Liquid War (v5.6.4) - Core algorithm




Introduction
============


  General remarks
  ---------------

    If you have played Liquid War, you must have noticed that your army always
    takes the shortest way to reach the cursor. So the fundamental stuff in
    Liquid War is path-finding. Once you've done that the game is quite easy to
    code. Not harder than any other 2D game. Still the path finding algorithm
    is an interesting one, for it's not a common method that we used.

    Basically, at each round (by round I mean a game logical update, this
    occurs 10 or 100 times/sec depending on the level and/or your machine), the
    distance from all the points of the level to your cursor is calculated. Now
    the point is to calculate this fast, real fast. In fact, a "gradient" is
    calculated for all the points of the level, and the value of this gradient
    is the distance required for a little pixel/fighter to reach your cursor,
    assuming that he takes the shortest way. Liquid War does this with a 10%
    error tolerance, and it's enough for keeping the game interesting.

    Once you have this gradient calculated, it's not hard to move your
    fighters. Basically, you just have to move them toward the adjacent point
    that has the lowest gradient value, ie is the closest to your cursor.

  History
  -------

    The Liquid War algorithm has been invented by my friend Thomas Colcombet In
    fact the Liquid War algorithm has been invented before the game itself. The
    game came as a consequence of the algorithm, he just thought "mmm, cool, we
    could make a game with that!".

    Later, I enhanced the algorithm, as I coded it. The consequences were a
    performance increase, especially on simple but big levels. I mean levels
    with wide areas for teams to move. Still the basis of the algorithm
    remained the same.

  Pros
  ----

    The Liquid War algorithm for path-finding is very efficient:

    * When you have to move lots of different points toward one single point.
      Good thing that's the rule of Liquid War!

    * When you have no clue about how your map will look like, ie if the walls
      are randomly placed. The complexity of the level doesn't influence much
      the speed of the algorithm. The size does, but the complexity, ie the
      number of walls, is not so important.

  Cons
  ----

    The Liquid War algorithm is very poor compared to other algorithms when:

    * You have several target destinations, that's to say Liquid War would be
      really slow if there were 100 teams with 10 players only.

    * You want to move one single point only.

    * > You want the exact (100% sure) path. In fact, this algorithm finds
      solutions which approach the best one but you can never figure out if the
      solution you found is the best, and the algorithm never ends. In the long
      term, the algo will always find the best solution or something really
      close but I don't know any easy way to figure out when you have reached
      this state.



Mesh
====


  Introduction
  ------------

    The first Liquid War algorithm used to calculate the gradient (the distance
    from a point to your cursor) for every single point of the map.

    With Liquid War 5, I used a mesh system. This mesh system is a structure of
    squares connected together. Squares may be 1,2,4,8 or 16 units large or any
    nice value like that, and the gradient is only calculated once for each
    square. Squares have connections between them, and each connection is
    associated to a direction.

    There are 12 directions:

    * North-North-West (NNW)

    * North-West (NW)

    * West-North-West (WNW)

    * West-South-West (WSW)

    * South-West (SW)

    * South-South-West (SSW)

    * South-South-East (SSE)

    * South-East (SE)

    * East-South-East (ESE)

    * East-North-East (ENE)

    * North-East (NE)

    * North-North-East (NNE)

  Example
  -------

    Well, let me give you an example, supposing that you level structure is:

    **********
    *        *
    *        *
    *       **
    *        *
    **********

    The * represent walls, that's to say squares where fighters can not go.

    Then the mesh structure would be:

    **********
    *11112233*
    *11112233*
    *1111445**
    *i1114467*
    **********

    In this mesh, there are 7 zones:

    * zone 1 has a size of 4. It's linked with zones 2 (ENE) and 4 (ESE).

    * zone 2 has a size of 2. It's linked with zones 3 (ENE,ESE), 5 (SE), 4
      (SSE,SSW) and 1 (SW,WSW,WNW).

    * zone 3 has a size of 2. It's linked with zones 5 (SSW), 4 (SW) and 2
      (WSW,WNW).

    * zone 4 has a size of 2. It's linked with zones 2 (NNW,NNE), 4 (NE), 5
      (ENE), 6 (ESE) and 1 (WSW,WNW,NW).

    * zone 5 has a size of 1. It's linked with zones 3 (NNW,NNE,NE), 7 (SE), 6
      (SSE,SSW), 4 (SW,WSW,WNW) and 2 (NW).

    * zone 6 has a size of 1. It's linked with zones 5 (NNW,NNE), 7 (ENE,ESE)
      and 4 (WSW,WNW,NW).

    * zone 7 has a size of 1. It's linked with zones 5 (NW) and 6 (WSW,WNW).

  Why such a complicated structure?
  ---------------------------------

    Because it allows the module which calculates the gradient to work much
    faster. With this system, the number of zones is reduced a lot, and
    calculus on the mesh can go very fast. At the same time, this mesh
    structure is complicated to understand by us humans but it's very easy for
    the computer.



Gradient
========


  Introduction
  ------------

    For each zone defined in the mesh, LW calculates an estimation of the
    distance between the cursor and this zone.

    The algorihm is based on the fact that to cross a zone which size is n, n
    movements are required. Easy, eh?

  Description
  -----------

    Here's the way the algorithm works:

    for each turn of the game, do:

    * pick up a direction between the 12 defined directions. They have to be
      chosen is a peculiar order to avoid weird behaviors from fighters, but
      let's suppose we just pick up the "next" direction, ie if WSW was chosen
      the last time, we pick up WNW.

    and then for each zone in the mesh, do:

    * Compare the potential of the current zone with that of its neighbor zone.
      The neighbor zone to be chosen is the one which corresponds to the
      direction which has been previously picked up, and by potential I mean
      "the distance to the cursor, estimated by the algorithm's last pass".

    * If potential_of_the_neighbor_zone > (potential_of_the_current_zone +
      size_of_the_current_zone) then potentiel_of_the_neighbor_zone =
      potential_of_the_current_zone + size_of_the_current_zone

  How can this work?
  ------------------

    Well, just ask my friend thom-Thom, he's the one who had the idea of this
    algorithm!

    The basic idea is that by applying this simple rule to all the zones, after
    a certain amount of time, it's impossible to find any place in the mesh
    where the rule is not respected. And at this time, one can consider the
    potiential is right in any point.

    Of course when the cursor moves the potential has to be recalculated, but
    you see, cursors move really slowly in Liquid War, so the algorithm has
    plenty of time to find a new stable solution...

  Demo
  ----

    It's possible to see this algorithm working by typing:

    ufootgrad[n]

    while playing, where [n] is the number of the team the gradient of which
    you want to view. The game is still running but you view a team's gradient
    being calculated in real time instead of seeing the fighters.

    If you type ufootgrad0 the display comes back to normal mode.



Move
====


  Introduction
  ------------

    Once the gradient is calculated for any zone on the battlefield, it's quite
    easy to move the fighters, hey?

    The following method is used to move the players:

    * A "main direction" is chosen for the fighter, this direction is chosen
      using the gradient calculated on the mesh.

    * Knowing which direction is the main one, a "level of interest" is applied
      to the 12 defined directions.

    There are 4 "level of interest" for directions:

    * Main directions: the direction calculated.

    * Good directions: these directions should lead the fighter to the cursor.

    * Acceptable directions: ok, one can use this direction, since the fighter
      shouldn't loose any time using it.

    * Unpossible directions: wether there's a wall or using this direction
      means the fighter will be farer from his cursor than before, it always
      means that this direction will not be used, never.

  Rules
  -----

    The fighters will try to find any matching situation in this list, and
    chose the first one.

    * The main direction is available, no one on it, OK, let's follow it.

    * There's a good direction with no one on it, OK, let's follow it.

    * There's an acceptable direction with no one on it, OK, let's follow it.

    * The main direction is available, but there's an opponent on it, I attack!
      By attacking, one means that energy is drawned from the attacked fighter
      and transmitted to the attacker. When the attacked fighter dies, he
      belongs to the team which killed him.

    * A good direction is available, but there's an opponent on it, I attack!

    * The main direction is available, but there's a mate on it, I cure him.
      That's to say that energy is given to the mate. This way, when there's a
      big pool of fighters from the same team, they re-generate each other.

    * None of the previous situations found, do nothing.

  Tips and tricks
  ---------------

    The behavior of the armies is quite tricky to set up. I had myself to try
    many algorithms before I came to something nice. In fact, I had to
    introduce some "random" behaviors. They are not really random for I wanted
    the game to behave the same when given the same keyboard input, but for
    instance, fighters will prefer NNW to NNE sometimes, and NNE to NNW some
    other times. By the way, I think Liquid War could stand as a nice example
    of the thoery of chaos.

