Some aspects of determining the level of illumination of curved surfaces from point sources

Abstract

As a rule, to determine the level of illumination of surfaces from point sources, a fairly simple regularity (the law of inverse squares) and template rules for constructing incident rays can be used. This regularity is most applicable for surface areas that are fragments of planes (or fragments close to planes). At the same time, when developing the design of the internal or external environment, objects and objects are very often encountered whose surfaces are curved. At the same time, one of the main tasks of designers and architects is to ensure a sufficient level of illumination of interior and exterior items to ensure the reliability of the perception of their shapes and colors, as well as to achieve the necessary level of visual comfort. In the end, due to the high complexity and variety of spatial forms, specialists have to use computer simulation software for calculations related to determining or checking the level of illumination. At the same time, tools involving manual calculations are becoming less and less relevant. In the process of software implementation of mathematical methods and algorithms for determining the level of illumination, it becomes important to eliminate the probability of making design errors associated with the inability of the software to logical thinking and analysis of obstacles to the propagation of light rays. In particular, when it comes to analyzing the nature of surface illumination from a point source (which can be arbitrarily considered almost any lighting device that uniformly scatters light, and whose dimensions are much smaller in comparison with the dimensions of surrounding objects), it turns out that the use of the inverse square law does not allow identify self-shadowing zones during its program implementation in the classical form without imposing additional restrictions. Such restrictions are manifested in the application of a number of logical operators and template algorithms for identifying areas of incidence of its own shadow. To avoid the need to develop appropriate algorithms, this study proposes to modify the notation form of the inverse square law by introducing additional mathematical functions into it. These functions will automatically track the local nature of the change in the angle of inclination of the tangents to the considered points of the illuminated surfaces. The corresponding modification will facilitate the process of software implementation of the process of reproducing the distribution of illumination over a curved surface.