Algorithm for designing building constructions expressed by nonlinear functions

Abstract

Abstract The aim of the work is to develop an algorithm for designing building constructions, namely their geometric construction (the geometrical location of points) in the form of an expression using the formula (equation) of geometric property of construction expressed in the projection by nonlinear functions. The article gives an algorithm for finding analytical dependencies of nonlinear functions used in applications. You must select a coordinate system before composing the curve equation. The type of the desired equation depends on the choice of the coordinate system. There are no rules that could guide one in choosing a coordinate system, and the ability to make the most rational choice is given only by experience. In this paper, the examples of the choice of coordinate systems show the form of functions, namely, their simplification. In some cases, geometric construction is the only way to present a graphic image of the building structure itself, no matter how complex it may be in the Cartesian coordinate system. The polar coordinate system is presented here as an alternative for unique structures and structures of increased complexity in the Cartesian coordinate system. This is achieved by establishing a relationship between the current coordinates of the point located on the projection of the construction and constants characterizing the properties of this construction, called a function on the plane and a surface in space in researches. The prospect of this approach has proven itself: in the construction of exquisite palace temples, beautiful architectural ensembles that make the space surrounding a person comfortable.