A Constraint-Based Figure-Maker

Abstract

In this paper, we describe a new kind of constraint-based figure-maker for parametrically defined curves. Figures are made by defining objects and imposing constraints on their geometric behavior. We present a formulation of constraints as three ways in which two scalar real valued functions may be compared. This lets us specify equality, optimality and inequality constraints. We also introduce the mechanism of connectors. Connectors are used to connect various geometric entities through constraints. Behavior of connectors depends only on the local properties of curves. Connectors remove the need for an object to know about the kinds of constraints or the kinds of other objects it is connected to in order to act to satisfy a constraint. This makes for a very manageable and scalable program as the number of objects and constraints grows. An objects is modified in response to deviation of its state from the desired state specified through constraints. We have implemented some general low-level methods of specifying and satisfying constraints. These basic mechanisms can be used as an assembly language and combined hierarchically to define very general constraints.