8adjacency

8adjacency refers to a concept used in grid-based systems, particularly in computer graphics, image processing, and game development, to define the neighbors of a given cell or pixel. In an 8-adjacency scheme, a cell is considered adjacent to all eight surrounding cells, including those diagonally positioned. This is in contrast to 4-adjacency, where only the cells directly above, below, left, and right are considered neighbors.

To illustrate, consider a central cell at coordinates (x, y). In an 8-adjacency model, its neighbors would be located at the following coordinates: (x-1, y-1), (x-1, y), (x-1, y+1), (x, y-1), (x, y+1), (x+1, y-1), (x+1, y), and (x+1, y+1). This inclusive definition means that a cell has a total of eight potential neighbors.

The choice between 4-adjacency and 8-adjacency depends on the specific application. 8-adjacency is often used when diagonal connections are important, such as in pathfinding algorithms where movement can occur in any of the eight directions, or in certain image filtering operations where the influence of surrounding pixels should include diagonal ones. Algorithms like Breadth-First Search (BFS) or Depth-First Search (DFS) can be implemented using either adjacency model to explore connected components or find paths within a grid. The computational cost can slightly differ, with 8-adjacency involving more checks per cell.