Research And Implementation Of Declarative Geometric Constraint System

The constraint-based CAD design technology can be divided into two categories: parametric technology and variational technology. The variational technology manipulates design models declaratively, which is independent of operation sequences, and achieves deformation design schemes more conveniently than the parametric technology. The declarative modeling and solving of geometric constraint system studied in this thesis has become one of the most critical unit techniques in modern CAD platforms, and has an important effect on the whole system performance.Considering the commonness of constraint modeling and solving algorithms, a unit constraint solving framework, named Constraint Broadcasting Automation (CBA), which is applicable to 2D design, 3D model shape modification and 3D assembly, is investigated. Several important concepts in CBA, including Virtual Body, Constraint Relation, and Constraint Component, are emphasized. And the object hierarchies with their attributes and operations in CBA kernel layer are consummated. The new integration framework between CBA and CAD platforms is discussed also.To make declarative constraint models is the precondition for that design models can be manipulated declaratively. From the decomposition viewpoint of geometric position and gesture parameters, the combinatorial expression of geometric elements and constraints is established. Subsequently, the technique used to construct the global constraint model of a B-rep model is presented. And, an approach to recognize geometric constraints increasingly in the process of local model shape modification is proposed.In order to determine constraint validity more effectively while constraint modeling, a parameter normalization transformation approach is used to improve the numerical singularity from differential variable scales. And moreover, the constraint matching priority is employed to change the matching sequence and direction of a given constraint. As a result, the subsequent decomposition and solving of constraint systems can be implemented more efficiently.The unstableness of constraint solving increases greatly due to the higher nonlinearity in three dimensional constraint systems. After the decouple property of position-gesture constraint combination is analyzed, several key criterions are defined and used to determine whether the constraints can be solved independently or not. Subsequently, based on the spherical geometry, the analytic solving method used to solve gesture constraints is proposed. Accordingly, the analytic strategy for solving decoupled position constraints is addressed through the combination of geometric projection and intersection.The model shape modification of a solid model actually reflects its inner topological and geometric changes. Assuming the topological structure of 3D models is unchanged, the approaches to update local geometric increasingly are investigated. After the direct method based on boundary geometry intersection is proposed and analyzed, an improved indirect strategy based on boundary geometry intersection plus to model reconstruction is presented.According to the above-mentioned achievements, two declarative prototype systems, CBAbench for 2D geometric design and CBAmodeller for 3D deformation design, are developed. The system structures and implementation techniques are described briefly, and several illustrative examples are given to show that the above theories and methods are feasible and valid.