Collision detection is essential in game development, but naive implementations often suffer from inefficient $O(N^2)$ complexity. QuadTrees offer an elegant spatial partitioning solution to dramatically reduce the number of checks needed.

The Problem

In a game with many moving objects, checking every object against every other object for collision (checking $N$ objects against $N-1$ others) results in a time complexity of $O(N^2)$. As the number of objects increases, performance drops drastically.

For example:

• 10 objects = 45 collision checks
• 100 objects = 4,950 collision checks
• 1,000 objects = 499,500 collision checks

This quickly becomes untenable.

The Solution: QuadTrees

A QuadTree solves the “broad-phase” of collision detection by spatially partitioning the game world. Instead of checking everything against everything, we only check objects that are spatially near each other.

How it works

1. Partitioning: The 2D space is divided into four quadrants (think of a grid being recursively subdivided).
2. Insertion: Objects are inserted into the node that spatially contains them.
3. Subdivision: If a node contains too many objects (exceeds a capacity threshold), it splits into four child nodes, and objects are redistributed into the appropriate children.
4. Retrieval: To check for collisions for a specific object, you query the QuadTree to return only the objects located in the same quadrant(s).

This reduces the number of checks significantly — typically to $O(N \log N)$ or better depending on spatial distribution.

What is a QuadTree?

A quadtree is a tree data structure in which each internal node has exactly four children. Quadtrees are the two-dimensional analog of octrees and are most often used to partition a two-dimensional space by recursively subdividing it into four quadrants or regions. The data associated with a leaf cell varies by application, but the leaf cell represents a “unit of interesting spatial information”.

— Wikipedia

In game development, QuadTrees excel when:

• Objects are distributed unevenly across the map
• You need fast spatial queries (“what’s near this object?”)
• The number of moving objects varies over time

When to Use QuadTrees

Good fit:

• Games with many dynamic objects (bullet hell, particle systems, RTS games)
• Open-world environments with sparse object distribution
• Scenarios where objects cluster in certain areas

Alternatives to consider:

• Uniform grid: Better for evenly distributed objects
• Spatial hash: Simpler implementation for certain use cases
• BVH (Bounding Volume Hierarchy): Better for 3D or when objects vary greatly in size

References

• Quadtree - Wikipedia
• JavaScript QuadTree Implementation
• Quick Tip: Use Quadtrees to Detect Likely Collisions in 2D Space