Dynamic geometry based on geometric constraints

Abstract

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations which lead to more than one possible solution. While the user is defining the geometric construction, he is responsible to resolve these ambiguities. However, when the user is dragging a geometric element, the system is responsible to choose the intended solution, that is, the same solution that the user would select if we could ask him again. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when this behavior is not the one the user intended. In this work we propose an architecture for dynamic geometry systems built upon a set of functional units which will allow to apply some well known results from the Geometric Constraint Solving field. A functional unit called emph{filter} will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.