Modelling of Components of Building Structures Using Discrete Structures of Computer Science

Abstract

Buildings are essential physical structures which serve several purposes including residential accommodation, factories, hospitals, laboratories, offices, schools, as well as religious places of worship such as church, mosque, shrine etc. A building is an aggregate of components such as roof, window, door and arch. From the perspective of computer graphics, each of these components can be formed from a point and a line. Several models dealing with aspects of building structures have been developed in the literature. Two of the popular generic models are the Tits Building model and the evolutionary computation (bioinformatics) model. While the former uses Discrete Structures of Computer Science (DSCS), specifically, set theory, graph theory and lattice theory, the latter is strictly based on genes derived from nucleotides in DNA Computing. In this paper, a novel DSCS model is presented using the qualitative equivalence behavior of a set of autonomous ordinary differential equations (ODEs). In the model, ODEs of the same kind are classified based on the phase portraits (i.e. geometrical shapes) generated from their equilibrium points. The model successfully presents a good representation of (aspects) of components of buildings, with focus on a door, and can be potentially simulated into computer software.

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