This article presents a new approach to finding possible placements of vector objects on a plane using discrete approximation. The proposed method significantly reduces the computational complexity of the problem by converting vector images into a discrete form represented by a pixel grid. This enables faster intersection checks between objects through the analysis of occupied grid elements, thus simplifying the process of modeling graphic placement. The paper describes an intersection-checking algorithm and its implementation in the form of software that allows testing various placement scenarios. An analysis of the accuracy and speed of the new method compared to traditional approaches is provided. The research results, presented in the form of graphs and tables, illustrate the effectiveness of the discrete approximation. Additionally, the modular design of the software simplifies its integration with existing optimization frameworks. Future work will focus on refining the accuracy of discrete representations and further expanding the method's application in parallel and distributed computing environments. The conclusions highlight the high potential of this method for use in optimal graphic placement tasks, particularly in manufacturing, printing, and computer graphics. The proposed approach lays the groundwork for further research into the application of discrete approximation in complex optimization problems.
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