Transformation of geometric models into orthogonal polyhedra using fuzzy logic
Purpose - This paper describes how non-orthogonal geometric models may be transformed into orthogonal polyhedral models. The main purpose of the transformation is to obtain a geometric model that is easy to describe and further modify without loss of topological information from the original model. Design/methodology/approach - The transformation method presented in this paper is based on fuzzy logic (FL). The idea of using FL for this type of transformation was first described by Takahashi and Shimizu. This paper describes both philosophy and techniques behind the transformation method as well as its application to some example 2D and 3D models. The problem in this paper is to define a transformation technique that will change a non-orthogonal model into a similar orthogonal model. The orthogonal model is unknown at the start of the transformation and will only be specified once the transformation is complete. The model has to satisfy certain conditions, i.e. it should be orthogonal. Findings - The group of non-orthogonal models that contain triangular faces such as tetrahedra or pyramids cannot be successfully recognized using this method. This algorithm fails to transform these types of problem because to do so requires modification of the structure of the model. It appears that only when the edges are divided into pieces and the sharp angles are smoothed then the method can be successfully applied. Even though the method cannot be applied to all geometric models many successful examples for 2D and 3D transformation are presented. Orthogonal models with the same topology, which make them easier to describe, are obtained. Originality/value - This transformation makes it possible to apply simple algorithms to orthogonal models enabling the solution of complex problems usually requiring non-orthogonal models and more complex algorithms.
modelling fuzzy logic geometric planes and solids