Map / Wall Generation

1. Automatic generation and maintenance of maps and walls Map / Wall Generation

2. Content Overview • Generating maps • What do we want in a map? Warcraft 3 map editor • RTS maps for Empire Earth • Wall Building • Generating intelligent barriers • Populating large worlds using limited resources • The Waterfall Algorithm

3. Generating an RTS map

4. RTS Map Generation: Overview • Place players on the map first • Grow land for each player • Land that has not been allocated is considered water • Analyze terrain and add features • Place resources around players fairly

5. Scripting for variety • Scripts are used to specify map parameters such that they can be modified quickly without programmer intervention • For example: • number of resources per player • maximum height of land • player land allocation • climate

6. Player placement - Step 1 • Inscribe a large disk on the map • Inner and outer radii can be set in a script

7. Player placement - Step 2 • 1 random point for each player is chosen within the disk; closest points are pushed apart • Closest points are pushed apart iteratively until distribution is satisfactory

8. Player placement – Step 3 • If the game has teams, they are assigned to adjacent player locations

9. Back it up - dummy players • Player locations will have allotted flat land and resources • We may want other areas of the map to also have these properties for player expansion

10. Where to put land? • This process is centered around the positions of the players which have just been determined • Why? Land is a very important resource in RTS games: Exhibit A • Each player must receive an equal amount of buildable land

11. Growing land: Clumps • Land is grown in around players in “Clumps” • Attributes of clumps can be set, such as: clump size, number of clumps per player, chaos level • Clumps grow (consume tiles) until they reach the predetermined size • When a clump is completed, a new clump is created a random distance and angle away until the number of clumps required are generated

12. Two methods for growing clumps • Completion Method: One clump is grown to completion before another is started • Step Method: Grows clumps one tile per iteration. This method is used to lay out each players’ land.

13. Keeping track of clumps • A 2-D array of all the tiles on the map is initialized such that all tiles are water • When a land clump is grown, it changes the value for its tile in the array to indicate that the tile is part of a land clump • When a land clump is grown for a player, the player’s enumerated value is placed into the land-water array

14. Different Map Types • Island Map: Require a new land tile for a player is not within some tile distance from another player’s land • Land Map: Allow players’ land to be adjacent to an enemy player’s land

15. Flat Clumps • While each player has been allocated an equal amount of land, nothing has been set about the conditions on the land • To ensure that each player has the same amount of buildable land, a subset of their land clumps are “Flat Elevation Clumps” • Flat Clumps are grown using the completion method and can only grow in a player’s existing land

16. Adding interesting terrain • Terrain can be generated using Fractals – “The Diamond-Square Algorithm”

17. Resource Allocation • Resources are placed on the map on a per-player basis • Placed within rings centered on a player’s starting location (number of resources and size of ring are attributes which can be changed with scripts) • For a particular resource, random locations in the ring are tried until an acceptable location is found • Why might a location be unacceptable? • Cannot be placed on a certain terrain • Must have a minimum distance to other resources • Cannot be too close to the player’s start location

18. What about the trees? • Trees are placed last because they are plentiful and restrict path finding. • Forest size, number of forests per player can be specified as attributes • Forest growth is not restricted by the players’ land boundaries (unlike most other resources) • Another type of clumps, “treeClumps” are used to grow forests • Forests cannot grow near other forests, and some areas are marked as forest-free

19. Flaws with this algorithm • High processing times • No ability to add specific terrain features • Often resulted in maps in which players had vastly different choke points, or even no access to other players • Resource placement system often created a resource advantage for certain players • Example of what these maps look like

20. Building Walls • Many RTS games allow the player to build walls to impede enemy mobility, so AI players must be able to as well • A good wall building algorithm can make NPC opponents much more formidable • In games with a map editor, an automated wall building feature would make a level designer’s job easier

21. Defining a Wall • A wall segment is a passive defensive structure which blocks movement over a single tile which it occupies • Wall segments are adjacent if they touch along the edges (not diagonals) • A wall is a set of wall segments which • Every wall segment has two adjacent wall segments • There is at least one interior tile • All interior tiles are connected through edges

22. To be crystal clear…

23. Greedy Algorithm • A greedy algorithm is one that always takes the best solution at the time • Must define a heuristic to determine how favorable a given action is • Always choose the solution with the lowest / highest value from the heuristic (depending on how your heuristic is defined) • Disadvantage: There is no guarantee that the overall solution will be optimal even if each step was optimal

24. Approach #1- Build Wall • Given a starting location which you would like to protect with the wall • Create a simple small rectangular wall directly surrounding the starting point • Using a series of moves, expand the wall until it meets the desired properties • Each “move” moves the interior space outward such that exactly one more tile is walled off and the new wall still meets our wall definition

25. Analyzing Permutations • In order to decide which move is best, we must consider all permutations • Each 3x3 square generates 68 permutations. • Once all permutations have been determined, calculate their heuristic value (in this case, how many wall segments must be added to accommodate including the interior node) • Option with the lowest cost is chosen

27. What about natural barriers? • Excellent question! • Natural barriers would create many more permutations, to the point where we are forced to ask the question, “Isn’t there a more efficient way to do this?” • The solution lies in realizing that there is a one-to-one relationship between a wall and the interior space protected by the wall

28. Paradigm shift • Instead of building the wall, we concentrate on building the space within the wall • We still start with the starting node from before (the location we’d like to defend) • The “move” described before simply becomes adding another tile to the interior space (using the same greedy algorithm)

29. Managing the nodes (tiles) • Closed list – the list of nodes that have been selected to be in the interior space • Open list – the list of nodes that are candidates for inclusion in the closed list (on the border) • On each iteration, the nodes on the open list are inspected, and the best candidate is moved to the closed list • This process is repeated until the desired size is achieved • Upon completion, the open list becomes the list of tiles on which to build the wall

30. Pseudocode

31. Keys to this algorithm • Traversal Function: for a given node, determine successor nodes (that become members of the open list) • Acceptance Function: determines whether or not the current wall is acceptable (# of nodes on the closed list, etc) • Heuristic Function: ranks open nodes, and thusly controls the shape of expansion. Must attempt to maximize area walled off while minimizing cost to do so

32. More on the Heuristic • Simply using the cost to include a node tends to result in asymmetric walls which stretch in one direction. • To correct this behavior, we add a term to the heuristic equation which increases the cost of nodes proportionally to their distance from the start node. • However, we must ensure that the distance does not out-weigh the cost of building • This results in a formula of this form f(n) = c * w(n) + d(n)

33. What about natural barriers? • This algorithm allows us to easily incorporate the possibility of natural barriers with some modifications • Traversal Function: must be changed to ignore natural barriers when looking for nodes to include • Heuristic Function: must consider natural barrier nodes to have no cost when considering including the bordering nodes in the open set • With these modifications, the algorithm takes advantage of natural barriers and tries to use them as free walls

34. Min/Max Distance Requirements • Minimum Distance: We may want to ensure that no wall segments are within a certain distance from the starting node. To accommodate for this, set the heuristic value (cost) of all nodes within the minimum distance to 0. • Maximum Distance: This can be done by monitoring the inclusion of nodes on the open list. If the node is at the maximum distance, add the node to a maximum distance list instead of the open list. Upon completion, we must merge the open list with the maximum distance list to get the full wall

35. Doors and Gates • We may want to have the ability to move friendly units in and out of the walled area • Brute force method: place openings randomly or at fixed intervals • More sophisticated: create paths (using A*) from starting node to all locations of interest outside the walls. Intersections between these paths and the wall are logical locations for doors

36. Diagonal Walls • With a few modifications, this algorithm can be adapted to games which do not allow diagonal movement • Heuristic: Cost function must ignore cost of walling off diagonally • Traversal: Ensure diagonal successor nodes are not added to the open list

37. Populating Large Worlds • Many actors in a large world map can consume an inordinate amount of resources • “Waterfall concept” helps to alleviate pressure on system resources • General idea is to devote the most system resources to units closest to the player, and limit actions of those far away.

38. Five Functional Components • The Context • The Character • The Personality • The Director • The Manager • Each of these is represented as a class in the architecture’s implementation

39. The Context • The “soul” of the AI • Set of all essential variables and data required to represent the state of an agent • Is the agent currently active? • Visual representation being used • State of thought process • Information is used by the Character class to affect agent behavior

40. The Character • Takes an instance of Context and uses the data contained therein to generate input for the agent- causes it to behave in a certain manner • Can be thought of as a script for the role the agent is playing • Will be sub-classed to generate a range of behaviors

41. The Personality • Allows multiple agents with the same Character to act in slightly different ways • Example: if an agent drives a vehicle • Character: Agent drives fast • Personality: provides a range from which the Character provides a range of minimum speed values • Ensures that agents are unique

42. The Director • Responsible for determining when agents fall in and out of the waterfall based on a complex set of rules • This helps maintain the illusion of a world teeming with active agents • Also chooses which Character an agent should use when it falls back into the “waterfall”

43. The Manager • Holds, instantiates, updates, renders, and destroys all AI agents • These functions could be absorbed into the Director if desired, but separating them eases management and encapsulates functionality • Deals with the physical aspect of AI: instantiates visual and functional piece of the game the user sees

45. Mechanics • Director determines if the Context needs to exit the waterfall • If yes, a new location is chosen for the Context, and agent is placed there • If not, a Character is chosen for the Context and the Context is assigned to a Character

46. Mechanics cont… • Next, the Character is allowed to operate on the Context • Path information • Collision information • Friend / foe information • Character never directly moves the agent; it leaves ‘suggestions’ the agent can use to affect its physical representation • The Director then determines if the agent has left the waterfall

47. Flow of the Waterfall • Purpose is to focus on the most interesting AI activity close to the player • Agents that have “exited” the waterfall may be recycled into a visible position or replaced with other agents • Most effective in a game where the player moves at a steady predictable rate • There must be a well-defined set of rules for when agents will enter and exit the waterfall

48. Exit Rules • Dependant on the type of game and visibility / line-of-sight distances (the shorter these distances, the better the system will work) • Examples of exit rules • The agent is farther than a certain distance away • The agent is behind the camera for a certain amount of time • The agent is outside the view cone for a certain amount of time

49. Entry Rules • Where to spawn the agent? • Very specific to the player’s location, movement, viewing direction • Some example rules • Enter agents behind the player, speed them up so they pass the player • Enter agents just out of player’s view distance • Enter agents into predetermined locations in anticipation of player’s arrival • What type of Character to spawn? • Are there too few agents with this Character in the Waterfall? • Are agents of this Character relevant to the game in the player’s current situation? E.g. more cops if the player is doing something illegal

50. Optimization • Just don’t do it • If an agent too far away or occluded, turn off unnecessary functions (animation, collision checks) • Do it, but only so often • Some things can be done just once in a while (update pathfinding, searching for downhill direction, other long searches)