Methodological principles of geometric modeling of fortification structures: shape, spatial structures, and planning organization

Abstract

The article examines the methodological principles of geometric modeling of fortification structures, in which the shape, spatial structure, and planning organization of positions are considered as an interconnected system of design decision-making. The relevance of the study is determined by the need for rapid and efficient design of fortification positions under complex natural and resource conditions, where the geometric parameters of structures directly influence their functionality, survivability, movement logistics, and energy consumption during construction and operation. The aim of the study is to develop a comprehensive methodology for the geometric modeling of fortification structures that integrates methods of applied geometry, geographic information systems, and building information modeling. The proposed approach is based on a multi-level spatial organization that includes the micro level (local geometric parameters of form), the meso level (nodes and spatial connections between elements), and the macro level (the planning organization of the network of communication passages and functional zones). The study proposes a geometric-topological model of a fortification position, which is considered as a network of nodes and connections within a specific terrain. To form the optimal configuration of the position, geographic information system data on terrain, hydrological conditions, existing infrastructure, and restricted areas are used. The modeling algorithm includes the construction of a topological scheme of the position, parameterization of the geometric characteristics of its elements, verification of compliance with regulatory and technological constraints, and evaluation of operational indicators such as the length of movement routes, network capacity, and volumes of earthworks. The practical significance of the study lies in the possibility of reducing the time required for preparing design solutions, decreasing excessive earthworks, and optimizing movement logistics within the fortification position. The proposed approach improves the efficiency of planning fortification facilities, ensures better adaptation to specific terrain conditions, and reduces material and energy costs during construction and operation. The obtained results can be applied in the design of fortification systems, planning of defensive positions, and development of information systems for supporting engineering decision-making in the field of construction.