In this study, we refer to the the mathematical theory behind convex polygons, the general procedure for constructing them using a given primitive triangle algorithm, and describe the process of visualizing them in a computational environment with only mathematical o�perations.
Initially, we present the mathematical foundations concerning convex polygons, including their properties, angles, and edges. We then examine the fundamental mathematical operations related to convex polygons, such as computing their area and convex hull, as well as calculating the linear functions of their edges for all pixel elements within their bounding boxes. In the second part of the study, we focus on the visualization of arbitrary convex polygons in a computational environment using OpenGL. Additionally, we provide code examples and implement algorithms for rasterization and area analysis.
Finally, we present the results of the tests conducted to evaluate the performance of the proposed system. We assess the speed and accuracy of the computations in various sce�narios and polygon sizes. The results demonstrate that the system provides efficient and accurate visualization of convex polygons using the OpenGL library.