Method of Setting the Positions of Node Points Determining the Envelopes of Shadows at Different Directions of Solar Rays and Angulation of Buildings

The paper proposes an analytical method for calculating the shadows of buildings and structures for the purpose of using them in the compiling of residential development plans. The method is angles, respectively determining the angle of the sun rays and position of buildings relative of the east-west direction. A graphical interpretation of these dependencies is given. The obtained analytical dependences are used for the automated determination of insolation indices at different positions of buildings and structures. A modification was made for the algorithm of finding the position of residential buildings based on the use of generalized coordinates and the synthesis of small motions, in which the requirements of the insolation regime are met, and the occupied area is minimized. With this method, at each iteration, the mutual position of the envelopes of shadows of buildings and various structures is studied. The paper also presents the results of calculations of the synthesis of moving of buildings with different heights and different sketches on the horizontal projection plane. With this synthesis of movements at each step of the calculations, the occupied area of the residential development decreases with the fulfillment of the insolation requirements.