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Architectural Applications of Several 3D Geometric Transformations

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This Demonstration considers the following surfaces: ellipsoid, hyperboloid of one sheet, elliptic paraboloid, hyperbolic paraboloid, helicoid, and Möbius strip, which can be represented by parametric equations of the general form . These surfaces can undergo further transformations, including rotation, translation, helical motion, and ruling.

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To illustrate the application of these methods in architecture, sketches of real-world examples are displayed, as well as maps showing their locations.

This Demonstration shows a set of six structures: their animated transformation in 3D, one or two matching sketches of a building, and a map for each of the six 3D surfaces. Short descriptions or legends for each graphic are given.

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Contributed by: Guenther Gsaller (February 2016)
Open content licensed under CC BY-NC-SA

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