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  • Author or Editor: Béla Iványi x
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The main objective of this paper is to classify the techniques of parametric design, and to make the existing classification system more exact. The previously created classification was based on shape and logical aspects, which granted a good approach for parametric design techniques and helped providing an overview. However this system, for the sake of scientific precision, needed further darification at points. In this paper a more precise classification is shown, which is based on the interpretation of patterns as graphs. This enables their topology to be studied in a more exact, mathematical way.

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This paper describes the adaptation of the formex configuration processing to the computer program Grasshopper 3D and focuses on the applied mathematical solutions. Formex algebra is a mathematical system, primarily used for planning structural systems like truss-grid domes and vaults, together with the programming language Formian. The goal of the research is to allow architects to plan truss-grid structures easily with parametric design tools based on the versatile formex algebra mathematical system. To produce regular structures, coordinate system transformations are used. Owing to the abilities of the parametric design software, it is possible to apply further modifications on the structures and gain special forms. The paper covers the basic dome types, and it introduces additional dome-based structures using special coordinate-system solutions based on a spherical coordinate system, vault structures and their modifications based on a cylindrical coordinate system and circular structures and their modifications based on polar coordinates. Moreover two rotational grid tools are introduced, which uses coordinate system transformations on a unique way to create surfaces of revolutions based on the given generating curve and create grid structures on these surfaces. It also describes the solution technique to implement the triangular grid version of every one of these tools based on diamatic domes. The adaptation of formex algebra and the parametric workflow of Grasshopper together give the possibility of quick and easy design and optimization of special truss-grid domes.

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