Surface modeling, sunlight reflected from facades

Abstract

There is a large number of complex surfaces of the facades of houses of the 2nd and higher orders. Each surface has its own reflection of sun rays. There is a need for an analysis of these reflections for the detection of zones of concentration of the stream of sun rays, which create zones of overheating, and zones with the diffuse reflection of sun rays. Detection of these zones makes it possible to correct facades at the design stage of a complex form to create a comfortable environment for existing homes and territories and allows to analyze the illumination of opposite buildings. The existing theory of congruence allows us to analyze the reflection of solar rays synthetically from a geometric point of view and to present them analytically. The two-parameter set of normals of the facade surface is layered on the corresponding surfaces of the normals to the main generatrices along the plane section. Relatively to the same generatrices congruence reflected by the surface sun rays is layered on the surface of reflected rays. It is advisable to use the systematization of reflecting surfaces on the principle of surfaces of normals to their generations, which makes it possible to use the surfaces of reflected rays with typical characteristics for certain types of surface of normals. Thanks to this method, quasi-focal lines of the surfaces of reflected rays can be obtained as reflection concentration and, in response, the overheating zone. From the indicated method directly, it is possible to select the shape of the facade surfaces according to the given conditions and to model them on the basis of the known surfaces of the reflected rays. On the basis of the specified analytic algorithm, it is possible to use reflecting surfaces of any complexity, in particular, surfaces of the 2nd order, developable surfaces, channel, transfer surfaces, surfaces of revolution and others, as well as joining surfaces along the lines of main sections. The article considers the modeling of reflected sun rays by means of analytical equations of surfaces of reflected rays. These calculations are necessary for designing facades of new homes, depending on the tasks. Further research is possible for computer visualization of surfaces of reflected sun rays.