Since decades, especially in CAD and CG, to solve various kinds of problems and/or to develop automatic systems, not only geometric modeling techniques but also combinatorial searches of geometric elements such as line segments have been applied extensively. Generally it is troublesome and time consuming to program the combinatorial searches for programmers because they are basically algorithmic and it would be difficult to formalize them. In this paper, a new programming technique called IFOG (Inductive Functional prOgramming for Geometric processing) is proposed. IFOG enables to realize easier programing for programmers, especially for beginners, than conventional programming techniques for geometric processing. In IFOG, geometric elements are expressed as their properties, and they are also instances of geometric classes that can be generalized from the instances inductively. Since the classes and instances are stored as text files in a PC, programmers can read and write them whenever they develop programs in IFOG. Therefore, they do not have to grasp the whole data of the relationships of geometric elements temporarily in their brains in their programming. The effectiveness of IFOG is indicated by using practical examples in this paper, and it has been verified by our experimental system.

Today, automotive design has to face numerous exciting challenges. The growing globalization causes an intensified competition amongst car manufacturers and forces them to reduce the required development time in order to shorten time to market, to appear first with attractive new products. Efficient and flexible processes and tools are necessary to handle the arising complexity efficiently. Parametric-associative 3D-CAD systems offer ideal conditions to face this challenge in virtual development. The present paper focusses on a special issue in automotive concept phasethe vehicle architecture layout process and required parameterization strategies. In most cases, parametric-associative relations defined within 3D-CAD models are of rigid kind. This implies that a formula, which is defined within a 3D-CAD model in order to evaluate a specific parameter, cannot change the input/output situation of involved parameters. In most application cases, this disadvantage can be neglected, but not in case of vehicle layouting in the early concept phase. Since geometric boundary conditions which define the geometric base of a vehicle concept can vary significantly, a rigid model parameterization is not the proper solution and prevents efficient reuse of 3D-CAD models. Additionally, rigid parameterization concepts lack of the required flexibility when having to manage multiple design variants in a single model. Therefore, the present paper outlines a possible strategy, which enables the use of advantages of parametric-associative design, while allowing changes of relations-evaluation behavior in context of respective technical issues and simultaneously preserving necessary geometrical model consistency.

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