## Ron Goldman## Information- Work address
- Department of Computer Science
6100 South Main Rice University Houston, Tx 77251-1892 - Office
- Duncan Hall 3116
- Work phone
- 713-348-5729
- Fax number
- 713-348-5930
- rng@cs.rice.edu
- Wife
- Jackie
- Daughter
- April
## Research InterestsMy 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 PublicationsHere 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 |