A Computer Algorithm for the Generation of Three Dimensional Acoustical Forms: Application to an Investigation of the Acoustics of a Fan Shaped Auditorium

Abstract

An examination of techniques employed for the computer modeling of building forms reveals that a basic approach is to construct 3D shapes by the assembly of individual planar elements, each of which is defined by a sequence of nodes. The geometric forms of auditoria are analysed and it is shown that the majority can be categorized in terms of a limited number of basic plan forms and cross sections. It is proposed that most of these basic categories can be collapsed to yield a single generic plan form and a single generic cross section that can be simply defined in terms of a number of node co-ordinates. An algorithm is developed for the rapid generation of 3D models of auditoria from the input of a limited number of dimensions related to the generic plan and sections identified in the earlier part of the paper. A number of models generated using this technique have been employed to investigate the effectiveness of stepped walls in general purpose auditoria with a wide fan shaped plan. The results obtained suggest that although the use of stepped walls is very effective in ensuring strong lateral reflections they tend to negate the beneficial effects that the use of the simple plan form brings to rooms intended for speech.