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PDF papers
id 5cf4
authors Barrionuevo, Luis F.
year 2004
source Proceedings of the Fourth International Conference of Mathematics & Design, Special Edition of the Journal of Mathematics & Design, Volume 4, No.1, pp. 179-187.
summary This paper deals with “Spirospaces”. These are a conversion to the third dimension of the two dimensional geometric entities called “Spirolaterals”.

Abelson, Harold, diSessa and Andera (1968) gave the first rules concerning Spirolaterals. To obtain a Spirolateral from a set of straight lines, the first of them must be one unit long and the following must be incremented one unit at each step, at the same time that they turn in a constant direction. Odds (1973) establish the variation of the rotation direction, either to the left or the right. However, he did not give a mathematical relation able to calculate open Spirolaterals. Krawczyk (2001) developed a computer program that generates Spirolaterals following the method suggested by Abelson. These are Spirolaterals obtained by enumeration without a predictive mathematical formula. Krawczyc went farther proposing Spirolaterals based in curved lines. He pointed out that there are a variety of spirolateral forms that have architectural potentiality. Following this, the architectural potentiality of Spirolaterals is the basis of this paper.

To take advantage of that potentiality a computer program was implemented to generate spatial configurations based in Spirolaterals. When a third dimension is given to the Spirolaterals they become Spirospaces. These new entities need spatial and design parameters to be useful for architectural purposes. Barrionuevo and Borsetti (2001) gave results about that work establishing the concept of Spirospaces.

The aim of this paper is to describe a work directed to improve rules and procedures concerning Spirospaces. It is expected that these procedures governed by the proposed rules can be employed as tools during the early steps in the architectural design process.

In this work some aspects concerning Spirospaces are considered. First, Spirolaterals are presented as the predecessors of Spirospaces. Second, Spirospaces are defined, together with their structural parameters. Architectural modeling is studied at the light of two special elements of the Spirospaces: Interstitial spaces and Object spaces. Next, a computer program is presented as the appropriate tool to model configurations having architectural potentiality. Finally, the results obtained running the computer program are analyzed to determine their possible use as architectural forms. Several graphic illustrations are presented showing steps going from the exploration of spatial alternatives to the selection of a specific configuration to be developed.

It is expected that the described computer program could be employed as a design aid tool. As the operation of the program generates a variety of spaces able to dwell architectural objects, it eases the search of configurations suitable to specific functions. The results obtained have the possibility of being exported to computer graphic applications able to add materials, lights and cameras.

keywords Spirolaterals, Spirospaces, architectural spaces, interstitial spaces, objectual spaces
series other
type normal paper
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