Calculation of the Area of the Transformed Object at Polypoint Transformations

Abstract

Modern methods and technologies of geometric modeling allow to reproduce complex processes of interaction in nature, design and monitor complex systems, obtaining possible scenarios for different situations and learning to respond to them.
 This paper considers the possibility of calculating the area of the plot, which is obtained after the polypoint transformations. In the course of polypoint transformations, the result is a set of points that are the object of transformations, such as the edge of a burning forest, or the contour of an oil slick, and so on. Usually, it is important not only to get a visual representation of this object, but also to calculate its area. The display of the object allows you to react quickly to the situation, namely, if it is the edge of a burning forest, you can see exactly where you need to send equipment, use human resources, evacuate residents of potentially dangerous areas. If it is possible to obtain the area of the burning forest edge, you can also calculate the damage from a natural disaster, choose reliable ways to prevent losses - both material and human losses among the population.
 This paper proposes an algorithm for calculating the area based on the obtained points using geolocation, which is relevant in the deformation modeling of real emergencies. It can be used in modeling forest fires, various air and water pollutions, and more. The algorithm calculates the area of geodata using triangulation; it allows to see user-interactions with the system and analyzes the possibility of obtaining reliable data. This paper provides examples of software output. The system can be used to solve problems that arise when modeling with polypoint transformations, as well as when it is necessary to determine the area of an object on a map.