Textile hybrid: based on isolated bent compression members Master ´ s degree in Parametric Design in Architecture
6.2. TOROIDAL VAULT
A vault is a typology of roof-enclosure very common in architecture. From ancient times until now it is still being considered a suitable shape for larger span structures. It possess qualities of spaciousness, lightweight and structural efficiency. This document deal with toroidal vault as a way to show that is possible create complex enclosures which belongs to this architectural shape.
6.2.1. DOUBLE CURVATURE SURFACES AND TOPOLOGICAL ASPECTS
6.2.1.1 GAUSSIAN CURVATURE
Gaussian curvature means that is the product of the principal curvatures of the surface in a determine point. Gaussian curvature is an intrinsic measure of curvature. When the Gaussian curvature has constant zero, is a developable surface or planar surface. When is positive the surface is synclasic, for example a sphere. When it is negative the surface in anticlastic, for example the hypar.
6.2.1.2 EULER-POINCARÉ CHARACTERISTIC
The Euler characteristic is a topological invariant that describes a structure regardless of the way it is bent. The schematic models develop by Euler are useful to define methodologies in order to get a topology. This models stand for concisely their applicability to discretize a toroidal surface.
6.2.1.3 TOPOLOGICAL ASPECTS
It will be presented many ways to implement a discrete topology on a torus surface. The most advanced academic field in the matter of toroidal topology is the chemistry and its studies in carbon nanotubes geometrical properties. Due to their functional and energetical features, the topology of this molecular structures offer some optimal approaches to develop a torus shape structure.
Figure C10: graphical gaussian curvature explanation.
Topologically, a torus can be considered as an object ing genus one and possessing one single hole. Every suit-able geometrical model for a molecular torus has to possess some radial array symmetry.
Figure C11: Euler-Poincaré characteristic’ s schematic explanations.
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