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Scholarly Interest Report
         
Ronald N. Goldman
Professor
Professor in Computer Science
 
e-mail:rng@rice.edu
 
  • B.S. (1968) Massachusetts Institute of Technology, Boston, MA
  • M.A. (1972) John Hopkins University, Baltimore, MD
  • Ph.D. (1973) John Hopkins University, Baltimore, MD
 
Primary Department
   Department of Computer Science
Picture
 
Department Affiliations
 
  • Ken Kennedy Institute for Information Technology
  •  
     
    Research Areas
     Computer Graphics, Geomatic Modeling
     
    Research Statement
     
     
    Selected Publications
     Abstracts
     

    Goldman., Wang, W. "Using invariants to extract geometric characteristics of conic sections from rational quadratic parameterizations." Int'l Journal of Computational Geometry and Applications (2005) In Press

     
     Refereed articles
     

    E. Vouga., S. Schaefer, and R. Goldman "On the Smoothness of Real-Valued Functions Generated by Subdivision Schemes Using Nonlinear Binary Averaging." Computer Aided Geometric DesignIn Press

     
     

    H. Wang, X. Jia, R. Goldman "Axial Moving Planes and Singularities of Rational Space Curves." Computer Aided Geometric DesignIn Press

     
     

    L. Buse, R. Goldman "Division Algorithms for Benstein Polynomials." Computer Aided Geometric Design, 25 (2008) : 850-865.

     
     

    N. Song, and R. Goldman "Mu-Bases for Polnomial Systems in One Variable." Computer Aided Geometric DesignIn Press

     
     

    S. Schaefer, E. Vouga, and R. Goldman "Nonlinear Subdivision Through Nonlinear Averaging." Computer Aided Geometric Design, 25 (2008) : 162-180.

     
     

    S. Schaefer, and R. Goldman "Non-Uniform Subdivision for B-splines of Arbitrary Degree." , 26 (2009) : 71-81.

     
     

    Goldman, R. "Curvature formulas for implicit curves and surfaces." Special Issue of CAGD on Geometric Modeling and Differential Geometry, 22 (2005) : pp 632-658.

     
     

    Goldman, R., Zhang, M., White, R., Wang, L., Kavraki, L., Hassett, B. "Improving conformational searches by geometric screening." Journal of BioinformaticsIn Press

     
     

    M. Zhang, R. White, L. Wang, R. Goldman, L. Kavraki, and B. Hassett "Improving Conformational Searches by Geometric Screening." Journal of Bioiinformatics (2004) In Press

     
     

    R. Goldman "Multisided Arrays of Control Points for Multisided Bezier Patches." Computer Aided Geometric Design, 21 (2004) : 243-261.

     
     

    R. Goldman and W. Wang "Using Invariants to Extract Geometric Characteristics of Conic Sections from Rational Quadratic Parametrizations." The International Journal of Computational Geometry and Applications (2004)

     
     

    R. Goldman, T. Ju, and S. Schaeffer "Recursive Turtle Programs and Iterated Affine Transformations." Computer and Graphics, 28 (2004) : 991-1004.

     
     

    R. Goldman, T. Ju, and S. Schaeffer "Turtle Geometry in Computer Graphics and Computer-Aided Design." Computer-Aided Design, 36 (2004) : 1471-1482.

     
     

    R.N. Goldman "On the Algebraic and Geometric Foundations of Computer Graphics." Transactions on Graphics, 21 (2002) : 1-35.

     
     

    R.N. Goldman, D. Subramanian "Compositional Synthesis of Optical Imaging Systems." AIEDAMIn Press

     
     

    R.N. Goldman, E. Chionh "Fast Computation of the Bezout and Dixon Resultant Matrices." Journal of Symbolic Computation, 33 (2002) : 13-29.

     
     

    R.N. Goldman, Geraldine Morin "The Affine Invariant Analytic Blossom." Computer Aided Geometric Design (2003) In Press

     
     Articles
     

    R. Goldman & C. Disibuyuk "A Unifying Functional Structure for Polar Forms and for Funcational Bernstein Bezier Curves." Journal of Approximation TheorySubmitted

     
     

    R. Goldman & S. Mann "R(4,4) as a Computational Framework for 3-Dimensional Computer Graphics,." Advances in Applied Clifford Algebras (2014)

     
     

    R. Goldman & X. Wang "Quatenrnion Rational Surfaces: Rational Surfaces Generated from the Quaternion Product of Two Rational Space Curves." Graphical Models (2014)

     
     

    R. Goldman, B. Yuan, D. Khechoyan "A New Objective Automatic Computational Framework for Evaluating and Visualizing the Results of Infant Cranial Surgery." BioMedCom 2014: The 3rd ASE International Conference on Biomedical Computing (Dec. 2014) Submitted

     
     

    R. Goldman, C. Disbuyuk, G. Budakci and H. Oruc "Generating Functions for B-Splines with Knots in Geometric or Affine Progression." Calcolo, 51 (2014) : 4.

     
     

    R. Goldman, G. Budakci, D. Disibuyuk, H. Oruc "Extending Fundamental Formulas from Classical B-Splines to Quantum B-Splines." Journal of Computational and Applied Mathematics (2014) Submitted

     
     

    R. Goldman, J. Alcazar "Finding the Axis of Revolution of an Algebraic Surface of Revolution." IEEE Transactions on Visualization and Computer GraphicsSubmitted

     
     

    R. Goldman, J. Alcazar "Two Essential Properties of (q, h) - Bernstein-Bexier Curves." Applied Numerical MathematicsSubmitted

     
     

    R. Goldman, P. Simeonov "A General Theory of Quantum B-splines." BITSubmitted

     
     

    R. Goldman, P. Simeonov "Generalized Bernstein Bases and Generalized Bezier Curves based on Generalized Blossoming." Numerical AlgorithmsSubmitted

     
     

    R. Goldman, P. Simeonov "Quantum Bernstein Bases and Quantum Bezier Curves." IMA Journal of Numerical AnalysisSubmitted

     
     

    R. Goldman, P. Simeonov & Y. Simsek "Generating Functions for the q-Bernstein Bases." SIAM Journal on Discrete Mathematics, 28 (2014) : 1009-1025.

     
     

    R. Goldman, S. Mann, J. Xia "Computing Perspective Projections in 3-Dimensions using Rotors in the Homogeneous and Conformal Models of Clifford Algebras." Advances in Applied Clifford Algebras, 24 (2014) : 465-491.

     
     

    R. Goldman, T. Sederberg, X. Wang "Complex u-Bases for Real Quadric Surfaces." Computer Aided Geometric DesignSubmitted

     
     

    Ron Goldman, Modeling Perspective Projections in 3-Dimensions by Rotations in 4-Dimensions, Graphical Models (2013), Vol. 75, pp. 41-55

     
     

    Ron Goldman and P. Simeonov, Quantum B-splines, BIT Numerical Mathematics (2013), Vol. 53, pp. 193–223.

     
     

    Ron Goldman and X. Wang, Mu-Bases for Complex Rational Curves, Computer Aided Geometric Design (2013), Vol. 30, pp. 623-635.

     
     

    Ron Goldman and C. Disibuyuk, A Unifying Functional Structure for Polar Forms and for Functional Bernstein Bezier Curves, Journal of Approximation Theory

     
     

    Ron Goldman, C. Disibuyuk, G. Budakci, and H. Oruc, Generating Functions for B-Splines with Knots in Geometric or Affine Progression accepte to appear in Calcolo.

     
     

    Ron Goldman, G. Budakci, C. Disibuyuk, H. Oruc, Extending Fundamental Formulas from Classical B-Splines to Quantum B-Splines, in Advances in Computational Mathematics

     
     

    Ron Goldman, S. Mann and X. Jia, Computing Perspective Projections in 3-Dimensions using Rotors in the Homogeneous Advances in Applied Clifford Algebras.

     
     

    Ron Goldman, X. Shi and X. Jia, Using a Bihomogeneous Sparse Resultant to Find the Singularities of Rational Space Curves, Journal of Symbolic Computation (2013), Vol. 53, pp. 1-25.

     
     

    RONALD GOLDMAN "MODELING PERSPECTIVE PROJECTIONS in 3-DIMENSIONS BY ROTATIONS IN 4-DIMENSIONS." GRAPHICAL MODELSIn Press

     
     

    RONALD GOLDMAN AND P.SIMEONOV "FORMULAS AND ALGORITHMS FOR QUANTUM DIFFERENTIATION OF QUANTUM BERNSTEIN BASES AND QUANTUM BEZIER CURVES BASED ON QUANTUM BLOSSOMING ." GRAPHICAL MODELS, 74: 326-334.

     
     

    RONALD GOLDMAN AND P.SIMEONV "QUANTUM B-SPLINES." BIT NUMERICAL MATHEMATICSIn Press

     
     

    RONALD GOLDMAN AND X. JIA "USING SMITH NORMAL FORMS AND MU-BASES TO COMPUTE ALL THE SINGULARITIES OF RATIONAL PLANAR CURVES." COMPUTER AIDED GEOMETRIC DESIGN 2012., 29: 296-314.

     
     

    RONALD GOLDMAN AND X.SHI "IMPLICITIZING RATIONAL SUFACES OF REVOLUTION USING MU-BASES." COMPUTER AIDED GEOMETRIC DESIGN 2012., 29: 348-362.

     
     

    RONALD GOLDMAN AND X.WANG "MU-BASES FOR COMPLEX RATIONAL CURVES." COMPUTER AIDED GEOMETRIC DESIGNSubmitted

     
     

    RONALD GOLDMAN, C. DISBUYUK, G. BUDAKCI AND H. ORUC "GENERATING FUNCTIONS FOR B-SPLINES WITH KNOTS IN GEOMETRIC OR AFFINE PROGRESSION." ADVANCES IN COMPUTATIONAL MATHEMATICSSubmitted

     
     

    RONALD GOLDMAN, P. SIMEONOV AND V. ZAFIRIS "q-BLOSSOMING: A NEW APPROACH TO ALGORITHMS AND IDENTITIES FOR q-BERSTEIN BASES AND q-BEZIER CURVES." JOURNAL OF APPROXIMATION THEORY 2012, 164: 77-104.

     
     

    RONALD GOLDMAN, S. MANN AND X. JIA "COMPUTING PERSPECTIVE PROJECTIONS IN 3-DIMENSIONS USING ROTORS IN THE HOMOGENEOUS AND CONFORMAL MODELS OF CLIFFORD ALGEBRA." ADVANCES IN APPLIED CLLIFFORD ALGEBRASSubmitted

     
     

    RONALD GOLDMAN, X.SHI AND X. WANG "USING MU-BASES TO IMPLICITIZE RATIONAL SURFACES WITH A PAIR OF ORTHOGONAL DIRECTRICES." COMPUTER AIDED GEOMETRIC DESIGN 2012. SPECIAL ISSUE ON GMP 2012, 29: 541-554.

     
     

    RONALD GOLDMAN, X.SHI, AND X.JIA "USING A BIVARIATE SPARSE RESULTANT TO FIND THE SINGULARITIES OF RATIONAL SPACE CURVES." JOURNAL OF SYMBOLIC COMPUTATIONIn Press

     
     

    Understanding Quaternions, Graphical Models (2011), Vol. 73, pp. 21-49.

     
     

    Convergence and Smoothness of Nonlinear Lane-Riesenfeld Algorithms in the Functional Setting, with N. Dyn, Foundations of Computational Mathematics (2011), Vol. 11, No. 1, pp. 79-94.

     
     

    Bezier and B-spline Curves with Knots in the Complex Plane, with K. Tsianos, Fractals Complex Geometry, Patterns, and Scaling in Nature and Society (2011), Vol. 19, pp. 67-86.

     
     

    P. Simeonov, V. Zafiris, and R. Goldman, h-Blossoming: A New Approach to Algorithms
    and Identities for h-Bernstein Bases and h-Bezier Curves, Computer Aided Geometric
    Design, (2011), Vol. 28, No. 9, pp. 549-565.

     
     

    P. Simeonov, V. Zafiris, and R. Goldman, q-Blossoming: A New Approach to Algorithms
    and Identities for q-Bernstein Bases and q-Bezier Curves, Journal of Approximation
    Theory (2012), Vol. 164, pp. 77-104.

     
     

    R. Goldman, A Homogeneous Model for Three-Dimensional Computer Graphics based
    on the Clifford Algebra for R3 , Guide to Geometric Algebra in Practice, edited by L.
    Dorst and J. Lasenby, Springer, London (2011), pp. 329-352.

     
     

    X. Jia and R. Goldman, Using Smith Forms and Mu-bases to Compute All the
    Singularities of Rational Planar Curves, submitted to Computer Aided Geometric Design.

     
     

    X. Shi and R. Goldman, Implicitizing Rational Surfaces of Revolution using μ -Bases,
    submitted to Computer Aided Geometric Design.

     
     

    X. Shi and R. Goldman, "Using μ -Bases to Implicitize Rational Surfaces with a Pair of Orthogonal Directrices." Submitted

     
     

    Minimal Generators for the Rees Algebra of Rational Space Curves of Type (1,1,d-2), with J. Hoffman, H. Wang, and X. Jia, European Journal of Pure and Applied Mathematics (2010), Vol. 3, No. 4, pp. 602-632.

     
     

    Set-Theoretic Generators of Rational Space Curves, with X. Jia and H. Wang, Journal of Symbolic Computation (2010), Vol. 45, pp. 414-433.

     
     

    E. Vouga, S. Schaefer, and R. Goldman, On the Smoothness of Real-Valued Functions Generated by Subdivision Schemes Using Nonlinear Binary Averaging, Computer Aided Geometric Design (2009), Vol. 26, pp. 231-242.

     
     

    H. Wang, X. Jia, and R. Goldman, Axial Moving Planes and Singularities of Rational Space Curves, Computer Aided Geometric Design (2009), Vol. 26, pp. 300-316.

     
     

    N. Song and R. Goldman, Mu-Bases for Polynomial Systems in One Variable, Computer Aided Geometric Design (2009), Vol. 26, pp. 217-230.

     
     

    S. Schaefer and R. Goldman, Non-Uniform Subdivision for B-splines of Arbitrary Degree, Computer Aided Geometric Design (2009), Vol. 26, pp. 75-81.

     
     

    X. Jia, H. Wang, and R. Golman, Set-Theoretic Generators of Rational Space Curves, accepted to appear in the Journal of Symbolic Computation

     
     

    X. Jia and R. Goldman, Mu-bases and Singularities of Rational Planar Curves, Computer Aided Geometric Design (2009), Vol. 26, pp. 970-988.

     
     

    E. Vouga, Goldman "Two Blossomin Proofs of the Lane-Riesenfeld Algorithm." Computing, 79 (2007)

     
     

    L. Buse, R. Goldman "Division Algorithms for Bernstein Polynomials." Compter Aided GeometricIn Press

     
     

    S. Schaefer, R. Goldman "Non-Uniform Subdivision for B-splines of Arbitrary Degree." Computer Aided Geometric DesignIn Press

     
     

    "Two Blossoming Proofs of the Lane-Riesenfeld Algorithm." Computer Aided Geometric DesignIn Press

     
     

    Goldman, R., Mann, S. "Counting pruned bezier curves." Mathematical Methods for Curves and Surfaces: Tromso 2004 (2005) : 169-178.

     
     Books
     

    R. Goldman, An Integrated Introduction to Computer Graphics and Geometric Modeling, CRC Press, Taylor and Francis, New York, 2009.

     
     Book chapters
     

    Ron Goldman "Polar Forms in Geometric Modeling and Algebraic Geometry." Topics in Geometric Modeling and Algebraic Geometry (2003) In Press

     
     Book reviews
     

    "After the Revolution: Geometric Algebra for Computer Scientists in the Twenty-First Century." Computer Aided Design, 40 (2008) : 655-656.

     
     Refereed conference papers
     

    R. Goldman "The Fractal Nature of Bezier Curves." Proceedings of Geometric Modeling and Processing: Theory and Applications (GMP 2004) (2004) : 3-11.

     
     

    R. Goldman and N. Song "A Computational Method for Constructing Sylvester-style Sparse Resultants." Proceedings of the Tenth International Conference on Applications of Computer Algebra (ACA-2004) (2004) : 81-89.

     
     

    R. Goldman and T. Ju "Hodograph Turtles." Proceedings of the IASTED Conference on Computer Graphics (2004)

     
     

    R. Khetan, R. Goldman, and N. Song "Sylvester A-Resultants for Bivariate Polynomials with Planar Newton Polygons." Proceedings of the 2004 International symposium on Symbolic and Algebraic Computation (ISSAC) (2004)

     
     Conference papers
     

    R. Goldman, M. Floater, T. Lyche, M-L Mazure, K. Morken, L. Schumaker (eds.) "Generating Functions for Uniform B-splines." Proceedings of the 8th International Conference on Mathematical Methods for Curves and Surfaces (2014) : 172-188.

     
     

    H. Wang, X. Jia, and R. Goldman, Set Theoretic Generators of Rational Space Curves, The Fourth International Workshop on Algebraic Geometry and Geometric Modeling (AGGM 2009), Lijiang, China, July 2009.

     
     

    R. Goldman, An Introduction to Geometric Modeling (Invited Presentation), Second International Workshop on Algebraic Geometry and Approximation Theory, Towson, Maryland, April 2009.

     
     

    R. Goldman, Four Open Mathematical Problems Related to Computer Graphics and Geometric Modeling (Keynote Presentation), International Conference on Computational and Information Sciences, NTNU and WSEAS, Houston, Texas, May 2009.

     
     

    R. Goldman, Nonlinear Lane-Riesenfeld Algorithms with Nonlinear Averaging Rules, Research Workshop on Subdivision and Refinability, Pontignano, Italy, October 2009.

     
     

    R. Goldman and K. Tsianos, B-Splines with Knots in the Complex Plane (Invited Presentation), Second International Workshop on Algebraic Geometry and Approximation Theory, Towson, Maryland, April 2009.

     
     

    R. Goldman and N. Dyn, Nonlinear Lane-Riesenfeld Algorithms with Nonlinear Averaging Rules: The Functional Setting, SIAM Conference on Geometric and Physical Modeling, San Francisco, California, October 2009.

     
     

    X. Jia and R. Goldman, Computing Singularity Trees of Rational Planar Curves Using μ Bases, The Fourth International Workshop on Algebraic Geometry and Geometric Modeling (AGGM 2009), Lijiang, China, July 2009.

     
     

    Goldman., Schaefer, S. "Freeform curves on spheres of arbitrary dimension." Proceedings of Pacific Graphics 2005 (2005) : 160-162.

     
     

    Goldman., Schaefer, S., Levin, D. "Subdivision schemes and attractors." Proceedings of Symposium onn Geometric Processing (SGP) 2005 (July 2005) : 171-180.

     
     

    R. Goldman and T. Ju "Morphing Rational B-spline Curves and Surfaces Using Mass Distributions." Proceedings of Eurographics 2003, Short Presentations (Sept 2003) : 61-68.

     
     

    Ron Goldman "Computer Graphics in its Fifth Decade: Ferment at the Foundations." Proceedings of Pacific Graphics 2003 (Oct 2003)

     
     Other
     

    Ron Goldman, Generating Functions for Uniform B-Splines, accepted for the Proceedings of the Eighth International Conference on Mathematical Methods for Curves and Surfaces.

     
     

    R. Goldman and R. Krasauskas "Toric Bezier Patches with Depth." Topics in Geometric Modeling and Algebraic Geometry (2003)

     
     

    Ron Goldman "Baseball Arithmetic and the Laws of Pseudoperspective." IEEE Computer Graphics and Applications, 21 (2001) : 70-78.

     
     

    Ron Goldman "Blossoming and Divided Difference." Geometric Modeling, Computing (Suppl), 14 (2001) : 155-184.

     
     

    Ron Goldman and G. Morin "On the Smooth Convergence of Subdivision and Degree Elevation for Bezier Curves." Computer Aided Geometric Design, 18 (2001) : 657-666.

     
     

    Ron Goldman and G. Morin "Trimming Analytic Func tions Using Right Sided Poisson Subdivision." Computer-Aided Design, 33 (2001) : 813-824.

     
     

    D. Cox, R. Goldman, and M. Zhang "On the Validity of Implicitization by Moving Quadrics for Rational Surfaces with No Base Points." Journal of Symbolic Computation, 29 (2000) : 419-440.

     
     

    E. Chionh, R. Goldman, and M. Zhang "Implicitization by Dixon A-resultants." Proceedings of Geometric Modeling and Processing 2000 (April 2000) : 310-318.

     
     

    R. Goldman and G. Morin "Poisson Approximation." Proceedings of Geometric Modeling and Processing 2000 (2000) : 141-149.

     
     

    R. Goldman and M. Zhang "Rectangular Corner Cutting and Sylvester A-Resultants." Proceedings of the 2000 International Symposium on Symbolic and Algebraic Computation (ISSAC) (August 2000) : 301-308.

     
     

    R. Goldman, M. Zhang, and E. Chionh "Efficient Implicitization of Rational Surfaces by Moving Planes." Proceedings of ASCM 2000 (2000)

     
     

    Ron Goldman "The Ambient Space of Computer Graphics and Geometric Modelng." IEEE Computer Graphics and Applications, 20 (2000) : 76-84.

     
     

    Ron Goldman and G. Morin "A Subdivision Scheme for Poisson Curves and Surfaces." Computer Aided Geometric Design (2000)

     
     

    Ron Goldman and Guido Walz "Spline Functions of Negative Degree." Calcolo, 37/3 (2000) : 125-138.

     
     

    E. Chionh, R. Goldman, and M. Zhang "On a Relationship Between the Moving Line and Moving Conic Coefficient Matrices." Computer Aided Geometric Design, 16 (1999) : 517-527.

     
     

    E. Chionh, R. Goldman, and M. Zhang "The Block Structure of Three Dixon Resultants and Their Accompanying Transformation Matrices." Department of Computer Science, Rice University (1999)

     
     

    E. Chionh, R. Goldman, and M. Zhang "Transformations and Transitions from the Sylvester to the Bezout Resultant." Department of Computer Science, Rice University

     
     

    E. Chionh, R. Goldman, and M. Zhang "a Set of Convolution Identities Relating the Blocks of Two Dixon Resultant Matrices." Department of Computer Science, Rice University (1999)

     
     

    Ron Goldman "The Rational Bernstein Bases and the Multirational Blossoms." Computer Aided Geometric Design, 16 (1999) : 701-738.

     
     

    "Blossoming with Cancellation." Special Issue of Computer Aided Geometric Design dedicated to P. de Casteljau, 16 (1999) : 671-689.

     
     

    E. Chionh, Ron Goldman, and M. Zhang "Hybrid Dixon Resultants." Proceedings of the Eighth IMA Conference on the Mathematics of Surfaces (1998)

     
     

    Ron Goldman and S. Lodha "Lattices and Algorithms for Bivariate Bernstein, Lagrange, Newton and Other Related Polynomial Bases based on Duality between L-bases and B-bases." Journal of Approximation Theory, 93 (1998) : 59-99.

     
     

    Ron Goldman and Y. Stafanus "On the Linear Independence of the Bivariate Discrete Convolution Blending Functions." Australian Computer Science Communications, 20 (1998) : 231-244.

     
     

    Ron Goldman, B. Joe, and W. Wang "Rational Quadratic Parametrizations of Quadrics." International Journal of Computational Geometry and Applications, 7 (1997) : 231-244.

     
    Creative Works
     Other - The Role of Algebraic Geometry in Geometric Modeling: Insight and Computation
     University of Kaiserslautern (May 2011) The Role of Algebraic Geometry in Geometric Modeling: Insight and Computation, (May 2011)
     
     Other - VISITING SCIENTIST University of Vilnius -- July 3-August 13, 2011
     
     
    Presentations
     Conference Committee Member
     

    "Mu-Bases for Complex Rational Curves, with X. Wang, Banff Conference on Algebraic Geometry and Geometric Modeling, Banff International Research Station for Mathematical Innovation and Discovery, Banff, Canada, January 2013.." (January 2013)

     
     

    "CAD/Graphics 2011."

     
     

    "GD/SPM11." (2011)

     
     

    Co-Organizer of meeting..  "Blossoming and the Lane-Riesenfeld Algorithm." Dagstuhl Meeting on Geometric Modelling, Dagstuhl, Germany. (May 2005)

     
     Conference Paper
     

    "A New Objective Automatic Computational Framework for Evaluating and Visualizing the Results of Infant Cranial Surgery Cambridge, MA December 2014."

     
     

    "Geometric Variations of the Lane-Riesenfeld Algorithm Dagstuhl, Germany May 2014."

     
     Invited Papers
     

    "Axial Moving Lines and Singularities of Rational Planar curves." SIAM Conf on Geometric Design and Computing, Phoenix, AZ. (November 2005) With F. Chen, N. Song

     
     

    "Modeling Analytic Functions with Poles: Extending the Poisson Representation in Laurent Series." SIAM Conf on Geometric Design and Computing, Phoenix, AZ. (November 2005) With G. Morin

     
     

    "Subdivision Algorithms for Circular Arcs." SIAM Conf on Geometric Design and Computing, Phoenix, AZ. (November 2005) With S. Schaefer, E. Vouga

     
     

    "Subdivision Schemes and Attractors." Symp on Geometric Processing (SGP) 2005, Vienna, Austria. (July 2005) With S. Schaefer, D. Levin

     
     Invited Talks
     

    "Generalized Quantum Splines with P. Simeonov, IMA Conference on the Mathematics of Surfaces, Birmingham, England, ." (September 2013)

     
     

    Quaternions  and  Dual  Quaternions  (Tutorial),  International  Conference  on  Shape

    Modeling and Applications (SMI), College Station, Texas, May 2012.

     
     

    "Introduction to Clifford Algebra." Third Annual Fall School: Shapes, Geometry, and Algebra (SAGA, (September 2011.)

     
     

    "Polynomials and Fractals: Polynomials as Attractors, Fractals with Control
    Points (." 24th International Conference of the Jangjeon Mathematical Society, (Turkey, July 2011,)

     
     

    "The Role of Algebraic Geometry in Geometric Modeling." SIAM Conference on Applied Algebraic Geometry,, (October, 2011.)

     
     

    "Understanding Quaternions: Rotation, Reflection and Perspective Projection." Third Annual Fall School: Shapes, Geometry, and Algebra (SAGA), (September 2011.)

     
     

    "An Introduction to Geometric Modeling." (April 2009)

     
     

    "B-Splines with Knots in the Comolex Plane." (April 2009)

     
     

    "B-spline Curves with Knots in the Complex Plane, with Konstantinos Tsianos." (July 2009)

     
     

    "B-spline Curves with Knots in the Complex Plane, with Konstantinos Tsianos." (September 2009)

     
     

    "Bezier and B-spline Curves with Knots in the Complex Plane." (June 2009)

     
     

    "The Marriage of Fractals and Splines: Fractals with Control Points, Splines as Attractors." (June 2009)

     
     

    "Understanding Quaternions." (October 2009)

     
     

    "Understanding Quaternions." (October 2009)

     
     

    "A Simple Class of Non-Linear Subdivision Schemes." Univeristy of Buenos Aires, Buenos Aires, Argentina. (June 2007)

     
     

    "A Simple Class of Non-Linear Subdivision Schemes." University of Science and Technology (UDTC), Hefei, China. (March 2007)

     
     

    "Blossoming." Columbia University, New York. (December 2007)

     
     

    "Global Knot Insertion Algorithms." University of Kaiserslautern, Germany. (February 2007)

     
     

    "Mu- Bases for Polynomial Systems in One Variable OR What ABout Non-Planar Curves?." Oberwolfach Mini-Workshop on Surface Modeling and Syzygies, (November 2007)

     
     

    "Mu-Bases for Polynomial Systems in One Variable." University of Science and Technology (USTC), Hefei, China. (March 2007)

     
     

    "Mu-Bases for Polynomial Systems in One Variable." University of Buenos Aires, Buenos Aires, Argentina. (June 2007)

     
     

    "Mu-Bases for Polynomial Systems in One Variable." INRIA, Antipolis, France. (February 2007)

     
     

    "Mu-Bases for Polynomial Systems in One Variable OR What About Non-Planar Curves?." Oberwolfach Mini-Workshop on Surface Modeling and Syzgies, Oberwolfach, Germany. (November 2007) With N. Song, X. Jia, D. Cox, R. Goldman

     
     

    "Some remarks on a Conjecture by David Cox." University of Buenos Aires, Buenos Aires, Argentina. (June 2007)

     
     

    "The Truth About Quaternions." University of Science and Technology (USTC), Hefei, China. (March 2007)

     
     

    "Three Problems in Search of a Graduate Student." SUNY at Stonybrook, Stonybrook, New York. (November 2007)

     
     

    "Three Problems in Search of a Gradute Student." University of Buenos Aires, Buenos Aires. (June 2007)

     
     

    "A Simple Class of Non-Linear Subdivision Schemes." Six International Conference on Curves and Surfaces, Avignon, France. (June 2006) With S. Scharfer, E. Vouga

     
     

    "Applications of Computer Algebra: Some Challenges for the Next Decade." Tenth International Conference on Applications of Computer Algebra (ACA-2004), (July 2004)

     
     

    "Introduction to Geometric Modeling." MSRI Workshop on Real Algebraic Geometry and Geometric Modeling, University of California, Berkeley. (April 2004)

     
     

    "The Fractal Nature of Bezier Curves." Geometric Modeling and Processing 2004, Beijing, China. (April 2004)

     
     

    "Computer Graphics in its Fifth Decade: Ferment at the Foundations." Pacific Graphics 2003, Canmore, Canada. (october 2003)

     
     Keynote Speaker
     

    "Four Open Mathematical Problems Related to Computer Graphics and Geometric Modeling." (May 2009)

     
     Lectures
     

    GENERATING FUNCTIONS FOR UNIFORM B-SPLINE,EIGHTH INTERNATIONAL CONFERENCE ON MATHEMATICAL METHODS FOR CURVES AND SURFACES, OSLO, NORWAY, JULY 2012

     
     

    QUANTUM SPLINES, NEW TRENDS IN APPROXIMATIONS THEORY, EIN GEDI, ISRAEL, JAN 2012

     
     

    PERSPECTIVE PROJECTION IN THE HOMOGENEOUS AND CONFORMAL MODELS USING ROTORS,APPLIED GEOMETRIC ALGEBRAS IN COMPUTER SCIENCE AND ENGINEERING 2012 (AGACSE 2012), LA ROCHELLE, FRANCE

     
     

    USING MU-BASES TO IMPLICITIZE RATIONAL SURFACES WITH A PAIR OF ORTHOGONAL DIRECTRICES.,GEOMETRIC MODELING AND PROCESSING (GMP 2012), HUANGSHAN, CHINA

     
     

    co-author.  "Axial Moving Planes and Singularities of Rational Space Curves." Applications of Computer Algebra (ACA), Austria. (July 2008) With H. Wang., X. Jia

     
     

    Speaker.  "Three Computational Advantages of Mu-Bases in the Analysis of Rational Planar Curves." Seventh International Conference on Mathematical Methods for Curves and Surfaces, Tonsberg, Norway. (June 2008) With X. Jia

     
     

    "Musings on Multisided Bezier Patches." Dagstuhl Conference on Geometric Modelling, Dagstuhl, Germany. (May 2002)

     
     

    "The Sylvester Resultant Matarix for Bernstein Polynomials." Fifth International Conference on Curves and Surfaces, St. Malo, France. (July 2002) With J. Winkler

     
     

    "Two Multisided Bernstein/Bezier/Barycentric Schemes: S-Patches and Toric Bezier." Oberwolfach Conference on Mathematical Methods in Geometric Design, Oberwolfach, Germany. (October 2002)

     
     Other
     

    "A Unifying Functional Structure for Plar Forms and for Functional Bernstein Bexier Curves Eigth International Conference on Curves and Surfaces June 2014."

     
     

    "Extending Fundamental Formulas from Classical B-splines to Quantum B-splines, with G. Budakci, C, Disibuyuk and H. Oruc. 14th International Conference on Approximation Theory, San Antonio, Texas." (April 2013.)

     
     

    "Towards a General Unified Theory of Classical and Quantum Splines, with P. Simeonov, 14th International Conference on Approximation Theory, San Antonio, Texas." (April 2013)

     
     

    "Towards an Algebra for Rational Curves and Surfaces in Two and Three Dimensions, with X. Wang, SIAM Conference on Applied Algebraic Geometry, Ft. Collins, Colorado." (August 2013)

     
     

    Co-Organizer.  "Non-linear Computational Geometry." IMA Workshop, Minneapolis, Minesota. (May 29-June 2007) With Co-Organizer

     
     

    Conference Chair.  "Pacific Graphics." Pacific Graphics, Maui, Hawaii. (October 29-November 2, 2007) With Conference Chair

     
     

    "A Combinatorial Approach to Counting Pruned Bezier Curves." Sixth International Conference on Mathematical Methods for Curves and Surfaces, Tromso, Norway. (July 2004)

     
     

    "A Computational Method for Constructing Sylvester-style Sparse Resultants." Tenth International Conference on Applications of Computer Algebra (ACA-2004), Beaumont, Texas. (July 2004)

     
     

    "Fractal Algorithms for Polynomial Curves." Coastal Workshop on Geometric Modeling, (June 2004)

     
     

    "Hodograph Turtles." Conference on Computer Graphics, Kauai, Hawaii. (August 2004)

     
     

    "Sylvester A-Resultants for Bivariate Polynomials with Planar Newton Polygons." International Symposium on Symbolic and Algebraic Computation (ISSAC), Santander, Spain. (July 2004)

     
     

    "Curvature Formulas for Implicit Curves and Surfaces." Workshop on Geometric Modeling and Differential Geometry, Erbach, Germany. (October 2003)

     
     

    "Fractal Bezier." 2003 Pacific Workshop on Geometric Modeling, Calgary, Canada. (October 2003)

     
     

    "Morphing Rational B-spline Curves and Surfaces Using Mass Distributions." Eurographics 2003, Short Presentation, Granada, Spain. (September 2003) With Tao Ju

     
     

    "The Analytic Blossom." SIAM Conference on Geometric Design and Computing, Seattle, Washington. (November 2003)

     
     

    "Toric Bezier Patches." SIAM conference on Geometric Design and Computing, Seattle, Washington. (November 2003)

     
     

    "Algorithms for Analytic Functions in Geometric Modeling." Journees du Groupe de Travail, Modelisation Geometrique, Dijon, France. (March 2001) With G. Morin

     
     

    "An Extended Domain for the Analaytic Blossom." SIAM Conference on Geometric Design and Computing, Sacramento, California. (November 2001)

     
     

    "Multisided Bezier Patches." (Invited Presentation) Hong Kong University Workshop on Geometric Computing, Hong Kong, China. (June 2001)

     
     

    "Three Implicitization Methods for Rational Surfaces." SIAM Conference on Geometric Design and Computing, Sacramento, California. (November 2001)

     
     

    "Baseball and Bezier." The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway. (July 2000)

     
     

    "Beta-Continuity Revisited: Determining a Set of Bezier Control Vertices for the Construction of Geometrically Continuous Curves and Surfaces." The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway. (July 2000) With B. Barsky

     
     

    "Blossoming Poisson Curves." The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway. (July 2000) With G. Morin

     
     

    "Discrete Approximations of Bezier Derivatives." Trends in Approximation Theory, Vanderbilt University, Nashville, Tennessee. (May 2000) With G. Morin

     
     

    "Extracting the Geometric Features of Conic Sections from Rational Quadratic Parametrizations." The Fifth International Conference on Mathematical Methods for Curves and Surfaces, Oslo, Norway. (July 2000) With W. Wang

     
     

    "From Bezier to Poisson." Joint Australia-Taiwan Workshop on Analysis and Applications, Taipei, Taiwan. (April 2000)

     
     

    "Implicitization by Dixon A-resultants." Geometric Modeling and Processing 2000, Hong Kong. (April 2000) With E. Chionh and M. Zhang

     
     

    "Poisson Approximation (Invited Presentation)." Geometric Modeling and Processing 2000, Hong Kong. (April 2000) With G. Morin

     
     

    "Rectangular Corner Cutting and Sylvester A-Resultants." International Symposium on Symbolic and Algebraic Computation (ISSAC), St. Andrews University, Scotland. (August 2000) With M. Zhang

     
     

    "Blossoming, the Cancellation Axiom, and Divided Difference." Dagstuhl Conference on Geometric Modelling, Daghstuhl, Germany. (May 1999)

     
     

    "Fast Computation of the Entries of the Bezout and Dixon Resultants (Invited Presentation)." Surface Approximation and Visualization Conference, Christchurch, New Zealand. (February 1999) With E. Chionh and M. Zhang

     
     

    "Implicitization Matrices in the Style of Sylvester with the Order of Bezout." Fourth International Conference on Curves and Surfaces, Saint-Malo, France. (July 1-7, 1999)

     
     

    "Subdivision for Analytic Functions Based on the Poisson Representation." Fourth International Conference on Curves and Surfaces, Saint-Malo, France. (July 1-7, 1999) With G. Moran

     
     

    "The Ambient Spaces of Computer Aided Design." MSRI Workshop on Mathematical Foundations of CAD, Berkeley, California. (June 1999)

     
     Seminar Speaker
     

    "Generalized Quantum Splines, Department of Mathematics, Tel Aviv University, Israel, ." (May 2013)

     
     

    "Quantum B-splines, Department of Computer Science, Texas A&M University, ." (October 2013)

     
     

    "The Fractal Nature of Bezier Curves and the Bezier Nature of Fractal Curves, Sam Houston State." (April 2013)

     
     

    "DUAL QUATERNIONS." HONG KONG UNIVERSITY, (JUNE 2012)

     
     

    "INTRODUCTION TO COMPUTER AIDED GEOMETRIC DESIGN: HOW DID CAGD DEVELOP?." DOKUZ EYLUL UNIVERSITY. (JULY 2012)

     
     

    "QUANTM SPLINES." UNIVESRITY OF SCEINCE AND TECHOLOGY OF CHINA, HEFEI . (JUNE 2012)

     
     

    "QUANTUM SPLINES." TEL AVIV UNIVERSITY, (JAN 2012)

     
     

    "QUANTUM SPLINES." DOKUZ EYLUL UNIVERSITY. (July 2012)

     
     

    "QUATERNIONS AND DUAL QUATERNIONS." UNIVERSITY OF SCIENCE AND TECHOLOGY OF CHINA, HEFEI. (JUNE 2012)

     
     

    "TECHNIQUES IN GEOMETRIC MODELING: BLOSSOMING, SUBDIVISION, AND KNOT INSERTION." DOKUZ EYLUL UNIVERSITY. (JULY 2012)

     
     

    "THE ROLE OF ALGEBRAIC GEOMETRY IN GEMETRIC MODELING." CHINESE ACADEMY OF SCIENCE BEIJING, (JUNE 2012)

     
     

    "UNDERSTANDING QUATERNIONS." BERKELEY. (APRIL 2012)

     
     

    "Understanding Quaternions: Rotation, Reflection and Perspective Projection." University of Tartu, Department of Mathematics, Tartu, Estonia. (September 2011)

     
     

    "Understanding Quaternions: Rotation, Reflection and Perspective Projection." Max Planck Institute, (May 2011)

     
     

    Speaker.  "Axial Moving Planes and Singularities of Rational Space Curves." Falai Chen, University of Science and Technology (USTC). (April 2008)

     
     

    Speaker.  "Curves, Surfaces, and Syzygies." Hans Hagen, Univeristy of Kaiserslautern, International Graduate School. (May 2008)

     
     

    Speaker.  "Non-Linear Subdivision." Shi-Min Hu, Tsinghua University. (April 2008)

     
     

    Speaker.  "Subdivision Algorithms in Zp." Nira Dyn, University of Tel Aviv, Israel. (March 2008)

     
     

    Speaker.  "Three Open Mathematical Problems Related to Computer Graphics and Geometric Modeling." Falai Chen, University of Science and Technology (USTC). (April 2008)

     
     

    Speaker.  "Three Problems in Search of a Graduate Student." Hoffman, Louisiana State University. (April 2008)

     
     Workshops
     

    Dagstuhl, Germany, May 2011.

     
     

    Speaker.  "An Analogue of the Lane-Riesenfeld Subdivision Algorithm for B-splines with Non-Uniform Knots." Dagstuhl Workshop on Geometric Design, Dagstuhl, Germany. (May 2008) With S. Schaefer

     
     

    Speaker.  "Global Knot Insertion Algorithms." Foundations of Computational Mathematics (FoCM 2008), Hong Kong. (June 2008) With S. Schaefer

     
     

    Speaker.  "Implicitizing Surfaces of Revolution." Hong Kong University Workshop on Algorithmic Algebraic Geometry, Hong Kong. (June 2008)

     
     

    "Algebraic Geometry and Geometric Modeling: Insight and Computation." Workshop on Algebraic Geometry and Geometric Modeling, Nice, France. (September 2004)

     
     

    "An Introduction to Multisided Toric Bezier Patches." International Workshop on Geometric and Visual Computing, Jinan, China. (April 2004)

     
     

    "Blossoming." Workshop on Algebraic Geometry and Geometric Modeling, Vilnius, Lithuania. (July 2002)

     
    Editorial Positions
     Associate Editor, Computer Aided Geometric Design. (2013 - 2013)

     Editor, Geometric Modeling, Daghstahl 2004. Springer-Verlag. (2004 - 2004)

     Associate Editor, Computer-Aided Design. (2001 - 2001)

     Associate Editor, Computer-Aided Geometric Design. (2003 - 2003)

     Associate Editor, Computer Aided Geometric Design. (2002 - 2002)

     Associate Editor, Computer Aided Geometric Design. (2005 - 2005)

     Associate Editor, Computer-Aided Design. (2003 - 2003)

     Associate Editor, Computer Aided Geometric Design. (2004 - 2004)

     Associate Editor, Computer-Aided Design. (2005 - 2005)

     Associate Editor, Computer-Aided Design. (2004 - 2004)

    Supervised Theses & Dissertations
     Suresh Kumar Lodha, Doctor of Philosophy Surface Approximation By Low Degree Patches With Multiple Representations. (1992) (Thesis Committee Member)

     Ayman W. Habib, Doctor of Philosophy Three Approaches to Building Curves and Surfaces in Computer Aided Geometric Design. (1997) (Thesis Director)

     Ming Zhang, Doctor of Philosophy Topics in Resultants and Implicitization. (2000) (Thesis Director)

     Henrik Weimer, Doctor of Philosophy Subdivision Schemes for Physical Problems. (2000) (Thesis Committee Member)

     Jiangchun Luo, Master of Science Part Assembly Using Static and Dynamic Force Fields. (2000) (Thesis Committee Member)

     Geraldine Morin, Ph.D. Analytic Functions in Computer Aided Geometric Design. (2001) (Thesis Director)

     Scott Schaefer, Master of Science A Factored, Interpolatory Subdivision Scheme for Surfaces of Revolution. (2003) (Thesis Committee Member)

     Tao Ju, Master of Science Convex Contouring of Volumetric Data. (2003) (Thesis Committee Member)

     Andrew M. Ladd, Master of Science Analysis of Probabilistic Roadmap Methods for Motion Planning and Applications to Polygon Manipulation. (2003) (Thesis Committee Member)

     Jan Philipp Hakenberg, Master of Science Smooth Subdivision for Mixed Volumetric Meshes. (2004) (Thesis Committee Member)

     Amarda Shehu, Master of Science Sampling Biomolecular Conformations with Spatial and Energetic Constraints. (2004) (Thesis Committee Member)

     Tao Ju, Doctor of Philosophy 3D Atlas of the Mouse Brain. (2005) (Thesis Committee Member)

     Ning Song, Master of Science A computational method for constructing Sylvester-style sparse resultants. (2005) (Thesis Director)

     Scott Schaefer, Intuitive Methods for 3D Shape Deformation. (2006) (Thesis Committee Member)

     Ning Song, Ph.D Mu-Bases and their Applications in Geometric Modeling. (2007) (Thesis Director)

     Matthew Simpson, Doctor of Philosophy On Log Canonical Models of the Moduli Space of Stable Pointed Genus Zero Curves. (2008) (Thesis Committee Member)

     Sridhar Lavu, Master of Science Volume Visualization and Volume Painting of Large Data Sets. (2009) (Thesis Committee Member)

     Travis McPhail, Doctor of Philosophy Techniques for Realtime Viewing and Manipulation of Volumetric Data. (2010) (Thesis Committee Member)

     Powei Feng, Master of Science Segmentation and Visualization of Volume Maps. (2010) (Thesis Committee Member)

     DeHoff Kevin, Doctoral Live Cell Compartment Tracking: Object Tracking in Oscillating Intensity Images. (2011) (Thesis Committee Member)

     Linda Hill, Masters Violin Virtuoso: A Live Analyzed Music Game. (2011) (Thesis Director)

     RENEE LAVERDIERE, DOCTORAL, ON GEOMETRY ALONG GRAFTING RAYS IN TEICHMULLER SPACE. (2012) (Thesis Committee Member)

     Po-Wei Feng, Doctoral Functional representation and manipulation of shapes with applications in surface and solid modeling. (2013) (Thesis Committee Member)

     Amanda Knecht, Doctoral Weak Approximation for Degree 2 del Pezzo Surfaces of Bad Reduction. (Thesis Committee Member)

     Anton Mishkinis, PhD Extension des méthodes de géométrie algorithmique aux structures fractales. (Thesis Committee Member)

     Sergey Podkorytov, PhD Espaces tangents pour les forms auto-similaires. (Thesis Committee Member)

     Taylor Martin, Lower Order Solvability of Links. (Thesis Committee Member)

    Awards, Prizes, & Fellowships
     John Gregory Memorial Award, Dagstuhl Meeting on Geometric Modeling (2005)

     Reviewer, Computer-Aided Design (2001)

     Reviewer, Transactions on Mathematical Software

     Reviewer, Computer Vision, Graphics, and Image Processing (2001)

     Member of the pProgram Committee, Geometric Modeling and Processing (2002)

     Member of the Program Committee, Pacific Graphics - 2001: The Ninth Pacific Conference on Computer Graphics, Tokyo, Japan and Applications (October 16-18, 2001)

     Co-organizer, Dagstuhl Meeting on Geometric Modeling, Dagstuhl, Germany (May 2002)

     Reviewer, Computer Aided Geometric Design

     Reviewer, Transactions on Graphics

     Member, Program Committee, Pacific Graphics - 2000: The Eighth Pacific Conference on Computer Graphics and Applications (2000)

     Co-organizer, Dagstuhl Meeting on Geometric Modeling 2002 (2000)

     Member, Program Committee, Geometric Modeling and Processing 2000: Theory and Applications (2000)

    Positions Held
     Co-Organizer, The Fourth International Workshop on Algebraic Geometry and Geometric Modeling (AGGM 2009). (2009 - 2009)