We consider the problem of finding a geometrical form of a body in a thermal radiation field, for which the thermal balance between the body and the surrounding air is minimal. The case of a point source of heat is investigated. To consider an analogous problem for buildings, one must know the value of incoming thermal energy to a unit square in relation to its orientation. We develop an application package in MATLAB that represents this relation in table form and takes into consideration the direct, diffuse, ground-reflected solar radiation and the thermal radiation of atmosphere.

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Natural lighting systems are important for the energy efficiency of the buildings. Thus the size of light openings should be optimized to provide visual comfort and decrease the energy needed to provide comfort in the environment. There exist tools to calculate solar energy gain in the buildings of mass construction with enclosing structures in the shape of horizontal and vertical planes. For structures with curvilinear surfaces systems of equations are compiled, to be solved by numerical methods with significant use of computer time. The article proposes a method of simulation solar energy gain for non-standard enclosing structures for buildings surrounded by existing housing using an apparatus of Balyuba-Naidysh point calculation (BN-calculus). Apparatus of BN-calculus allows forming of a point set optimized to match the shape of a geometrical object. Received point set is used to form elementary solid angles within which energy inflows from direct, scattered and reflected solar radiation into computational points are calculated. The sum of elementary values of energy inflows defines the total value of energy gain of the room.

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