Creating and Manipulating Constrained Models

The success of constraint-based approaches to geometric modeling has been limited by difficulty in creating constraints, solving them, and presenting them to users. This paper addresses all three issues. We facilitate the creation of constrained models by using placement operations to specify constraints as well as positions, with no extra work on the part of the user. We augment Snap-Dragging[Bie89], an earlier successful technique for specifying geometric models, to give the user the option of making persistent the relations it helps create. Because the technique provides both the constraints and an initial solution to them, we can use the techniques of constrained dynamics to maintain the relationships as a user drags the models. This differential approach to constraints avoids many of the difficulties in constraint-based systems, such as solving non-linear algebraic equations. Our approach suggests methods for displaying and editing constraints as well. This research was sponsored in part by Apple Computer, Siemens Corporation and Silicon Graphics Incorporated. The first author is supported in part by a fellowship from the Schlumberger Foundation, Inc. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of Schlumberger, Siemens, SGI or Apple.