Geometric constraints play an important role in the parameterization and design of geometric models. We describe an application of the Direct Manipulation Device (Dmd) concept to interactive specification and editing of geometric constraint networks. A Dmd is a virtual interactive device for visualizing an instance of an abstract data type and for performing operations on the data using direct manipulation. We present a methodology for using Dmds in geometric applications and demonstrate Dmds for numerous constraints.
We consider many common constraint types, such as distances and angles between points, and also a probabilistic position constraint, which treats the position of a point as a suitably distributed random variable. The Dmd for this constraint specifies the random variable's mean vector and covariance matrix. The underlying representation of a constraint network is a labeled bi-partite graph having object nodes, constraint nodes, and arcs that connect constraint nodes to object nodes. The arcs are labeled to distinguish the a-symmetric role that points possess relative to the constraints.