Crate hierarchical_pathfinding

A crate to quickly approximate Paths on a Grid.

Introduction

Finding Paths on a Grid using regular A* and Dijkstra is usually a rather expensive Operation, since every Tile on the Grid is considered a Node, leading to those algorithms having to store and visit hundreds of Nodes for a fairly short Path. Combined with the fact that Grids usually have several Paths with the exact same Cost makes a naive implementation of regular Pathfinding Algorithms rather inefficient.

The idea behind Hierarchical Pathfinding is to improve that Process by collecting sections of the Grid into Chunks and pre-calculating and caching the cost (and possibly the Paths) of walking between the different entrances of the Chunk. The final process of finding a Path between two points can then use that knowledge by treating the Grid as a Graph with Entrances as Nodes and the cached costs (and Paths) as Edges, resulting in a much smaller Graph that can be easily searched.

Since the Graph is usually not an exact representation of the Grid, the resulting Paths will be slightly worse than the actual best Path (unless config.perfect_paths is set to true). This is usually not a problem, since the purpose of Hierarchical Pathfinding is to quickly find the next direction to go in or a Heuristic for the total Cost of a Path or to determine weather or not a Goal is reachable. All of these are not affected by the exact Cost or Path. The only time where the actual best Path would noticeably differ from this implementation's result is in the case of short Paths of roughly Length < 2 * chunk_size. That is why this implementation calls the regular A* search after HPA* confirmed the Path to be short. (This behavior can be turned of using the Config).

This crate provides an implementation of a Hierarchical Pathfinding Algorithm for any generic Grid. Paths can be searched using either A* for a Path to a single Tile, or Dijkstra for searching multiple Targets. It handles solid walls in the Grid and actually finding a Path that ends near a wall.

Examples

Creating the Cache:

use hierarchical_pathfinding::{prelude::*, Point};

// create and initialize Grid
// 0 = empty, 1 = swamp, 2 = wall
let mut grid = [
    [0, 2, 0, 0, 0],
    [0, 2, 2, 2, 0],
    [0, 1, 0, 0, 0],
    [0, 1, 0, 2, 0],
    [0, 0, 0, 2, 0],
];
let (width, height) = (grid.len(), grid[0].len());

let cost_map = [
    1,  // empty
    10, // swamp
    -1, // wall = solid
];

let mut pathfinding = PathCache::new(
    (width, height), // the size of the Grid
    |(x, y)| cost_map[grid[y][x]], // get the cost for walking over a Tile
    ManhattanNeighborhood::new(width, height), // the Neighborhood
    PathCacheConfig { chunk_size: 3, ..Default::default() }, // config
);

Note that the PathCache never actually asks for the Grid itself. This allows the user to store the Grid in any format they want (Array, Vec, HashMap, kd-tree, ...), as long as they are somehow able to access a specific (x, y) on the Grid when asked.

The provided function takes a Position on the Grid as parameter and returns, how "expensive" it is to walk across the Tile at that Position. This Cost is what will be used for calculating the Cost of a Path to find the most optimal one. A negative Cost implies that the Tile cannot be walked across.

Unfortunately, it is necessary to provide this function to every method of PathCache, since storing it would make the Grid immutable. See also Updating the PathCache.

Note: If copying the Cost function everywhere would create too much Code / less readable code, currying may be used:

const COST_MAP: [isize; 3] = [1, 10, -1];

// only references the Grid when called
fn cost_fn<'a>(grid: &'a [[usize; 5]; 5]) -> impl 'a + FnMut(Point) -> isize {
    move |(x, y)| COST_MAP[grid[y][x]]
}

let mut pathfinding = PathCache::new(
    (width, height), // the size of the Grid

    // simply call the creator function to take a reference of the Grid
    cost_fn(&grid),

    // ...
);

// ...

let path = pathfinding.find_path(
    start, goal,

    // function can be reused at any time
    cost_fn(&grid),

);

Pathfinding

Finding the Path to a single Goal:

let start = (0, 0);
let goal = (4, 4);

// find_path returns Some(Path) on success
let path = pathfinding.find_path(
    start,
    goal,
    cost_fn(&grid),
);

assert!(path.is_some());
let mut path = path.unwrap();

assert_eq!(path.cost(), 12);

For more information, see find_path.

Finding multiple Goals:

let start = (0, 0);
let goals = [(4, 4), (2, 0)];

// find_paths returns a HashMap<goal, Path> for all successes
let paths = pathfinding.find_paths(
    start,
    &goals,
    cost_fn(&grid),
);

// (4, 4) is reachable
assert!(paths.contains_key(&goals[0]));

// (2, 0) is not reachable
assert!(!paths.contains_key(&goals[1]));

For more information, see find_paths.

Using a Path

The easiest information obtainable from a Path is its existence. Despite being an approximation of an optimal Path, HPA* is 100% correct when it comes to the existence of a Path. Meaning that if HPA* cannot find a Path, no one can, and if HPA* returns a Path, it is valid, given correct Neighborhood and Cost functions.

The next step is to obtain information about the Path itself. The part that is always available is the total Cost of the Path. Once again, it is just an approximation. However, it gives a pretty good estimate of the actual Cost, with only minimal deviations.

As for following the Path, HPA* was designed to allow Units to immediately start moving and minimize lost time when the surroundings change in a way that alters the Path. That is why it does not calculate the full Path immediately. It does, however, generate the first steps of the Path without too much overhead. That is why it is advised to mostly use the next() method of the returned Path for a few steps.

let mut player = Player {
    pos: (0, 0),
    //...
};
let goal = (4, 4);

let mut path = pathfinding.find_path(
    player.pos,
    goal,
    cost_fn(&grid),
).unwrap();

player.move_to(path.next().unwrap());
assert_eq!(player.pos, (0, 1));

// wait for next turn or whatever

player.move_to(path.next().unwrap());
assert_eq!(player.pos, (0, 2));

Updating the PathCache

The PathCache does not contain a copy or reference of the Grid for mutability and Ownership reasons. This means however, that the user is responsible for storing and maintaining both the Grid and the PathCache. It is also necessary to update the PathCache when the Grid has changed to keep it consistent:

let (start, goal) = ((0, 0), (2, 0));

let path = pathfinding.find_path(start, goal, cost_fn(&grid));
assert!(path.is_none());

grid[0][1] = 0;
grid[4][4] = 2;
 
assert_eq!(grid, [
    [0, 0, 0, 0, 0],
    [0, 2, 2, 2, 2],
    [0, 1, 0, 0, 0],
    [0, 1, 0, 2, 0],
    [0, 0, 0, 2, 2],
]);

pathfinding.tiles_changed(
    &[(1, 0), (4, 4)],
    cost_fn(&grid),
);

let path = pathfinding.find_path(start, goal, cost_fn(&grid));
assert!(path.is_some());

Configuration

The last parameter for PathCache::new is a PathCacheConfig object with different options to have more control over the generated PathCache. These options are mostly used to adjust the balance between Performance and Memory Usage, with the default values aiming more at Performance. The PathCacheConfig struct also provides defaults for low Memory Usage PathCacheConfig::LOW_MEM or best Performance PathCacheConfig::HIGH_PERFORMANCE

let mut pathfinding = PathCache::new(
    (width, height), // the size of the Grid
    cost_fn(&grid), // get the cost for walking over a Tile
    ManhattanNeighborhood::new(width, height), // the Neighborhood
    PathCacheConfig {
        chunk_size: 3,
        ..PathCacheConfig::LOW_MEM
    }
);

assert_eq!(pathfinding.config().chunk_size, 3);

Modules

generics	A Module for generic implementations.
neighbors	A crate with the most common Neighborhoods
prelude	The prelude for this crate.

Structs

AbstractPath	A Path that may not be fully calculated yet.
PathCache	A struct to store the Hierarchical Pathfinding information.
PathCacheConfig	Options for configuring the PathCache

Type Definitions

NodeID	The Type used to reference a Node in the abstracted Graph
Point	A shorthand for Points on the grid