In this paper, the systems of real estate mass appraisal in some selected European countries will be discussed, in comparison with those of individual countries on other continents, in terms of similarities and differences in law, institutional scope and subjects responsible for its execution. With selected countries serving as an example, the practical aspects of operating the real estate owners’ taxation system will be discussed as well the data acquiring process, considered price-making factors, proceeding methodology and circumstances taken into account in real estate cadastral valuation, giving consideration to national specificity.

Determining the weights of market features of real estate in explaining their prices is one of the basic objectives of market analysis, performed as part of the property value estimation process. In practice, property appraisers usually settle for basic methods of determining weights, for example based on the principle of ceteris paribus or on the basis of linear correlation coefficients. The article proposes the use of curvilinear correlation coefficients for this purpose; an attempt of such use was made and the obtained results were compared with the weights determined on the basis of linear correlations. The conducted analyses proved that the inclusion of curvilinear correlations at the stage of market analysis, allows for extracting a greater number of features recognized as price-creating, i.e. leads to a smaller loss of market information and is a more reliable tool for determining the weights of attributes in price explanation.

The key goal of the market analysis carried out for property valuation purposes is to select pricing attributes of real properties and to assign so-called weights to them, which would illustrate their influence on the prices in a given market (Regulation 2004). Correlation analysis is a very useful tool in this respect. However, the fact that it is limited to the use of classical Pearson’s linear correlation coefficients is too much of a simplification due to the frequently occurring heterogeneity of the real estate market. The research paper proposes to use the possibilities offered by the broadly understood correlation analysis which, among linear correlations, takes into account not only Pearson’s correlation but also rank correlations. At the same time, analyses of various non-linear correlations are being carried out where linear relationships are not reliable enough. The aim of this research is the simultaneous verification of the existence of various types of correlative relationships, taking into account the nature of random variables that the analyses relate to, and the nature of relationships between them. This approach makes it possible to adjust the weighting of market attributes, the values of which are improved in a few subsequent steps, in order to eventually approach the optimal result as close as possible.

One of the key elements in real estate appraisal of residential buildings is the usable area. To determine the monetary value of real estate, appraisers in Poland often rely on transaction data registered in the Real Estate Price Register (REPR). However, the REPR may contain meaningful gaps, particularly on information concerning usable areas. This may lead to difficulties in finding suitable comparative properties, resulting in mispricing of the property. To address this problem, we used linear and nonlinear models to estimate the usable area of buildings with multi-pitched roofs. Utilizing widely available data from the Topographic Objects Database (BDOT10k) based on LiDAR technology, we have shown that three parameters (building’s covered area, building’s height, and optionally the number of storeys) are sufficient for a reliable estimate of the usable area of a building. The best linear model, using design data from architectural offices, achieved a fit of 95%, while the best model based on real data of existing buildings in the city of Koszalin, Poland achieved 92% fit. The best nonlinear model achieved slightly better results than the linear model in the case of design data (better fit by approximately 0.2%). In the case of existing buildings in Koszalin, the best fit was at 93%. The proposed method may help property appraisers determine a more accurate estimation of the usable area of comparative buildings in the absence of this information in the REPR.

The development of generalisation (simplification) methods for the geometry of features in digital cartography in most cases involves the improvement of existing algorithms without their validation with respect to the similarity of feature geometry before and after the process. It also consists of the assessment of results from the algorithms, i.e., characteristics that are indispensable for automatic generalisation. The preparation of a fully automatic generalisation for spatial data requires certain standards, as well as unique and verifiable algorithms for particular groups of features. This enables cartographers to draw features from these databases to be used directly on the maps. As a result, collected data and their generalised unique counterparts at various scales should constitute standardised sets, as well as their updating procedures. This paper proposes a solution which consists in contractive self-mapping (contractor for scale s = 1) that fulfils the assumptions of the Banach fixed-point theorem. The method of generalisation of feature geometry that uses the contractive self-mapping approach is well justified due to the fact that a single update of source data can be applied to all scales simultaneously. Feature data at every scale s < 1 are generalised through contractive mapping, which leads to a unique solution. Further generalisation of the feature is carried out on larger scale spatial data (not necessarily source data), which reduces the time and cost of the new elaboration. The main part of this article is the theoretical presentation of objectifying the complex process of the generalisation of the geometry of a feature. The use of the inherent characteristics of metric spaces, narrowing mappings, Lipschitz and Cauchy conditions, Salishchev measures, and Banach theorems ensure the uniqueness of the generalisation process. Their application to generalisation makes this process objective, as it ensures that there is a single solution for portraying the generalised features at each scale. The present study is dedicated to researchers concerned with the theory of cartography.

At the beginning of this article, it was shown that the indicators of the current so-called social distance determined by decision-makers at various stages of the epidemic development are imprecise, do not sufficiently take into account spatial relations, are unclear in public perception, and do not contain specific practical solutions. Therefore, this study undertakes the task of giving the term “social distancing” precise features, defined on the basis of geometry, and providing solutions in typical cases of the living space of the population. The geometry of the distribution of people in various situations of everyday life was considered: people standing during concerts or religious ceremonies, sitting during meals in collective catering rooms and participating in lectures, cultural, entertainment or sports events. In the latter group of tasks, the concept of building a people-distribution scheme must be adapted to the existing, arbitrary grid of real places of a lecture hall, theater hall, cinema, or stadium. The article contains some practical examples with comments and an evaluation of benefits, both in terms of ensuring safety and in terms of effective use of space.