Keywords: virtual reality, constraint-based manipulations, allowable motions, constraint solving, constraint recognition.

Virtual Reality (VR) technology is a natural extension of 3D computer graphics with advanced input and output devices and it brings a completely new environment to the CAD community. However, most existing VR modelling systems only offer very limited tools for object modelling and lack the sophisticated modelling and modification tools for creating complex solid models in a VR environment. One of the most important reasons is the low accuracy and reliability of 3D input devices that prevent users from precise design activities. In this paper, constraint-based 3D direct manipulations are acquired through incorporating constraints into the VR environment for intuitive and precise solid modelling. Solid modelling in the VR environment is precisely performed in an intuitive manner through precise constraint-based manipulations.

Constraint-based manipulations are accompanied with automatic constraint recognition and precise constraint satisfaction for establishing the hierarchically structured constraint-based data model. Once a constraint is recognized, the recognized constraint will be precisely satisfied under the current allowable motions of an object and be inserted into the hierarchically structured constraint-based data model. The satisfied constraint further restricts the subsequent motions of the object. Constraint-based manipulations are realized by allowable motions for precise 3D interactions in the VR environment. The allowable motions are represented by 3 basic translation DOFs (degree-of-freedoms) and 3 basic rotational DOFs as a mathematical matrix for conveniently deriving the allowable motions from constraints.

The allowable motions are derived from constraints through constraint solving. A procedure-based DOF incorporation method for 3D constraint solving is presented for deriving the allowable motions. If there is only one constraint applied to an object, the remaining DOFs of the object can be directly obtained by DOF analysis. The DOF analysis is to analyse the remaining basic translational DOFs and the remaining basic rotational DOFs that correspond to the constraint. If there are multi-constraints (more than one) applied to an object, the remaining DOFs of the object can be obtained by DOF incorporation. The DOF incorporation for solving multi-constraints is based on the DOF analysis for solving individual constraints. The DOF incorporation is realized by the "AND" Boolean operations between the corresponding elements with the same position at the first and the second columns and the intersections between the allowable ranges of the translations or rotations along the same axis in the allowable motion matrices that respectively correspond to individual constraints.

Constraints are implicitly incorporated into the VR environment for constraint-based manipulations by automatic constraint recognition. A rule-based constraint recognition engine is developed for automatic constraint recognition. The system recognizes the constraints between objects from the current position and orientation of the manipulated object according to a rule base. The rule base defines some of the rules that are applied to the constraint recognition for recognizing some specified constraints.

To reduce the searching time for detecting various types of constraints from various objects and to enhance the modelling efficiency, some special constraint-based manipulations are also implemented as modelling operations for solid modelling in the VR environment.

The presented constraint-based manipulations have been implemented in our VR-based solid modelling prototype system. In this system, the user can create solid models in the VR environment in an intuitive manner through precise constraint-based manipulations.

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