1. Artificial Intelligence in Game Design
Map Representation and Path Finding

2. Path Creation Strategy Path Planning Movement
“Where to move to”
“How to get there”
“Get there”
Current location
Idea: Specify goal location and let AI find path from current position to goal

3. Waypoints Path = graph structure Vertices = waypoints on path
Edges between waypoints directly reachable from one another
Current location

4. Waypoints and Costs Goals:
Provide waypoints that let characters reach all locations on level
Can SEEK any location from some waypoint
Minimize number of waypoints
Cost of path planning = O(number of waypoints)2
Key idea:
Waypoint creation done offline (during game design)
Path planning done many times during gameplay

5. Defining Waypoints Defining waypoints manually
Usually at points where direction change necessary
Corners
Intersections
Doors
Character must be able to directly seek waypoint from any adjacent waypoint
Character must be able to directly seek all points in map from some waypoint

6. Defining Waypoints Manually

7. Defining Waypoints Convenient to generate waypoints automatically
Simplest case: simple 2D grid (square or hex)
Some points impassible (water, mountains, etc.)

8. Defining Waypoints Automatically
Can often use floor tiles
Used by level designer to create level
Used to define visibility, lighting areas, where sounds can be heard, etc.
Usually triangular or rectangular

9. Defining Waypoints Automatically
One waypoint per tile
Usually in center
Link waypoints in adjacent tiles
May still need to tweak manually
Make sure all points directly reachable from a waypoint
Add strategic waypoints (cover, shadow, etc.)
Make special waypoints for door entry, exit, etc.

10. Triangular Mesh Generation
Automatically generating triangular tiles that cover level
Connect some two adjacent walls to form a triangle
Continue connecting adjacent walls and/or adjacent borders
Continue until all walls are part of some triangle

11. Waypoint Cleanup Can automatically remove some “redundant” waypoints
Not an endpoint (degree > 1)
All adjacent points can directly reach each other without using that waypoint
Often based on visibility (ray tracing)

12. Path Creation Path = list of adjacent waypoints
Move along path using FollowPath steering
Seek “close enough” to next path waypoint 73 73 27 21 45
Desired path 27 45 21

13. Path Creation Initial waypoint = May need to test each
Waypoint in same tile as character
Closest waypoint to character
May need to test each
Avoid going backward initially
Less of a problem with small tiles
Seek that first waypoint
Goal:ATM
Should seek this first

14. Path Creation Reaching goal = Arrive at goal from that last waypoint
Character in same tile as goal
Character at waypoint nearest goal
Arrive at goal from that last waypoint

15. Hierarchical Paths Simple maps at different levels of detail
Better than single map with thousands of points
Single best solution to minimizing pathfinding costs
Connect points on high-level maps to entrances/exits on low level maps

16. Hierarchical Paths Requires hierarchical representation of location Me
At podium
Path to room 301 exit
Room 301
Path from 301 exit to Meshel Hall exit
Meshel Hall
Path from Meshel Hall exit to Kilcawley Center entrance
Holy Grail
Path from Kilcawley Center entrance to Computer Lab entrance
Under seat D001
Computer Lab
Path from Computer Lab entrance to seat D001
Kilcawley Center

17. Path Planning
Good path
May have several possible paths from current location to goal
Need to find “best” path
Otherwise character does not look intelligent!
Goal
Bad path

18. Edge Costs “Best” path defined by edge costs
Good path
Cost = 22
“Best” path defined by edge costs
Time to travel path
Distance, etc.
Best path = path with smallest total cost 6 4 4 3 5 4
Goal 7 5 4
Bad path
Cost = 47 5 4 2 5 3 4 4

19. Terrain-based Costs Can base cost on terrain type
Grass = 1
Desert = 2
Forest = 3
River = 20
Often multiply by edge distance
5 miles of desert = cost of 10
8 miles of grass with ¼ mile river = cost of = 13

20. Other Edge Costs Danger
Cost of traveling through enemy territory = 5 * normal cost
Important part of tactical movement

21. Other Edge Costs Visibility Dark = factor of 3 Fog = factor of 2
Can also add to danger
Long path now best

22. Character Edge Costs
Different characters may have different edge costs
Grass = 2
Desert = 2
Forest = 10
River = 30
Grass = 1
Desert = 3
Forest = 2
River = 10
Squad cost = max(individual costs)

23. Non-Symmetric Edge Costs
Often harder to go one direction than another
Stairs
Jumping from one level to lower level
Will have different costs in each direction
Two directed edges instead of one directed edge
No second edge in “one way” path 1 4 2

24. Turning Costs
Some characters require time to realistically make a direction change
Part of edge cost
Separate edge from location to same location
Align
Arrive 3 5 4
Seek

25. Inflection Points Waypoints often near convex corners
Shortest path in wide areas
Better than putting waypoint in center of area
Path given by floor tiles
Faster path

26. Inflection Points Put waypoint at each convex corner
Move out some safeRadius from corner
Connect waypoints visible from one another
safeRadius
safeRadius

27. Inflection Points
Potential problem: “jagged” areas could create too many waypoints
Solution: Only add waypoints for obstacles between critical areas (such as doors)
Recursively add waypoints until critical areas connected
Irrelevant inflection points

28. Inflection Points
Automatic creation of waypoints on arbitrary racing track

29. Path Smoothing
Problem: Grid-based floor tiles with waypoints at center
Jagged” paths
Too many unnecessary turns
Better to create path using non adjacent nodes

30. Path Smoothing Recursive algorithm: Draw line between start and goal
Stop at obstacle
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