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_Geometric method of flood zones calculating_ Abstract This paper proposes a solution for calculating flood zones using triangulated irregular network analysis. The suggested approach can be used for visual estimation of surface models and solving some design problems. Keywords: Flood zone, triangulated irregular network, computational geometry, GIS, CAD, drainage system Introduction Currently, many software solutions exist for automated civil, industrial and transportation construction projects. However, designers still perform certain tasks manually as no satisfactory solution has been proposed for all of them. For example, designing drainage systems involves visually assessing the slope directions on a surface model since practical algorithms for automatically constructing flood zones have not yet been developed. We define the problem of calculating flood zones. Definition: The task of calculating flood zones over a certain surface area is to find the set of regions where water accumulations will form after a given amount of precipitation. Determining flood zones is particularly relevant in GIS and CAD as it enhances the visual representation of terrain models, justifies the need for constructing stormwater drainage systems in specific areas, and clearly demonstrates errors during design processes. Review of Existing Methods for Calculating Flood Zones Currently, two main approaches are used to solve the problem of calculating flood zones worldwide. 1. Hydrological approach - applied at a macro level for territories with an area of tens or hundreds of square kilometers. 2. Hydrodynamic approach - used for modeling water behavior on a micro level and requires powerful hardware support for simulating very small water flows. Note that accurate solutions to the problem of calculating flood zones require considering numerous factors such as soil permeability, groundwater presence, air temperature, etc., which can only be solved using hydrodynamic approaches. However, in practice, approximate geometric approaches are sufficient for designing geo-objects. The author proposes a new algorithm for calculating flood zones suitable for GIS and CAD systems in civil, industrial and transportation construction projects. Algorithm of Calculating Flood Zones Based on Geometric Approach The proposed algorithm is based on analyzing the triangulated irregular network (TIN) surface. TIN can be loosely defined as a triangulation where each node has its Z-coordinate assigned to it. Using "Nodes, simple edges, and triangles" structure for representing the surface allows significantly increasing the speed of algorithms used in this approach. Algorithm Steps: 1. Find all "break lines" - edges of TIN where slope exposure changes direction (Fig. 1, 2a). 2. For each break line find node with minimal Z-coordinate (h). Then construct contour at level h – geometric place of points on the surface having height h and lower heights in any neighborhood (Fig. 2b). This models water filling up to level h. The flood zone boundary will correspond to part of this contour passing through a break line. If constructed contour consists of several contours, discard those not related to current break line. Thus, we consider only some local surface area where a flood zone may form. Check if contours contain boundary nodes with lower heights within them. If yes, water will overflow the surface boundaries; thus, no flood zone at level h exists. Otherwise, assume that the flood zone is found and add it to the list of flood zones. Step 3: Construct connectivity tree for all found flood zones. If one flood zone fully includes another (Fig. 2v), consider larger contour as parent and smaller as child. Step 4: For each flood zone construct a catchment area – list of triangles from which water will flow into the corresponding flood zone. Step 5: Calculate volume of water for each catchment area by formula \( V_i = S_i \cdot V \) where \( S_i \) is the area of the corresponding catchment area. Step 6: For each flood zone starting with leaves in the connectivity tree, check if it overflows. If overflow occurs, proceed to Step 7. Otherwise, use bisection method to find water level corresponding to required volume (limiting iterations up to 10). Construct contour on surface within corresponding flood zone at found level. Step 7: Calculate overflow of water as follows: If the checked catchment area has a parent, no overflow occurs; water simply rises higher in the parent flood zone. Thus, check the parent flood zone for overflow. Otherwise, find nodes through which the flood zone contour passes and distribute overflowed volume to adjacent catchment areas proportionally to triangle modeling flow into corresponding catchment (Fig. 3). Note that some water will also spill off the surface. Water Overflow S Fig. 3. Triangle proportional to which additional water volume is calculated for corresponding catchment area This procedure continues until all flood zones have overflowed. After this, add contours of processed parent flood zones at maximum fill level to the list of flood zones. End algorithm. The algorithm's complexity is \( O(N^2C) \), where N – number of nodes in TIN and C – number of break lines. Complexity includes contour construction procedure with complexity \( O(N) \) repeated for all break lines, i.e., C times. Conclusion This work proposes an algorithm for calculating flood zones applicable to automated design systems for civil, industrial, and transportation projects. The distinctive feature of this algorithm compared to known ones is the use of a geometric approach to solving the problem of calculating flood zones. However, the proposed algorithm uses only terrain models without considering wells or drainage pipes on the ground. Therefore, further modification will be aimed at more accurate modeling of water drainage systems. References 1. Kovalenko V.V., Modeling hydrological processes. St. Petersburg: Hydrometeoizdat, 1993 – 250 p. 2. Rouch P., Computational hydrodynamics. Moscow: Mir, 1980 – 616 p. 3. Skvortsov A.V., Delaunay triangulation and its applications. Tomsk: Tomsk University Press, 2002. – 128 p. Author Natalia Mirza PhD at Tomsk State University Department of Computer Science. 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