Constraint Based Automatic Construction and Manipulation of Geometric Figures

Abstract

An important component of an Intelligent Tutoring System (ITS) for teaching geometry is its capacity to transform a figure into as many different figures as possible, yet all of which respect the same underlying logical specification. Given a logical specification for a figure, (i) a figure can be constructed automatically from the objects and properties in the spepification; and (ii) once constructed, one can transform a figure through displacement of any of its objects and still obtain a figure that respects the specification. For a student user, this feature provides an invaluable tool for graphical exploration and discovery of properties induced by the logical specification. Our problem domain is automatic construction of figures; and we address this issue in restricted cases using Constraint Logic Programming We present solutions to cases in which figures can be constructed automatically and in which there is also a natural notion of completeness for our system. For this automatic figure construction system, we describe an implementation, written in Prolog III, which makes use of both constraints and coroutines provided in the language. Results of experimentation are also included, as well as ways in which the system can be extended to handle non restricted cases. 1