Ron Goldman is a professor of computer science at Rice University in Houston, Texas. Dr. 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. Dr. Goldman’s current research interests lie in the mathematical representation, manipulation, and analysis of shape using computers. His work includes research in computer-aided geometric design, solid modeling, computer graphics, polynomials, and splines. He is particularly interested in algorithms for polynomial and piecewise polynomial curves and surfaces, as well as in applications of algebraic and differential geometry to geometric modeling. His most recent focus is on the uses of quaternions and Clifford algebras in computer graphics. Dr. Goldman has published over a hundred articles in journals, books, and conference proceedings on these and related topics. He has also published two books on computer graphics and geometric modeling: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling and An Integrated Introduction to Computer Graphics and Geometric Modeling. Dr. Goldman is currently an associate editor of Computer Aided Geometric Design. Before returning to academia, Dr. Goldman worked for 10 years in industry solving problems in computer graphics, geometric modeling, and computer-aided design. He served as a mathematician at Manufacturing Data Systems Inc., where he helped to implement one of the first industrial solid modeling systems. Later, he worked as a senior design engineer at Ford Motor Company, enhancing the capabilities of their corporate graphics and computer-aided design software. From Ford, he moved on to Control Data Corporation, where he was a principal consultant for the development group devoted to computer-aided design and manufacture. His responsibilities included database design, algorithms, education, acquisitions, and research. Dr.Goldman left Control Data Corporation in 1987 to become an associate professor of computer science at the University of Waterloo in Ontario, Canada. He joined the faculty at Rice University in Houston, Texas, as a professor of computer science in July 1990.

• Preface.- Theory.- Computation.- Rethinking Quaternions and Clif ford Algebras.- References.- Further Reading.- Author Biography.

Ron Goldman is a professor of computer science at Rice University in Houston, Texas. Dr. 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. Dr. Goldman’s current research interests lie in the mathematical representation, manipulation, and analysis of shape using computers. His work includes research in computer-aided geometric design, solid modeling, computer graphics, polynomials, and splines. He is particularly interested in algorithms for polynomial and piecewise polynomial curves and surfaces, as well as in applications of algebraic and differential geometry to geometric modeling. His most recent focus is on the uses of quaternions and Clifford algebras in computer graphics. Dr. Goldman has published over a hundred articles in journals, books, and conference proceedings on these and related topics. He has also published two books on computer graphics and geometric modeling: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling and An Integrated Introduction to Computer Graphics and Geometric Modeling. Dr. Goldman is currently an associate editor of Computer Aided Geometric Design. Before returning to academia, Dr. Goldman worked for 10 years in industry solving problems in computer graphics, geometric modeling, and computer-aided design. He served as a mathematician at Manufacturing Data Systems Inc., where he helped to implement one of the first industrial solid modeling systems. Later, he worked as a senior design engineer at Ford Motor Company, enhancing the capabilities of their corporate graphics and computer-aided design software. From Ford, he moved on to Control Data Corporation, where he was a principal consultant for the development group devoted to computer-aided design and manufacture. His responsibilities included database design, algorithms, education, acquisitions, and research. Dr.Goldman left Control Data Corporation in 1987 to become an associate professor of computer science at the University of Waterloo in Ontario, Canada. He joined the faculty at Rice University in Houston, Texas, as a professor of computer science in July 1990.

• Preface.- Theory.- Computation.- Rethinking Quaternions and Clif ford Algebras.- References.- Further Reading.- Author Biography.

Ron Goldman is a professor of computer science at Rice University in Houston, Texas. Dr. 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. Dr. Goldman’s current research interests lie in the mathematical representation, manipulation, and analysis of shape using computers. His work includes research in computer-aided geometric design, solid modeling, computer graphics, polynomials, and splines. He is particularly interested in algorithms for polynomial and piecewise polynomial curves and surfaces, as well as in applications of algebraic and differential geometry to geometric modeling. His most recent focus is on the uses of quaternions and Clifford algebras in computer graphics. Dr. Goldman has published over a hundred articles in journals, books, and conference proceedings on these and related topics. He has also published two books on computer graphics and geometric modeling: Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling and An Integrated Introduction to Computer Graphics and Geometric Modeling. Dr. Goldman is currently an associate editor of Computer Aided Geometric Design. Before returning to academia, Dr. Goldman worked for 10 years in industry solving problems in computer graphics, geometric modeling, and computer-aided design. He served as a mathematician at Manufacturing Data Systems Inc., where he helped to implement one of the first industrial solid modeling systems. Later, he worked as a senior design engineer at Ford Motor Company, enhancing the capabilities of their corporate graphics and computer-aided design software. From Ford, he moved on to Control Data Corporation, where he was a principal consultant for the development group devoted to computer-aided design and manufacture. His responsibilities included database design, algorithms, education, acquisitions, and research. Dr.Goldman left Control Data Corporation in 1987 to become an associate professor of computer science at the University of Waterloo in Ontario, Canada. He joined the faculty at Rice University in Houston, Texas, as a professor of computer science in July 1990.

• Preface.- Theory.- Computation.- Rethinking Quaternions and Clif ford Algebras.- References.- Further Reading.- Author Biography.