## path-finding

This library provides a variety of path finding and graph operations. Work in progress.

### 18 releases(5 breaking)

 0.8.0 Apr 21, 2023 Apr 16, 2023 Apr 9, 2023 Mar 31, 2023 Mar 29, 2023

#166 in Algorithms

77KB
1.5K SLoC

# Path finding library

This library will contain standard path finding algorithms and return the resulting graph object. You can search for paths in a graph based or grid based structure.

Currently supported:

• Construct graphs
• Graph operations
• Create grids
• Grid operations
• Create Minimum Spanning Tree (MST) from a graph
• Find path with Depth-First Search (DFS)
• With Bidirectional Breadth-First Search (BBFS)
• With the Dijkstra algorithm
• With the A* algorithm, with heuristic:
• Euclidean distance
• Manhattan distance
• TBC: with a Hierarchical Path-Finding A* (HPA*), with heuristic:
• Euclidean distance
• Manhattan distance

## How to use

At the moment, we have following major concepts:

• Edge
• Node
• Graph
• Vec3
• Grid

You only need to pass edges to the graph. The nodes are generated automatically. Each pathfinding method will accept a graph, and return a graph that only contains the edges and nodes of the result.

Alternatively, you can also create a graph if you provide an adjacency matrix. Edges and nodes will be generated automatically.

If you want to use the A* path-finding algorithm, please make sure to provide positional information for each node.

Additionally, we work on a support for each of those algorithms based on a 2D grid based structure.

### Create Graph

• Create Edge
``````pub fn your_function() {
graph::Edge::from(
0 /* edge index */,
0 /* source node */,
1 /* destination node */,
0.1, /* weight */
);
}
``````
• Create Graph from edges
``````pub fn your_function() {
graph::Graph::from(Vec::from([edge1, edge2]));
}
``````
• Create Graph from adjacency matrix
``````pub fn your_function() {
let mut matrix: &[&[f32]] = &[
&[0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 8.0, 0.0],
&[4.0, 0.0, 8.0, 0.0, 0.0, 0.0, 0.0, 11.0, 0.0],
&[0.0, 8.0, 0.0, 7.0, 0.0, 4.0, 0.0, 0.0, 2.0],
&[0.0, 0.0, 7.0, 0.0, 9.0, 14.0, 0.0, 0.0, 0.0],
&[0.0, 0.0, 0.0, 9.0, 0.0, 10.0, 0.0, 0.0, 0.0],
&[0.0, 0.0, 4.0, 14.0, 10.0, 0.0, 2.0, 0.0, 0.0],
&[0.0, 0.0, 0.0, 0.0, 0.0, 2.0, 0.0, 1.0, 6.0],
&[8.0, 11.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 7.0],
&[0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 6.0, 7.0, 0.0]
];

}
``````

### Graph operations

You may want to get some information or mutate the graph in some way. Therefore, the graph currently supports three functions for convenience operations or to provide data for a heuristic function.

#### sorted_by_weight_asc

``````pub fn your_function() {
let edges: Vec<Edge> = graph.sorted_by_weight_asc(); // will return a vector with edges ascending by weight
}
``````

#### offer_positions

``````pub fn your_function() {
// provide a hashmap, mapping the node id to a position - used for a* pathfinding heuristics
graph.offer_positions(HashMap::from([(1, Vec3::from(0.1, 0.2, 0.3))]));
}
``````

### Create Grid

• Create Grid from cost matrix

In some cases, such as 2D games, a grid based structure is advantageous. The grid can be created by passing a cost matrix to the construction function `::from`. At each entry of the matrix you provide an unsigned integer, indicating the effort it takes to move to this position from any neighbouring position. In the example below moving from position `(0, 0)`to position `(0, 1)` will require an effort, or require a cost, of 2. Equivalently, moving from `(2, 2)` to `(1, 1)` will incur a cost of 1. Based on this information, we want to provide a support for grid based structures in each path finding algorithm.

``````pub fn your_function() {
let grid = grid::Grid::from(&[
&[4.0, 2.0, 1.0],
&[2.0, 1.0, 0.0],
&[3.0, 4.0, 7.0]
]);
}
``````

### Grid operations

#### outside

Check if a position is outside the grid. Pass a coordinate to the function below.

``````pub fn your_function() {
grid.outside((0, 1));
}
``````

#### within

Check if a position is within the grid. Pass a coordinate to the function below.

``````pub fn your_function() {
grid.within((0, 1));
}
``````

#### node_id

Convert your coordinate to a node_id

``````pub fn your_function() {
grid.node_id((0, 1));
}
``````

#### cost

Retrieve the cost required to move to a provided node id

``````pub fn your_function() {
grid.cost(3);
}
``````

### Minimum spanning tree

``````pub fn your_function() {
let mst_graph = graph::minimum_spanning(graph);
}
``````

For graphs

``````pub fn your_function() {
let dfs = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(DepthFirstSearch {}) /* used algorithm */
);
}
``````

For grids

``````pub fn your_function() {
let dfs = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(DepthFirstSearch {}) /* used algorithm */
);
}
``````

For graphs

``````pub fn your_function() {
let bfs = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(BreadthFirstSearch {}) /* used algorithm */
);
}
``````

For grids

``````pub fn your_function() {
let dfs = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(BreadthFirstSearch {}) /* used algorithm */
);
}
``````

For graphs

``````pub fn your_function() {
let bi_bfs = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(BiBreadthFirstSearch {}) /* used algorithm */
);
}
``````

For grids

``````pub fn your_function() {
let bi_bfs = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(BiBreadthFirstSearch {}), /* used algorithm */
);
}
``````

For graphs

``````pub fn your_function() {
let dijkstra = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(Dijkstra {}) /* used algorithm */
);
}
``````

For grids

``````pub fn your_function() {
let bi_bfs = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(Dijkstra {}), /* used algorithm */
);
}
``````

You can use the A* path-finding algorithm by providing either an existing heuristic function as shown below. Or you provide your own heuristic function. In case you use an existing heuristic function, make sure to provide the positional information for the nodes.

For graphs

``````pub fn your_function_with_euclidean_distance() {
let a_star = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(AStar { heuristic: Box::from(euclidean_distance) }), /* used algorithm + euclidean distance heuristic function */
);
}
``````
``````pub fn your_function_with_manhattan_distance() {
let a_star = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(AStar { heuristic: Box::from(manhattan_distance) }), /* used algorithm + manhattan distance heuristic function */
);
}
``````

For grids

``````pub fn your_function_with_euclidean_distance() {
let a_star = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(AStar { heuristic: Box::from(euclidean_distance) }), /* used algorithm + euclidean distance heuristic function */
);
}
``````
``````pub fn your_function_with_manhattan_distance() {
let a_star = path::in_grid(
4 /* source */,
1 /* target */,
&grid,
Box::from(AStar { heuristic: Box::from(manhattan_distance) }), /* used algorithm + manhattan distance heuristic function */
);
}
``````

Similar to the A* path-finding algorithm, you can provide either an existing heuristic function as shown in the previous section. Or you provide your own heuristic function. In case you use an existing heuristic function, make sure to provide the positional information for the nodes.

In addition to the functionality of A*, this algorithm will require you to pass the graph to the Hierarchical A* instance. The reason is simple, the algorithm will divide the graph into segments on creation and cache information required in the subsequent path-finding process.

``````pub fn your_function_with_euclidean_distance() {
let a_star = path::in_graph(
4 /* source */,
1 /* target */,
&graph,
Box::from(HierarchicalAStar { heuristic, graph }), /* used algorithm and graph */
);
}
``````

~2.5MB
~49K SLoC