How Does Pathfinding Work in Video Games?

Understanding Pathfinding in Video Games

Pathfinding is an essential component of many video games, enabling characters or objects to navigate their environments efficiently. By leveraging advanced algorithms and data structures, pathfinding ensures smooth and realistic movements, improving gameplay experiences. At the core of pathfinding lies the concept of graphs, which form the foundation for navigation in game worlds.

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Graphs: The Foundation of Pathfinding

A graph is a discrete structure that represents objects (nodes or vertices) and their relationships (edges). Formally, a graph is represented as:
$G = (V, E)$
Where $V$ is the set of vertices, and $E$ is the set of edges connecting the vertices.

In pathfinding, graphs are used to model maps or paths in the game world. Each vertex can represent a location, while edges denote possible routes between them.

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Shortest Path Problem in Graphs

The shortest path problem involves finding the minimum distance between two specific vertices in a graph. In weighted graphs, the path with the smallest total weight is sought.

Pathfinding algorithms solve this problem by determining the fastest or most efficient route for characters to move through the game environment. This process is crucial for creating responsive and immersive experiences.

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Dijkstra's Algorithm

Dijkstra's algorithm is one of the most widely used shortest-path algorithms. It begins at a source node and iteratively calculates the shortest distance to all directly connected nodes. Key steps include:

• Assigning a distance of zero to the source node and infinity to others.
• Using a priority queue to select the unprocessed node with the smallest distance.
• Updating the distances of neighboring nodes based on edge weights.

Dijkstra’s algorithm ensures all shortest paths are found, but its approach can be inefficient when searching for a path to a single target.

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A* Algorithm

The A* algorithm builds on Dijkstra’s method by incorporating a heuristic to prioritize paths more effectively. It calculates a score $f(n)$ for each node:
$f(n) = g(n) + h(n)$
Where:

• $g(n)$: Cost from the start node to the current node.
• $h(n)$: Estimated cost from the current node to the goal (heuristic).

The heuristic function $h(n)$, often based on the Euclidean distance, helps the algorithm focus on nodes closer to the target. This makes A* more efficient than Dijkstra for single-source, single-target searches.

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Pathfinding in 2D Video Game Grids

In 2D video games, environments are often represented as grids where each cell corresponds to a traversable or non-traversable area. Pathfinding algorithms navigate these grids to determine optimal movements. Games in tactical or strategy genres frequently use such systems for controlling player and enemy actions.

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Comparison: Dijkstra vs. A*

Aspect	Dijkstra	A*
Efficiency	Searches all paths, often visiting unnecessary nodes.	Focuses on promising paths using heuristics, reducing unnecessary exploration.
Heuristic Use	Does not use heuristics; relies solely on known distances.	Incorporates heuristics to estimate costs and improve efficiency.
Optimality	Always finds the optimal shortest path.	Finds the optimal path if the heuristic is admissible (does not overestimate the cost).

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Conclusion

The A* algorithm is better suited for pathfinding in 2D video game grids due to its efficiency and focus. By leveraging heuristics, A* reduces the number of nodes visited, resulting in faster and more responsive gameplay. For game developers, this makes A* the preferred choice for implementing navigation in grid-based environments.

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References:
Husni, M. H. (2022). Comparison of Dijkstra and A Algorithms in Pathfinding for Two-Dimensional Grid-Based Video Games*. Mathematical Discrete Paper 2022.