The Truth About Quaternions

Speaker:	Professor Ron GOLDMAN
		Department of Computer Science
		Rice University

Title:		"The Truth About Quaternions"

Date:		Monday, 9 October 2006

Time:		11:00am - 12 noon

Venue:		Room 1504 (via lift nos. 25/26)
		HKUST

Abstract:

Unit quaternions provide a compact representation for rotations in
3-dimensions, and they are useful as well for performing interpolation
between rotations for key frame animation. A quaternion is defined as a
sum -- q = a + bi + cj + dk -- that is, as a sum of a scalar and a vector!
In this talk we shall answer the following questions:

1.	What does it mean geometrically to add a scalar and a vector?

2.	How are quaternions related to the standard homogeneous
	coordinates of Computer Graphics?

3.	Is there a coordinate free notion of quaternion multiplication?

4.	What are the advantages and disadvantages of adopting quaternions
	to represent rotations in 3-dimensions?


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Biography:

Ron 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.  In 2002, he
published a book on Pyramid Algorithms:  A Dynamic Programming Approach to
Curves and Surfaces for Geometric Modeling.  He is currently an associate
editor of Computer Aided Geometric Design.

Dr. Goldman's 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, and splines.  He is particularly interested in algorithms for
polynomial and piecewise polynomial curves and surfaces, and he is
currently investigating applications of algebraic and differential
geometry to geometric modeling.  In 2005, he was awarded the John Gregory
Memorial Award at the Dagstuhl meeting on Geometric Design for his
outstanding contributions in Geometric Modeling.