Second-order curves in architectural and building design

Abstract

Straight lines, circles and second-order curves are widely used in architectural and building design as the mainform-making elements. Straight lines are used in the design of gridwork building structures and engineering facilities. Smooth curves composed of the sections of the second-order curves are used to form complex curvilinear wave surfaces. The grid shells of smooth wave curves have become one of the main means for the form-making of avant-garde buildings, including skyscrapers and high-tech buildings. The article deals with the architectural design of the modern airport terminal developed by Samoo Architects & EngineersKorean company.For the geometric analysis weusedan engineering method for designing compound lines formed by the arcs of the second-order curves. It is shown that second-order curves allow us to approximate the curvilinear section of the support profile on the terminal facade. For an unambiguous determination of the support profile, it is sufficient to fix eight points of the profile with tangents indicated in the three of them. The terminal roof surface is formed by the movement of a smooth wave curve of a variable shape along horizontal, parallel to each other, rectilinear guides. The use of second-order curves for the approximation of the undulating roof grade enables to considerably simplify the mathematical description of the roof surface. Approximation algorithms are practically realized by means of computer graphics and specialized software tools.