Advances in Mathematical Sketching: Moving Toward the Paradigm's Full Potential

by

Joe LaViola

Summary

The paper focuses on mathematical sketching, specifically with the building of an application that will allow for sketching of expressions and the animation of drawn diagrams that correspond to those applications. The system is MathPad2. The UI depends heavily on the user to do numerous actions by way of a lasso and tap. The expressions must be manually segmented by the user. Associations can be made between the mathematical equations and the diagrams. These can be implicit such as a variable in an expression appears on a diagram. Or they can be explicit, by having the user draw a line between two entities that should be associated. MathPad is capable of graphing functions, solving equations and evaluating expressions. The system uses Matlab as its backend.

To aid with the recognition users must provide a sample (10 to 20) of each symbol they will use for the system to train on. Key points in the stroke are used for recognition. Pairwise examination provided an improvement in recognition over past versions of the system. LaViola is able to achieve 90.8% parsing accuracy.

The need for fixing diagrams to match what the user drew to what the math specifies is also covered. Sketching cannot have the precision that math must. Angle, location and size of the various parts of the diagram are adjusted.

The author wishes this system to be used by students. A mathematical notebook of sort. One in which the diagrams can be animated depending on the expressions we compose.

Discussion

There seems to be a lot of dependency on the lasso as a means of interaction. This paper reminds me of the work Adler is doing. It is difficult to be precise when sketching, and in the engineering world precision is required for the computation produced from these sketches to be accurate. Adler is attempting to do this by using an additional mode of interaction (voice). LaViola is doing something similar by using the equations as an additional mode.

Citation

LaViola, J. "Advances in Mathematical Sketching: Moving Toward the Paradigm's Full Potential", IEEE Computer Graphics and Applications, 27(1):38-48, January/February 2007.