CO2301 Games Development 1 Week 11 Pathfinding Considerations

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CO2301 - Games Development 1Week 11Pathfinding
Considerations

• Gareth Bellaby

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Topics

• Final comments on algorithms
• Representations
• Path Smoothing
• Maps and Data
• Reacquiring Waypoints

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Topic 1

• Final comments on algorithms

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Other Search Variants

• A is good but explore other variants.
• Iterative Deepening. Developed for depth-first
  but equally applicable to A. Use A but only to
  a pre-set maximum depth (or even pre-determined
  time).
• Once fully explored, increase the depth of the
  search by one.
• Carry on the process until the goal is found.
• Might seem inefficient since nodes are revisited
  but overhead can be negligible.
• Bidirectional search. Start two simultaneous
  searches from the start and the goal nodes.

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Matching Algorithm and Game

• A
• dynamic terrain, lots of moving obstacles.
• Dijkstra
• static terrain, pre-generated.
• can always reacquire the waypoint so can be used
  if some dynamic obstacles are expected, e.g.
  other entities running around.

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Matching Algorithm and Game

• You can use more than one algorithm in the same
  game.
• Different algorithms can be used at different
  levels of reasoning, e.g. coarse/fine,
  strategic/tactical, etc.
• There are also pragmatic variants such as
  relaxing the admissability criteria.

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Efficiency

• A is at its most inefficient if a path doesn't
  exist.
• In such a situation it will examine every
  possible location.
• This may be a common occurrence depending on the
  game, e.g. lots of units moving and the one under
  consideration has its path blocked to the goal.
• Use a pre-analysis of the map to determine
  whether a path is possible.

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A efficiency

• Uses lots of memory, therefore can be
  inefficient.
• The biggest overhead is the constant allocation
  and deallocation of substantial amounts of
  memory.
• Instead pre-allocate memory. Use a memory bank of
  nodes.
• See Rabin, "A speed optimizations", Games Gems,
  for this and other optimisation techniques. The
  book also has several other good pathfinding
  articles.

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Matching physical reality

• It may be that you don't have to worry too much
  about the physical reality of the map.
• Not doing collision detection.
• Errors are acceptable.
• Respond to errors if the occur, e.g. use crash
  and turn
• Store local information. Cache recently found
  paths.
• Data is cheap. Reduce complex calculations by
  increasing the number of locations.
• Remember what I've said about dynamic memory.
• You do have be concerned about cache misses. This
  will be dealt with next year by Laurent.

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Level of Detail

• Do a coarse grained map analysis to calculate the
  main movement path. Do a fine grained analysis to
  calculate the precise movement.
• Do fine grained detailed pathfinding for the
  immediate location.
• Break a level up into areas. Set up broad paths
  of movement between the areas.

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Level of Detail

• Think about the using other representations, e.g.
  columns and queues.
• Squad movement, e.g. Dawn of War, Total War.
• If possible delay calculations, e.g. ignore
  unseen objects.

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Topic 2

• Representations

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Map types

• You have used a square grid with only horizontal
  and vertical movement.
• Other representations can be used.
• These representations may be more efficient than
  a square grid because
• Search through less data since the representation
  is simplified.
• May help to identify significant locations on the
  map.
• Use the representation to select significant or
  useful locations, e.g. two identical rooms, but
  one has a good sniping position.

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Alternatives

• See Rabin, "A speed optimizations", Games Gems,
  for a discussion about the relative advantages
  and disadvantages.
• Grid rectangular, hexagonal.

• Waypoints.

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Alternatives

• Regions (polygons, could use the actual polygons
  of the floor). Does not have to be a regular
  pattern. A region could be room or an area on a
  map.

• Points of visibility (convex points - describes a
  minimal path.

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Topic 3

• Path Smoothing

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Path Smoothing

• The path generated by the pathfinding algorithms
  are composed of unnatural looking straight lines
  and abrupt turns. This is true whichever
  representation is used.
• Path Smoothing is about smoothing the path and
  making something more aesthetically pleasing.

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Smoothing

• Smoothing is the operation whereby you capture
  the essence of a set of data whilst leaving out
  the noise.
• Smoothing is carried out by creating a function.
• Last week you saw a mathematical function. A
  function "in mathematics, is an expression,
  rule, or law that defines a relationship between
  one variable (the independent variable) and
  another variable (the dependent variable)."
  Encyclopædia Britannica
• So a function takes an input and calculates an
  output according to some mathematical rule or
  operation.

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Interpolation

• Set of points. Want to draw a line through them,
  but we want this to be a aesthetically pleasing
  curve.
• Need to calculate points in between our known
  points. This method is know as interpolation.
• Interpolation means to take a set of discrete
  points at given intervals and generate the
  continuous function that passes through the
  points.
• Laurent will do interpolation with you in the
  context of animation.

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Path Smoothing

• There are many ways to interpolate data. I will
  introduce a method of generating a curve called
  the Catmull-Rom spline.
• I will quickly pass over how it does this, but
  essentially you generate tangents based on the
  position of the sample points.
• For more details see Van Verthe section 9.6 and
  Rabin, "A Aesthetic Optimizations", Games Gems.

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Catmull-Rom spline
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Catmull-Rom spline

• Need four points.
• The curve is derived for the line between the
  second and third points.
• The line is calculated as a sequence of discrete
  locations.
• The calculation is carried out for each component
  of the four points.
• Bicubic polynomial.

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Catmull-Rom spline

• You don't need to derive all of the points of the
  curve.
• An efficiency gain can be made by using
  predetermined intervals. This allows you to
  pre-calculating the value of t.

• Quarter interval

• Half interval

• Three quarter interval

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Catmull-Rom spline

• In order to derive the line between the second
  and third points (the middle) use all four
  points.
• In order to derive the line between the first and
  second points (the first third) use the first
  points twice, i.e. p1 and p2 are the same.
• In order to derive the line between the third and
  last points (the last third) use the last points
  twice, i.e. p3 and p4 are the same.

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Topic 4

• Maps and Data

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Grids

• You could use a stable grid, i.e. one which you
  have pre-prepared and lay down on the map. This
  allows you to work with the map design.
• However, could move the grid around, i.e. every
  time you pathfind lay a new grid onto the map in
  a different location
• Obviously sacrifices design, repetition of search
  data, sharing of data, etc.
• Can bypass map problems because a difficulty with
  one grid may disappear when you lay down a
  different grid.

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Map design

• The AI developer should work closely with the
  level designer. This relationship may include the
  artists as well.
• Change the design of the level to work with the
  AI.
• Don't include features which are difficult to
  navigate.
• Convex is better than concave.

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Map design
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Map design
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Map design
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Map design
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Map design - encode features

• Use elements of the scene to improve the AI. For
  example, It is possible to use colours or
  textures to provide information.
• Whether a location is inside or outside.
• Where a choke point exists.
• The best path to take between two points.
• These don't have to be visible, just usable.

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Data

• Use data instead of pathfinding.
• Data is cheaper than running an search
• Do good map design
• Embed information within the world.

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Topic 5

• Reacquiring Waypoints

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Reacquiring Waypoints

• Entities will almost certainly move off your
  waypoints or grid during the course of a game,
  e.g. due to combat or to go around obstacles.
• Assume that this is the case and that you will
  need a "reacquire waypoint/grid" routine.
• This can be an example of the use of level of
  detail in AI.

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Reacquiring Waypoints

• Do not have to worry about realism too much
• Crash and turn can work surprising well.
• If you want you could employ a local A.
• However, it does looks poor if an entity moves
  away from its target.

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Reacquiring Waypoints

• Do not necessarily return to the current
  movement node.
• Select the current and the next node in the
  tree.
• Choose the node closest to the target by
  reference to the direction of movement of the
  nodes.

• Direction of movement is 1 to 2.
• If in the green area, move to node 2.
• If in the beige area, move to node 1.