SweepandPrune

SweepandPrune is an algorithm used in computer graphics and computational geometry for collision detection. It is particularly effective for detecting collisions between large numbers of objects, such as particles in a simulation or polygons in a scene. The algorithm works by first sorting the objects based on their position along one axis, typically the x-axis, creating a "sweep line" that moves across the scene. As the sweep line encounters the start of an object's bounding box, the object is added to an active list. When the sweep line encounters the end of an object's bounding box, it is removed from the active list. While an object is in the active list, it is considered a potential collision candidate with other objects currently in the active list. This pruning step significantly reduces the number of pairwise comparisons that need to be performed. The "prune" part refers to the process of eliminating objects from consideration that cannot possibly be colliding with the current object being examined. This is typically done by checking the objects in the active list against the current object's bounding box along the other axes. If an object's bounding box does not overlap with the current object's bounding box along any axis, it is pruned from further comparison. The efficiency of SweepandPrune depends on the spatial distribution of the objects and the choice of sorting axis. Its time complexity is generally better than brute-force O(n^2) pairwise checks, often approaching O(n log n) under favorable conditions.