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Direct Manipulation Devices for the Design of
Geometric Constraint Networks

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.

Magnenat-Thalmann, N., Thalmann, D. (eds),
* Communicating with Virtual Worlds, *
pp. 294-305, Springer, 1993
(proceedings, Computer Graphics International '93, Lausanne, June 1993.)