Terrain Analysis

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Terrain Analysis

• CS 370
• Spring, 2003

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REMINDER

• One week from tomorrow is the Party!
• 5-9 pm
• Pizza and soft drinks will be provided
• If youre going to need lab machine(s) for your
  game, please coordinate with us ASAP
• The system staff need plenty of lead time. Next
  Thursday wont really cut it

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Overview

• Representing space and terrain
• Path-finding
• Position-finding
• Higher-level analyses

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Spatial reasoning is really hard

• Humans have incredible perceptual/motor skills
  dedicated to handling aspects of it
• Humans appear to have rich representations of
  space and shape at multiple levels of description
• Pop quiz
• Which is farther west, San Diego, CA or Reno, NV?
• Which is further north, Chicago or Milan?
• Simplification Construct discrete underlying
  representation

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From the developers side

• The first of many hurdles to cross is to prevent
  the game from freezing every time we path some
  unit across the screen. This game freeze can
  be considered the plague of pathfinders. Its a
  game killer, and one of the most significant
  problems we will need to solve until we all have
  5-trilliahertz computers with googles of memory
• Dan Higgens (Empire Earth team from Stainless
  Steel Studios, Inc.),

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From the players perspective

• Managing that army can be a bit annoying at
  times, though, because of AoMs errant
  pathfinding. On more than one occasion, Id try
  to send my units to a specific spot on the map
  and theyd end up on a hill overlooking the spot
  where I wanted them to be. Other problems include
  units getting trapped between rows of bushes,
  units jerking this way and that as they move,
  and units hugging a cliff instead of simply
  walking down the road in front of them (which
  results in them moving much slower than they
  should).
• Age of Mythology review, PC Gamer, 2002

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Game designers have to cheat like crazy

• Use simplified representations of space
• Sometimes hand-constructed, by level designers
• Sometimes automatically constructed, when random
  terrain or user-level map editors are used

http//www.gamasutra.com/features/20010912/sterren
_02.htm
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Three families of spatial solutions

• Tiles
• Waypoints
• Quad trees

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Tiles

• Variations
• Can be rectangular or isometric, depending on
  perspective
• Some games use hexagonal grids to model distances
  traveled on diagonals more accurately
• Tradeoffs
• Very simple
• Uniform resolution can waste storage on
  uninteresting regions of space

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Quad Trees

• Carve up space according to where objects arent
• Stop conditions
• Uniform contents
• Maximum depth on recursion reached
• Tradeoffs
• Provides variable resolution
• More intricate to generate and use

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Waypoints

• Annotate terrain with hand-selected places that
  movable entities can be in
• Adjacency relationships between waypoints
  indicate ways to move from one to the other
  (including travel time)
• Additional annotations can be used to indicate
  other properties
• whether line-of-sight exists between two
  waypoints
• Part of a room or a base or some interesting
  location
• Environment conditions, such as light/dark, types
  of movement required
• Tradeoffs
• Can analyze to derive many useful tactical
  properties
• Generally must be entered by hand

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Example Using waypoints for tactics
Waypoint
Visible and trafficable
Visible only
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Where would be good sniper posts?
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Where would be good sniper posts?
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Where are the choke points?
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Where are the choke points?
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How would you sneak up on them?
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How would you sneak up on them?
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How would you trap them?
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How would you trap them?
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Path-finding

• All three spatial solutions give rise to common
  formal framework for finding paths
• Graph search
• Costs on links of graph
• Results from early AI research universally used
  in game development
• E.g., A search and its successors
• Game developers have invented many improvements
• Nothing like trying to live within a tight CPU
  budget to unleash creativity!

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A Formalization

• Node a state in your search corresponding to a
  place in your terrain representation
• Node contains path to get from start to that
  place
• Multiple paths can go through the same place, so
  there can be more nodes than places
• Children nodes corresponding to adjacent places
  in your terrain representation.
• Links between nodes have costs.
• Depends on distance
• Depends on difficulty of movement
• Can roll in other factors, e.g.
  concealment/visibility, to incorporate tactical
  factors

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A formalization, continued

• Start, Goal nodes
• g(n) cost to get to this node from your
  starting position
• Sum of costs so far along this path
• h(n) Estimate of cost remaining to goal
• Intuition Path cost estimate g(n) h(n)
• Use estimate to explore cheapest paths first
• If h never overestimates cost remaining, then h
  is admissible
• If h is admissible, then A is guaranteed to be
  optimal
• Will always find the cheapest path
• Will always examine the fewest nodes

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A

• Let Open make-node(start), Closed
• If Open then return failure
• Let N best node from Open
• If place(N) goal then return N
• For each child C of N,
• Is there a node N2 with place(N2) place(C) in
  Open or Closed?
• If so, replace path(N2) with path(C) if f(N2) gt
  f(C)
• Otherwise, add C to Open
• Move N to Closed

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Demo

• http//www.ccg.leeds.ac.uk/james/aStar/

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Modification Iterative deepening

• Observation For a search of depth k, there are
  many more nodes at the depth of k than the entire
  search tree for k-1
• Technique Add a maximum depth of search
• Start with small but semi-reasonable estimate
• If failure, search again with larger maximum
  depth
• Tradeoffs
• Search the same space near the start over and
  over again
• Memory requirements can be dramatically smaller

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Modification Cleaning up paths

• With large pieces of space, paths generated can
  be unnatural
• Solution Use a post-processing step to clean
  them up

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Influence maps

• Helps identify interesting positions on a map
• Start from things of interest
• E.g., friendly/enemy units, resources
• Propagate numerical values to neighbors
• Add/subtract values from different sources as
  appropriate
• Analyze patterns of numerical values to select
  positions, boundaries
• Where to put a mine or storage shed
• The front between two warring nations

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Demo

• http//www.ccg.leeds.ac.uk/james/influence/

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Frontier Improving spatial representations

• Goal Provide human-like spatial representations
  in computer games
• More realistic opponents
• More realistic comrades

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Example Visual computation of cognitive maps

• Hill, Randall W., Jr., Han, Changhee, Van Lent,
  Michael. - "Applying Perceptually Driven
  Cognitive Mapping To Virtual Urban Environments.
  14th Innovative Applications of Artificial
  Intelligence Conference (IAAI 02)

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Demo nuSketch Battlespace
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Some references

• Brockington, M. 2000. Pawn captures Wyvern How
  computer chess can improve your pathfinding. GDC
  2000.
• Davis, I. 2000. Warp Speed Path Planning for
  Star Trek Armada, AI and Interactive
  Entertainment Papers from the 2002 AAAI Spring
  Symp., AAAI Press, Menlo Park, Calif.
• Forbus, K., Mahoney, J., and Dill, K.. 2001. How
  qualitative spatial reasoning can improve
  strategy game AI. AI and Interactive
  Entertainment Papers from the 2001 AAAI Spring
  Symposium. AAAI Press, Menlo Park, CA
• Liden, L. 2001. Using nodes to develop strategies
  for combat with multiple enemies. AI and
  Interactive Entertainment Papers from the 2001
  AAAI Spring Symposium. AAAI Press, Menlo Park,
  CA
• Pinter, 2001. Toward more realistic pathfinding.
  Gamasutra.com
• Rabin, S. (Ed.) 2002. AI Game Programming Wisdom.
  Charles River Media, Inc. Hingham, Mass.
• Stout, B. 1996. Smart Moves Intelligent
  Path-finding. Game Developer Magazine, October.
• Van der Sterren, W. 2001. Terrain reasoning for
  3D Action Games. GCD 2001

• Most of these are available on
• www.gamasutra.com
• www.qrg.northwestern.edu/aigames.org/index.html