Pathfinding in games
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The document discusses pathfinding in games, focusing on algorithms used for navigating non-player characters and units in various gaming genres. It outlines space representation techniques, including data structures like grids and graphs, and explores several algorithms, comparing their efficiencies, such as breadth-first search, depth-first search, Dijkstra's, and A*. Additionally, it addresses challenges related to dynamic changes in the game environment and coordinating multiple units for movement.
Pathfinding in games
- 2. Hi, This is Adrian I am here because I love to build games and also to give presentations. Today’s is about...
- 4. Our goal Reach a target as well as possible.
- 5. Artificial intelligence Non-player character (FPS) Armies of units (RTS) Enemies (Tower Defense) Use cases Player exploration Objective display GPS (Racing)
- 7. Racing Test Drive Unlimited 2
- 8. RPG Mass Effect 2
- 9. Get objec positio Basic repetitive procedure Close object to target Estimate distance to target Get object positione object o target
- 11. Grid Each cell is denoted by its row and column. 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 1, 7 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 2, 7 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 3, 7
- 12. Graph Node are connected through edges. 1 3 2 6 5 8 4 7
- 13. Convex polygons Convex = all segments with extremities inside lie inside.
- 15. Random backstepping Take one step in the direction of the target. Avoid obstacles by taking a step back. Simple algorithms Obstacle tracing Similar to random backstepping, calculates the collision before it happens.
- 16. Advanced algorithms ◆ Breadth-first search (BFS) ◆ Depth-first search (DFS) ◆ Best-first search ◆ Dijkstra’s algorithm ◆ A* algorithm
- 17. BFS vs DFS BFS is wide; DFS is deep.
- 18. Worst-case space complexity Worst-case time complexity Implementation BFS vs DFS Small: linear in the length of the current path. Large: linear in the area of the explored surface, as it explores useless paths. By using a first-in, first-out (FIFO) data structure, e.g., a stack. DFS Large: linear in the perimeter of the explored surface. Small: quadratic in the length of the minimum path. By using a last-in, first out (LIFO) data structure, e.g., a queue. BFS
- 19. Dijkstra’s algorithm ◆ Solves the single-source shortest path problem. ◆ Invented by Edsger Dijkstra, Turing award winner. ◆ Used in many games for efficient pathfinding. ◆ More efficient than BFS and DFS in terms of time. ◆ More complex in implementation too.
- 20. Dijkstra pseudocode ◆ Start with two sets of graph nodes S and T. ◆ S contains the source node and T all others. While the target node is not in S, do: ◆ Find the node in T that is closest to a node in S. ◆ Move that node from T to S. ◆ Relax the edges from the node to T.
- 21. Dijkstra efficiency ◆ To find the closest node, one can use an efficient data structure, such as a simple heap, to answer queries for the minimum in a totally-ordered set. ◆ Its operations take worst-case O(n) time, where n is the number of nodes. With a simple heap, the worst-case time complexity is O(m ⨉ log n), where m is the number of edges. ◆ By using Fibonacci heaps, one can reduce the time complexity down to O(m + n ⨉ log n), as m >> n.
- 22. A* algorithm ◆ A “combination” of BFS and Dijkstra. ◆ Does not use exact distances between nodes. ◆ Estimates the distance by using a heuristic. ◆ The heuristic should not overestimate the distance. Possible heuristics: ◆ Manhattan distance - go straight, no diagonals. ◆ Diagonal distance - go only 45 deg. diagonals. ◆ Euclidean distance - distance in the plane.
- 23. A* traversal The A* will visit the heuristically closest nodes to the target.
- 24. 3. Dynamic changes What about updates on the world?
- 25. Distance recalculation Opportunities: ◆ With every nth iteration of the algorithm. ◆ When the processor is idle. ◆ When a unit reaches a waypoint or a corner. ◆ When the “near world” has changed. Challenges: ◆ Previously computed data is thrown away. ◆ Can be show for large maps.
- 26. Path splice Main idea: ◆ Splice the large path into smaller paths. ◆ Only recalculate one or more of the smaller paths. ◆ Handle the coordination of multiple units - see image. Challenges: ◆ Responds poorly to large changes.
- 27. Region partition Main idea: ◆ Partition the map into regions. ◆ Each unit depends of a specific region. ◆ Propagate a change only within the region. Challenges: ◆ Responds badly to large changes - see image.
- 28. Obstacle prediction Main idea: ◆ Incorporate heuristics that predict how obstacles will move in the future - see image. Challenge: ◆ Depending on the game, the move may be easy, hard, or impossible to predict.
- 29. 4. Multiple units How can we coordinate them?
- 30. Individual movement Algorithm: ◆ Find the center of a set of units. ◆ Compute the path from the center to the target. ◆ Move each individual unit in parallel, along the path - see image.
- 31. Coordinated movement Algorithm: ◆ Identify a leader among the units. ◆ Compute the path from the leader to the target. ◆ Move the leader along the path. ◆ Make the other units flock around the leader unit - see image.
- 32. Thank you. Any questions? You can find me at @dumitrix