Constraint-Based Design for 3D Shapes

Abstract This paper proposes an ATMS-based geometric reasoning system for feature-based 3D solid modeling. Here, every feature is described by a set of geometric constraints such as distances between edges and angles between faces. The system has to evaluate the constraints in order to determine the attributes of all the geometric elements in the features. Therefore, the modeling process can be considered as a constraint satisfaction problem. Our ATMS-based approach overcomes two serious drawbacks of conventional rule-based approaches: inefficiency and poor conflict handling. For the first problem, a state reduction method, represented as an ATMS justification, resolves the problem of combinatorial explosion in the rules' pattern matching. Here, intermediate states are defined by the degree of freedom: the determined geometric elements have zero degrees, and free faces, edges, and vertices have three, four, and three degrees, respectively. Each constraint invocation reduces the degree; that is, it increases the level of determinacy of the status. For the second problem, the ATMS's label update propagation mechanism resolves conflicts of constraints. It distinguishes conflicting situations from redundant or under-constrained ones, and the minimum diagnosis technique detects which constraint causes the conflict. The use of an ATMS as a propositional reasoning function has various advantages over rule-based systems, such as avoidance of infinite loops and reasoning without pattern matching. The paper also considers the computational efficiency of our approach and proves its practicality by presenting data on an actual product.