This paper presents a new algorithm for solving the hidden surface (or line) problem to generate realistic images of 3-D scenes composed of polygons more efficiently. The algorithm preprocesses the environment's database to create a "binary space partitioning" (BSP) tree, which allows for faster visibility determination during image generation. The tree is constructed by recursively splitting polygons based on their planes, resulting in a structure that can be traversed to determine visibility priorities. These priorities are assigned such that the polygon closest to the viewing position has the highest priority, enabling efficient determination of visible surfaces. The algorithm is particularly effective for static environments where only the viewing position changes, as is common in simulations. The preprocessing phase involves creating a BSP tree that can be used to quickly determine which polygons are visible at each pixel during image generation. This approach reduces the computational effort required during image generation by leveraging the static nature of the environment. The paper also discusses the theoretical foundations of the algorithm, including the properties of BSP trees and their use in generating visibility priorities. It describes the construction of the BSP tree, the traversal process to determine visibility priorities, and the application of the tree in image generation. The algorithm is designed to handle both 2-D and 3-D environments, with the 3-D case being of particular interest. The paper also addresses the combinatorial aspects of BSP trees, including the maximum number of regions that can be created by a given number of planes or polygons. It provides formulas for calculating the maximum number of regions in 2-D and 3-D spaces, which are important for understanding the efficiency and scalability of the algorithm. The algorithm is implemented using a recursive procedure that constructs the BSP tree and then traverses it to determine visibility priorities. The traversal order is chosen to ensure that the polygon closest to the viewing position is processed first, allowing for efficient determination of visible surfaces. The paper also discusses the limitations of the algorithm, including the potential increase in the number of polygons in the BSP tree compared to the original database, but notes that this has not been observed in practical applications so far. Overall, the algorithm provides an efficient solution to the hidden surface problem, particularly for static environments, by leveraging the structure of the BSP tree to reduce computational effort during image generation.This paper presents a new algorithm for solving the hidden surface (or line) problem to generate realistic images of 3-D scenes composed of polygons more efficiently. The algorithm preprocesses the environment's database to create a "binary space partitioning" (BSP) tree, which allows for faster visibility determination during image generation. The tree is constructed by recursively splitting polygons based on their planes, resulting in a structure that can be traversed to determine visibility priorities. These priorities are assigned such that the polygon closest to the viewing position has the highest priority, enabling efficient determination of visible surfaces. The algorithm is particularly effective for static environments where only the viewing position changes, as is common in simulations. The preprocessing phase involves creating a BSP tree that can be used to quickly determine which polygons are visible at each pixel during image generation. This approach reduces the computational effort required during image generation by leveraging the static nature of the environment. The paper also discusses the theoretical foundations of the algorithm, including the properties of BSP trees and their use in generating visibility priorities. It describes the construction of the BSP tree, the traversal process to determine visibility priorities, and the application of the tree in image generation. The algorithm is designed to handle both 2-D and 3-D environments, with the 3-D case being of particular interest. The paper also addresses the combinatorial aspects of BSP trees, including the maximum number of regions that can be created by a given number of planes or polygons. It provides formulas for calculating the maximum number of regions in 2-D and 3-D spaces, which are important for understanding the efficiency and scalability of the algorithm. The algorithm is implemented using a recursive procedure that constructs the BSP tree and then traverses it to determine visibility priorities. The traversal order is chosen to ensure that the polygon closest to the viewing position is processed first, allowing for efficient determination of visible surfaces. The paper also discusses the limitations of the algorithm, including the potential increase in the number of polygons in the BSP tree compared to the original database, but notes that this has not been observed in practical applications so far. Overall, the algorithm provides an efficient solution to the hidden surface problem, particularly for static environments, by leveraging the structure of the BSP tree to reduce computational effort during image generation.