Geometric Constraint Satisfaction Problems Research Articles

Coordinate-free geometry and decomposition in geometrical constraint solving

In CAD, a designer usually specifies mechanisms or objects by the means of sketches supporting dimension requirements like distances between points, angles between lines, and so on. This kind of geometric constraint satisfaction problems presents two aspects which solvers have to deal with: first, the sketches can contain hundreds of constraints, and, second, the problems are invariant by rigid body motions. Concerning the first issue, several decomposition methods have been designed taking invariance into account by fixing/relaxing coordinate systems. On the other hand, some researchers have proposed to use distance geometry in order to exploit invariance by rigid body motions. This paper describes a method that allows us to use distance geometry and decomposition in the same framework.

Defining tools to address over-constrained geometric problems in Computer Aided Design

This paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modeling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci’s witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

Special Issue on Collaborative Engineering

Special Issue on Collaborative Engineering

Singularity analysis of geometric constraint systems

Singularity analysis is an important subject of the geometric constraint satisfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint matching of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a differentiation algorithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.

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This paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modeling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci’s witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

Knowledge-based tools for development of engineering theories

An approach to solving of the knowledge integration problem on the basis of engineering theories had been considered by Vittikh ( Artif. Intell. Engng, 1997, 11). Current paper describes constraint-oriented tools for generation of engineering models which are organized around a constraint-oriented knowledge base. It also allows use of them for maintaining this approach. Many efforts in the field of artificial intelligence are concentrated on solving geometric constraint satisfaction problems in a specific domain. This paper describes the solving of a geometric constraint system called ANMEC that has been created with the use of these tools. The way the system is applied to tasks of mechanism's analysis and synthesis is considered.

Using A Constraint-oriented Knowledge-based System For Optimum Mechanical Engineering Design

Many efforts in the field of artificial intelligence are concentrated on solving geometric constraint satisfaction problems in specific domain. We describe and analyse how solving geometric constraint system called ANMEC is applied to a task of mechanism optimization. The interactive system ANMEC organized around a constraint-oriented knowledge base that contains required knowledge of 2-D and 3-D geometry. It allows ANMEC to perform analysis, dimensional synthesis and optimization of planar and spatial mechanisms by automatic generating and combining analytical closed-form solution with iterative numerical methods. In addition, analytical solution may be simplified by a general-purpose symbolic algebra system with human guidance. An example in Mechanical Engineering is given.