IFOG: Inductive Functional Programming for Geometric Processing

Abstract

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.