Geometria delle linee curve per la genesi della forma

Knowledge of the geometry of curves assumed and still today assumes a leading role in the design of shape. The arts and applied sciences use this theory for the construction of products that require a certain level of geometric accuracy. In general terms, we can affirm that the quality of the surfaces composing an architectural or designed shape depends on the quality of the lines to which these surfaces belong. Thus, the theory of lines, and therefore knowledge of their properties, becomes crucial for a correct design of shape, both through analogical as well as digital drawing. In the history of the architecture and design project, some remarkable properties of lines and surfaces strongly conditioned their success. Thus, particular classes of lines and surfaces affirmed themselves in the practice of design; in fact, some of their properties made them particularly suitable to be controlled through the drawing, in the design phase, and to be reproduced on site, in the construction phase. This short essay aims to explain the relationships between these properties and the design of shape. The properties that directly influence the geometric control of designed surfaces are analyzed, illustrating, finally, the application of some notable classes of curves, selected as they all belong to recurrent surfaces in architecture and design.