The authors redefine and generalize the so-called relative ratio of compactness of solid with respect to sphere and cube introduced by Mahdavi and Gurtekin. The authors propose such new indicators as a relative ratio of solid compactness in the shape of a prism-shaped solid related to a cuboid with a square base and a given height (e.g. the height of the analyzed storey), a solid compactness indicator defined for the basis of the prism relative to the square. They introduce also other indicators: a relative defect of the perimeter and area. The test of indicators formulated and described in the paper was carried out in two groups of buildings: existing (spotted locally) and those whose designs can be found in the selected catalog available on the website. In addition to the compactness ratios calculated for existing and designed buildings, an analysis of the size of the indicators for the adopted building research models was made. Proposed indicators allow for a description of the compactness of the building model with an indication of the deviation from the real ideal solid. The introduced geometric determinants of solids may be useful in the initial phase of searching for satisfactory design solutions.
Many factors affect energy demand, and knowing their impact is very important for being able to design a low-energy building. In this group of factors, there are those that cannot be changed and improved after the building is constructed, so taking them into account when choosing a project is important for energy savings. This group includes geometric parameters. We propose a geometric method of assessing the energy demand of a single-family house. The idea is to predict the level of energy demand by calculating the values of simple geometric parameters in the first stage of design. Based on the analysis of 30 realistically designed single-family houses, we show that the geometric indicators expressed by the base area Af, and perimeter P at a fixed building wall height h, perfectly characterize the amount of energy, both usable and final. Moreover, we show linear relationships between the nominated A/V and non-nominated EWA/FA, RCcd compactness ratios. This relationship allows one indicator to be measured with another. As a result, we show how a designer can use a simple calculated index RCcd to find out the level of energy demand.
The application of geometry of roofs (straight skeletons) and, related to that, Voronoi diagrams for polygons to solve optimization tasks such as determination of the routes of surveys of regions with minimal static moments with respect to the sides of polygons is discussed. A special interpretation of the notion of static moment with respect to the segment of line and a polygon with respect to the border is explained and an appropriate theorem is formulated and proved. Examples of potential employment of these notions have been indicated.
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