The use of Weber’s focal-directorial plane curves as approximation of top view contour curves at architectural buildings objects

Abstract

One of the major aims when researching some problems in architectural design of buildings is to fully understand and adequately apply the underlying scientific foundations that architects use in their projects. In this paper we analyze the application possibilities of the Weber's focal-directorial curves in the approximation of ground-base contour line of architectural objects i.e. buildings. Thus, a Weber's curve with m foci and n directrices was defined. Furthermore, particular qualifiers were introduced in order to estimate the level of adequacy of the conducted approximation. The importance of the research can be sought in the fact that the exact procedure has been created with its applicability in architectural-urban design of contemporary forms as well as in the domain of the historical heritage and conservation in the sense of the creating proper geometrical models for further computer aided use.

A Focal Curve Approximation of a Borromini Oval Contour

“…The starting point of the approximation method is finding algebraic curves which can approximate the curvilinear shape of structures. In the research of González et al (2018), Huylebrouck (2007), Petrović et al (2016Petrović et al ( , 2018 and Samper et al (2017), specific algebraic curves were analysed for such a purpose. Herewith, the Weberian curves with two, three and four collinear foci are investigated as a possible solution for the approximation (Fig.…”

“…The second class of investigations underlines the following question: what geometric shape, that is, curve, best fits the contour of particular architectural object either as the whole or one of its components. This problem has been treated by multiple authors including González et al (2018), Samper et al (2017), Petrović et al (2016Petrović et al ( , 2018 and Huylebrouck (2007). In the research of Samper et al (2017), the comparison of the types of conics and hyperbolic-cosine curves in the approximation of Gaudi's geometric forms has been carried out.…”

“…Huylebrouck, expressing doubts that a naked eye can determine the difference between visually similar curves or is able to recognize certain proportions in paintings, suggested using the application of "the least squares method, developed in celestial mechanics and since applied in various fields, to art and architecture, especially since modern software makes computational difficulties non-existent" (2007: 59). The research of Petrović et al (2018) successfully derived a Weberian focaldirectorial curve that best fits the contour of the Dorton Arena floor plan as well as the contour of the Great Hall of the Textile Fair floor plan in Leskovac, Serbia.…”