«Architecton: proceedings of higher education» № 37 March 2012

Theory of architecture

Babich Vladimir N.C.Sc. (Technology), Professor, | |

Kremlev Alexander G.D.Sc. (Physics and Mathematics), Professor, Chair of Multimedia Technologies, |

# IT-BASED MATHEMATICAL MODELLING FOR ADDRESSING ARCHITECTURE AND TOWN-PLANNING CHALLENGES

Contemporary architecture and town-planning practice is characterised by broad use of mathematical modelling methods for simulating social, economic, technological and other processes and objects in a city environment, supported by massive high-quality information (based on wide and multilevel use of computer facilities, software and hardware).

IT-based mathematical modelling includes relevant data gathering, data processing (data management or structuring), data transformation algorithm (encapsulation), development of a mathematical model, model geometrisation (computer visualisation), and geometric constructions (transformations).

Any mathematical model is some sort of abstraction reflecting chosen essential properties of objects or processes under consideration. The selection and formalisation procedure provides a mathematical description of the phenomenon, i.e. its mathematical model which can be further investigated by mathematical methods. The use of mathematical models and modelling results takes place on the basis of their interpretation in real contexts. Their use will be justified and effective if the model is sufficiently adequate and mathematical results may be practically implemented. To understand a certain phenomenon (on the basis of its mathematical description) mathematics develops, like any usual language does, metaphors (figurative representations) making it possible to explain this phenomenon by associating it with another phenomenon which is more habitual or perceived as such.

Along with mathematical methods, use is made of information (computer) technologies for problem solving, computing experiments are performed, and the mathematical model is numerically processed. Particularly noteworthy are the capabilities of contemporary information technologies and software for processing spatial information and constructing digital 3D models. Geometrisation of town-planning (architectural) projects involves the use of geometric modelling methods enabling professionals to visualise objects under investigation or, more precisely, their models.

**Key words**: IT-based mathematical modelling, algorithm, systems analysis

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