CHAPTER 6 – Blossoming (2003) (0)
Duality between L-bases and B-bases (2007) (0)
Corrigendum to Example 4 in "μ-Bases for complex rational curves" [Computer Aided Geometric Design 30 (2013), 623-635] (2014) (0)
Integration of Bernstein basis functions (1990) (0)
Mu-bases and their applications in geometric modeling (2007) (0)
Solid modeling(Panel Session) (1983) (0)
Quantum Lorentz degrees of polynomials and a Pólya theorem for polynomials positive on q-lattices (2021) (0)
Editorial: Geometric Modelling (2004) (0)
Compositional synthesis of optical imaging systems (2002) (0)
New Trends in Non-uniform Subdivision (2009) (0)
Two Surfaces Suffice (1992) (0)
A Set of Convolution Identities Relating the Blocks of Two Dixon Resultant Matrices (1999) (0)
Spline functions of negative degree (2000) (0)
Rational curves over generalized complex numbers (2019) (0)
Some properties of Be´zier curves (1990) (0)
B-Spline Curves and Surfaces (2009) (0)
Unimodal Properties of Generalized Ball Bases (1993) (0)
Relationships between identities for quantum Bernstein bases and formulas for hypergeometric series (2020) (0)
Using Dual Quaternion to Study Translational Surfaces (2018) (0)
q-Blossoming for analytic functions (2018) (0)
An Upside Down Approach to the Koch Curve (2022) (0)
Knot Insertion Using Forward Differences (1994) (0)
7 Two Surfaees Sufliee (1992) (0)
CHAPTER 5 – Bezier Approximation and Pascal's Triangle (2003) (0)
05221 Report of the Dagstuhl seminar on - Geometric Modelling (2005) (0)
Computing Perspective Projections in 3-Dimensions Using Rotors in the Homogeneous and Conformal Models of Clifford Algebra (2014) (0)
Beta-continuity revisited: determining Bézier control vertices to construct geometrically continuous curves and surfaces (2001) (0)
CHAPTER 3 – Hermite Interpolation and the Extended Neville Algorithm (2003) (0)
Geometric continuity (1990) (0)
CHAPTER 8 – Pyramid Algorithms for Multisided Bezier Patches (2003) (0)
Ruled Surfaces of Revolution with Moving Axes and Angles (2021) (0)
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 (1993) (0)
Two additional advantages of complex μ-bases for non-ruled real quadric surfaces (2016) (0)
Pruned Be´zier curves (1990) (0)
CHAPTER 1 – Introduction: Foundations (2003) (0)
Geometric Algebra for Computer Science, Leo Dorst, Daniel Fontijne, Stephen Mann. Morgan Kaufmann (2007), 626, $ 69.95, ISBN: 978-0-12-369465-2 (2008) (0)
Explicit μ-bases for conic sections and planar rational cubic curves (2016) (0)
On the Existence and the Coefficients of the Implicit Equation of Rational Surfaces (1994) (0)
Part 1: Elimination and Bivariate Resu I t an t s (1995) (0)
Building Fractals with a Robot Swarm (2017) (0)
Editorial: Special issue on Geometric Modeling (Dagstuhl 2005) (2007) (0)
CHAPTER 4 – Newton Interpolation and Difference Triangles (2003) (0)
A unified approach to non-polynomial B-spline curves based on a novel variant of the polar form (2015) (0)
Arising naturally inmechanical design, these shapes areeasier to analyze anduseinsolid modeling systems thanthemore general quadric surfaces. Quadrics ofRevolution (1983) (0)

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Ron Goldman is affiliated with the following schools:

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