Explain area sub-division algorithm for hidden surface removal

Area sub-division, also known as spatial division, is a type of hidden surface removal algorithm used in computer graphics to determine which surfaces and parts of surfaces are visible from a certain viewpoint. Here's a step-by-step explanation of how it works:

1. Scene Division: The algorithm starts by dividing the entire scene into smaller areas or sub-areas. This can be done using a variety of methods, such as quadtree, octree, or BSP (Binary Space Partitioning) tree structures.

2. Visibility Determination: For each sub-area, the algorithm determines whether it is visible from the viewpoint. This is typically done by comparing the depth (distance from the viewpoint) of each object in the sub-area. If an object is behind another object from the viewpoint, it is considered hidden.

3. Subdivision: If a sub-area contains more than one object, and these objects overlap from the viewpoint, the sub-area is further subdivided. This process is repeated until each sub-area contains only one object or no objects overlap.

4. Rendering: Once all sub-areas have been processed, the visible objects are rendered to the screen. The objects are typically rendered from back to front (i.e., from farthest to nearest), so that nearer objects correctly obscure farther ones.

5. Repetition: The algorithm repeats this process for each new viewpoint or as objects move within the scene.

The area sub-division algorithm is efficient for scenes where there is a lot of empty space or where objects are relatively far apart. However, it can be less efficient for complex scenes with many overlapping objects, as it may require a lot of subdivisions.