FALLAVOLLITA, Federico.
'Le superfici rigate'
In MIGLIARI, Riccardo. Geometria Descrittiva. vol. 2. pp.153-224
CittàStudiEdizioni, De Agostini Scuola Spa, 2009. ISBN 978-88-251-7330-7
Abstract
In this second volume of Descriptive Geometry, the methods and the constructions, explained in the first volume, are applied to the study of the shapes that most frequently recur in engineering projects and in architectural and design projects. These shapes may be abstract, like the plane and the twisted curves, the surfaces and the polyhedrons, or, on the contrary, they may be formal and technical solutions that the applications of descriptive geometry traditionally offer to the art of constructing, and they refer to: the arcs and the vaults, the roofs, the stone and wood cutting. The relative constructions, be they of abstract or concrete shapes, are shown, mostly, using digital representation methods, since these methods unite the power of the analogical representation, visual, to the accuracy of the calculation and they allow, thus, an agile and clear solution of the problems dealt with. It seemed therefore right to open the volume with two chapters on the techniques of the mathematical and numerical representation that describe, with a speech of a general nature, that is, without referring to a specific software, those useful hints and solutions that may help to obtain the best quality of the model. The volume closes with analogous considerations that concern the modern theory of chiaroscuro, namely the rendering. Federico Fallavollita wrote parts of the chapter of the surfaces and vaults. In particular, wrote the chapter on ruled and developable surfaces. Here to follow the index of the chapter on ruled surfaces: 2.3 The ruled surfaces - 2.3.1 The construction of a ruled generic surface, p. 154 - 2.3.2 The quadrics, ruled surfaces, p. 161 - 2.3.3 Cones and cylinders quadrics, p.162 - 2.3.4 One-Sheeted Hyperboloid, p. 168 - 2.3.5 Hyperbolic paraboloid, p. 175 - 2.3.6 Equilateral hyperbolic paraboloid, p. 182 - 2.3.7 Genesis of projective quadrics, ruled surfaces, p. 185 - 2.3.8 Some properties of projective quadrics, p. 188 - 2.3.9 The polar system with respect to a quadric, p. 195 - 2.3.10 The center, the diameters and the axes of a quadric, p. 198 - 2.3.11 The stereographic projection of a hyperboloid, p. 201 - 2.3.12 Graphics Properties and metric properties of ruled surfaces, p. 203 - 2.3.13 Developable surfaces, p. 213 - 2.3.14 Special cases of developable surfaces: cylinders and cones, p. 219 - 2.3.15 Development of the cone and the cylinder on a plane, p. 220
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