Wall Building for RTS Games

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Wall Building for RTS Games

• Patrick Schmid

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Age of Empires
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Age of Empires
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Stronghold
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Walls

• Walls
• Barbed wire
• Fences
• Sandbags
• Force fields

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Intelligent Wall Placement

• Locations to protect
• Use natural barriers
• Wall cost
• Distance from a given location
• Size of protected area

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Possible Solutions

• Build rectangular wall
• Add walls to level via map editor
• Wall-building algorithm

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Problem Definition

• Protect a given location by blocking the movement
  of enemy units
• Implies
• Block all access routes
• No breaks

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Preliminaries

• Restricted to tile-based maps
• Obstruction footprints confined to tiles
• Wall segment
• Passive defensive structure
• Blocks unit movement over a single tile
• Two wall segments are adjacent when they touch
  along the edges (not diagonals)
• Four adjacent wall segments (neighbors) for each
  free standing wall segment
• Each wall segment of a wall has two neighbors

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Definitions

• A wall is a set of wall segments connected
  together in such a way that
• Every wall segments has exactly two unique
  neighbors (? wall segments linked in circular
  fashion)
• At least one interior tile (tile inside the
  walled-off area)
• All interior tiles (interior area) are connected
  through edges (not diagonally).

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Examples
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Acceptance Criteria

• Minimum / maximum distance from location to
  protect
• Minimum / maximum number of interior tiles
• Maximum number of wall segments (cost of building
  wall)

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Definition of Problem

• On a given tile map, build a wall that fits the
  definition, protects the given location, and
  meets the given acceptance criteria.

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Wall-building algorithm

• Starting location (given) that needs to be
  protected
• Apply an initial wall around this location
• Move wall outwards greedily remove an existing
  wall segment and place it in a different
  location, so that
• Net gain of exactly one interior tile
• Resulting wall still meets the wall definition
• Some moves might require addition of extra wall
  segments
• Stop when acceptance criteria are met

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Possible wall segments
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Possible moves
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Does this work?

• Every group allows 17 possible moves 68
  possible moves
• Common patterns can be used to reduce number of
  cases
• Natural barriers act similarly to wall segments
• Natural barriers will greatly increase the number
  of possible moves
• ? Large number of moves

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Is there a better way?

• Instead of expanding wall, expand interior area
• Once expansion is done, generate wall around
  interior area

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Definitions

• Node representation of the smallest area, e.g.
  a tile or a waypoint, that can be obstructed by
  the placement of game objects
• Graph with every edge connecting two nodes
• Edge defines path units can take
• Nodes sharing same edge are called adjacent

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Definitions (cont.)

• A node can have any number of adjacent nodes
• A wall segment that is part of a wall still only
  has two neighbors
• Interior tile ? interior node
• Interior area ? set of interior nodes
• Starting location ? starting node
• Move ? process of adding new nodes to the
  interior area

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New wall-building algorithm

• Start with starting node
• Expand interior area by adding one node per step
• Select the node to add using a greedy methodology
  (? heuristic function)
• Stop when acceptance criteria are met

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Data structures

• Closed list
• Nodes in the interior area
• Open list
• Nodes bordering the interior area
• Ranked by heuristic function
• After node was moved to closed list, add new
  neighboring nodes

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Traversal Function

• Get all successor nodes for a particular node
• Power to block individual node to prevent the
  interior area from spreading into undesirable
  areas
• Frequently used by heuristic function to get list
  of successor nodes for cost calculation

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Heuristic Function

• f(n) is cost function representing the cost of
  adding node n to interior area
• c is a constant larger than the maximum possible
  distance from the starting node
• w(n) is the cost of walling off node n
• d(n) is the distance from node n to the starting
  node

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w(n)

• Number of wall segments needed to keep the new
  node walled off from the outside area
• Only w(n) generates asymmetric walls stretching
  in only one direction
• Why?
• List of successor nodes tends to be arranged in a
  certain order.
• Beginning of list gets preference over nodes with
  same cost further down the list
• Leads to expansion in general direction of
  successor node at the top of the list

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d(n)

• Add distance from starting node
• Maximize the minimum wall distance from the
  starting node for same wall cost ? good for
  defensive purposes
• Distance-related part has to be less significant
  than portion related to walling-off
• Achieve this by multiplying cost of walling off
  with the maximum distance (c)

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Minimum distance

• Gives priority (0) to the nodes closer than the
  required minimum distance
• Need to adjust acceptance function to require
  that all nodes have reached minimum distance
• Used to protected important location, e.g.
  building, from enemy fire

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What about natural barriers?

• Traversal has to ignore natural barriers
• Heuristic function needs to treat barriers as
  free wall segments and ignore them in the
  calculation of w(n)
• Efficient implementation Change node traversal
  to ignore barriers

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Map Edges?

• Inaccessible, maybe even permanent fog of war
• Requires impassable terrain around them
• Treated as natural barriers
• Embraced as part of game play
• Traversal cannot find nodes past the map edges
• Heuristic function has no cost for those nodes
• Area past the edges treated as invisible natural
  barrier

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Maximum Distance?

• Do not let open nodes at maximum distance become
  interior nodes
• Undermines functionality of open list!
• Introduce maximum distance list
• Holds nodes located at max distance
• Before adding a node to open list, check its
  distance
• If equal to max distance, add it to max distance
  list
• Upon completion, merge open and max distance list
  to get final solution
• Used to place wall within manageable distance, or
  ensure protective cover of tower fire

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Doors and Gates?

• A wall without doors and gates is not that
  useful!
• Simply place gates at evenly spaced locations in
  the wall
• Dumb solution
• Might place a gate right in front of a natural
  barrier
• Might not get us to all interesting locations
• Smart solution Create paths from starting
  location to interesting outside locations. Where
  path and wall intersect, place a gate.

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Diagonal Walls?

• Walls might be connectable diagonally
• Cost function needs to ignore cost of walling off
  a diagonal direction
• Diagonal successor nodes may not be added to open
  list

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Demonstration
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Actual Games

• Author of chapter (Mario Grimani) worked on
• Age of Empires II The Age of Kings
• Age of Empires II The Conquerors
• Age of Mythology
• Sovereign
• Everquest II

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Reference

• Mario Grimani Wall Building for RTS Games. AI
  Game Programming Wisdom 2