Developing a Procedure to Transfer Geometrical Constraints from the Plane into Space

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Knoll, Eva
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International Society for Geometry and Graphics
Topology teaches us that the two dimensional plane and three dimensional space have a comparable structure. In fact, this apparent parallel is deeply rooted in our consciousness and is applied in many domains, including various fields in the design industry, through the use of such tools as descriptive geometry and perspective drawing. From the particular point of view of the designer, however, this parallel in structure has often been simplified to plans, sections and elevations i.e. 2-D slices through a 3-D object. It has therefore not been an integral part of the design process, but rather a tool of representation of the design process. In the following paper, the relationship between plane and space will be explored as a design element. The question will be answered whether it is possible, starting with a 2-dimensional system of design parameters, to construct a 3-dimensional object based on the spatial equivalents of the initial parameters. To illustrate this process, the painting Opus 84 of Hans Hinterreiter (1902-1992), a Swiss Concrete painter, will be re-interpreted in space.
Hinterreiter, Hans , Constructivism , Geometry , Dimensions , Design
Knoll, E. (1998). Developing a Procedure to Transfer Geometrical Constraints from the Plane into Space. In Proceedings of the 8th International Conference on Engineering Computer Graphics and Descriptive Geometry, 1, pp. 63-67.