An Incremental Algorithm to Support Geometric Constraint Satisfaction in Engineering Design Arquimedes Lopes da Silva Federal Technology Center of Goias – CEFETGO Salgado Oliveira University – Goiânia e-mail: als@cefetgo.br Edgard Lamounier Jr. Federal University of Uberlândia – UFU Faculty of Electrical Engineering – Computer Graphics Laboratory e-mail: lamounier@ufu.br ABSTRACT This paper presents a set of algorithms to efficiently support geometric constraint satisfaction during engineering design. Based upon an incremental graph construction approach, these algorithms satisfy each new inserted constraint by exploiting the degrees of freedom of the involved geometric entities. The objective is to avoid satisfying the entire constraint set from scratch due to a new constraint insertion. A prototype system has been developed and is presented to demonstrate the flexibility gained by the proposed incremental algorithms. KEY WORDS: CAD, engineering design, geometric constraints, incremental graph-based algorithms. 1. Introduction During the life cycle of an engineering product, several design alternatives are tested before beginning its manufacturing process. Therefore, it is of fundamental importance to provide engineers with computational tools which allow them to test different design alternatives, with decisive information, at the appropriate time. Traditional CAD tools allow the modeling of a product to be made in terms of its dimensions and absolute coordinates. Hence, the determination of a product model values is done through numeric manipulations, which must be sequentially managed by engineers. It has been noted that such process hinders the necessary flexibility for creativity required by early design stages [10]. Recently, it has been noted that CAD projects, based on the constraint paradigm [9], provides engineers with the required training of thought for exploiting different design solutions. This approach allows engineers to create an engineering design in terms of geometric constrains imposed on geometric entities. Thus, the geometry of a project can be modified in a more natural and efficient way [22]. However, some constraint-based systems re-satisfy the entire set of design constraints, when a new constraint is inserted [5,18]. This process is time-consuming and poorly contributes to the man-machine interactivity demanded by CAD systems. This work presents an algorithm to support interactive constraint-based design. Based on an incremental approach, the algorithm is designed to speed up the constraint satisfaction process during engineering design. A prototype system has been implemented to evaluate the feasibility of the proposed techniques. 2. Related work In the last years, it has been noticed an increasing number of constraints-based algorithms to support engineering design [4, 5, 18, 20]. The purpose of this section is to present a classification of the current approaches of these algorithms and to discuss their main characteristics. As shown in Figure 1, the current approaches based on constraints can be divided in two main categories: those based on equations and those based on geometric construction. 2.1 Equation-based Approach The equation approach treats a group of geometric and engineering (performance, cost, weight etc) constraints as equations. For this reason, researchers argue that this approach provides a better platform mathematics to support the preliminary phases of engineering projects like functions such tolerance analysis and sensibility analysis. Proceedings of the Sixth International Conference on Information Visualisation (IV’02) 1093-9547/02 $17.00 © 2002 IEEE