Workshop on Mathematical User Interfaces
Pen-based Input of Geometric Constructions
Abstract:
Pen-based input is the classical approach to drawing. Without computers,
using a pen was the natural approach to do drawings, and the simplicity of
this “device” always called for similar electronic solutions.
Today, a broad range of electronic input devices is available that try to
pair the simplicity of input with the power of computing. They come in all
sizes: from small touch-screens with stylus in personal digital assistants,
via desktop-size input tablets or interactive displays, to electronic
whiteboards with rear- or front-projection. These devices all share a direct
interaction paradigm.
The challenge in using these devices for geometric constructions is to
automatically annotate the drawn objects with their relations to the other
objects. A basic example is the drawing of a right-angled triangle: How can
we automatically recognize the user’s intention to have a right angle? Can
we do that at all? Do we really want to do that? If not – what is the
easiest pen-compatible way to have the user add this information? We will
demonstrate several approaches to these problems, implemented in a
development version of Cinderella.
Another interesting issue is the presentation of hand-drawn figures: Is it
possible to preserve the look of a sketch while still guaranteeing
mathematically correct figures? Using the additional information gathered by
automatic theorem proving we show some solutions.