Ron GoldmanRon Goldman


Work address
Department of Computer Science
6100 South Main
Rice University
Houston, Tx 77251-1892
Duncan Hall 3116
Work phone
Fax number

Research Interests

My current research interests lie in the mathematical representation, manipulation, and analysis of shape using computers. I am particularly interested in algorithms for polynomial and piecewise polynomial curves and surfaces, and I have investigated both parametrically and implicitly represented geometry. My current work includes research in computer aided geometric design, solid modeling, computer graphics, and splines. Click here for a short biography.

Recent Publications

Here are some of my recent publications:


  • Modeling Projections in 3-Dimensions by Rotations in 4-Dimensions, accepted to appear in Graphical Models.
  • Quantum B-splines, with P.Simeonov, accepted to appear in BIT Numerical Mathematics.
  • Formulas and Algorithms for Quantum Differention of Quantum Bernstein Bases and Quantum Bezier Curves Based on Quantum Blossoming, with P. Simeonov, Graphical Models (2012), Special Issue of selected papers from the 8th Dagstuhl Seminar on Geometric Modeling 2011, Vol. 74, pp. 326-334.
  • Using Mu-Bases to Implicitize Rational Surfaces with a Pair of Orthogonal Directorices, with X. Shi and X. Wang, Computer Aided Geometric Design (2012), Special Issue on GMP 2012, Vol. 29, pp. 541-554.
  • Implicitizing Rational Surfaces of Revolution using Mu-Bses, with X. Shi, Computer Aided Geometric Design (2012), Vol. 29, pp. 348-362.
  • Using Smith Normal Forms and Mu-bases to Compute All the Singularities of Rational Planar Curves, with X. Jia, Computer Aided Geometric Design (2012), Vol. 29, pp. 296-314.
  • q-Blossoming: A New Approach to Algorithms and Identities for q-Bernstein Bases and q-Bezier Curves, with P. Simeonov and V. Zafiris, Journal of Approximation Theory (2012), Vol. 29, pp. 296-314.
  • h-Blossoming: A New Approach to Algorithms and Identities for h-Bernstein Bases and h-Bernstein Bases and h-Bezier Curves, with P. Simeonov and V. Zafiris, Computer Aided Geometric Design, (2011), Vol. 28, No. 9, pp. 549-565.
  • 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. 28, No. 9, pp. 549-565.


  • Rethinking Quaternions: Theory and Computation,, Synthesis Lectures on Computer Graphics and Animation, ed. Brian A. Barsky, No. 13, San Rafael: Morgan & Claypool Publishers, 2010.
  • An Integrated Introduction to Computer Graphics and Geometric Modeling, CRC Press, Taylor and Francis, New York, 2009.
  • Geometric Modeling, Dagstuhl 2002, S. Hahmann, G. Brunnett, G. Farin, and R. Goldman (eds.), Springer-Verlag, 2004.
  • Topics in Algebraic Geometry and Geometric Modeling, co-edited with R. Krasauskas, AMS Contemporary Mathematics, Vol. 334, 2003.
  • Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling, Morgan Kaufmann Publishers, Academic Press, San Diego, 2002.
  • Knot Insertion and Deletion Algorithms for B-spline Curves and Surfaces, co-edited with Tom Lyche, SIAM, 1993.

Complete List of Publications

Other Links

  • Rice University Computer Science Department
  • Rice Computer Graphics/Geometric Design Home Page