Mathematical Sketching: A New Approach for Creating and Exploring Dynamic Illustrations

Dr. Joseph LaViola
Thursday, March 2, 2006
1:30PM - CSB 232

Abstract


Diagrams and illustrations are often used to help explain mathematical concepts. They are commonplace in mathematical and physics textbooks providing a form of physical intuition to otherwise abstract principles. Similarly, students often use pencil and paper to create diagrams for math problems as an intuitive aid in visualizing relationships between variables, constants, and functions. However, such static diagrams generally assist only in the initial formulation of mathematical expressions but not in the ``debugging'' or analysis of those expressions which can be a severe visualization limitation even for simple problems.

To overcome these limitations I developed mathematical sketching, a novel approach to rapidly interacting with and visualizing mathematical concepts through the fluid association of handwritten mathematical notation and free-formed diagrams. Mathematical sketching derives from the familiar pencil-and-paper process of drawing supporting diagrams to facilitate the formulation of mathematical expressions; however, with a mathematical sketch, users can also leverage their physical intuition by watching their hand-drawn diagrams animate in response to continuous or discrete parameter changes in their written formulas. In this talk, I will discuss the critical components of mathematical sketching and present the results of an initial user evaluation in the context of a prototype application called MathPad^2.

Short Bio


Joseph J. LaViola Jr. is currently a postdoctoral research associate in Computer Science at Brown University. He works under the direction of Andries van Dam and Robert Zeleznik in the Computer Graphics Group. His primary research interests include pen-based interactive computing, 3D interaction techniques, predictive motion tracking, multimodal interaction in virtual environments, and user interface evaluation. His work has appeared in journals such as Presence and IEEE Computer Graphics & Applications, and he has presented research at conferences including ACM SIGGRAPH, the ACM Symposium on Interactive 3D Graphics, IEEE Virtual Reality, and Eurographics Virtual Environments. He has also co-authored "3D User Interfaces:

Theory and Practice", the first comprehensive book on 3D user interfaces. Joseph received a Sc.M. in Computer Science in 2000, a Sc.M. in Applied Mathematics in 2001, and a Ph.D. in Computer Science in 2005 from Brown University.