Scurry

An A-star 2D polygon map search implementation and set of polygon, geometry and vector utility functions for Elixir.

Quickstart

Wx Demo

Start a wxwidgets demo of a-star by running Scurry.Wx.start();

$ mix deps.get
$ mix compile
$ iex -S mix
Erlang/OTP 25 [erts-13.1.3] [source] [64-bit] [smp:8:8] [ds:8:8:10] [async-threads:1] [jit:ns] [dtrace]

Interactive Elixir (1.14.2) - press Ctrl+C to exit (type h() ENTER for help)
iex(1)> Scurry.Wx.start()

The start point is a green crosshair.
The cursor position is a red crosshair if inside the main polution, gray if outside.
Moving the mouse will show a line from start to the cursor.
- It'll be green if the there's a line of sight.
- It'll be gray if not, and there'll be a small red crosshair at the first blockage, and small gray crosshair all subsequent blocks.
Holding down left mouse button will show full search graph in bright orange and a thick green path for the found path.
Releasing the left mouse button resets the start to there.
- You can place the start outside the main polygon.

How to use

Adding scurry to your list of dependencies in mix.exs:

def deps do
  [
    {:scurry, "~> 2.0"},
  ]
end

Then, update your dependencies:

$ mix deps.get

Internals

There's better API documentation than this see the hexdocs, especially see the quickstart.

mix docs
open doc/index.html

Vectors

In lib/vector.ex you'll find the basic vector operations (dot, cross, length, add/sub) needed. A vector is a tuple of numbers, {x, y}.

Lines

A line is a tuple of vectors, {{x1, y1}, {x2, y2}}.

Polygon

In lib/plygon.ex you'll find the various polygon related functions, such as line of sight, nearest point, convex etc.

A polygon is a list of vertices (nodes) that are {x, y} tuples that represent screen coordinates.

In elixir, it looks like

polygon = [{x, y}, {x, y}, ...]

The screen coordinate 0, 0 is upper left the x-axis goes left-to-right and y-axis top-to-bottom. Polygons must be defined clockwise and not-closed. This is important for convex/concave vertex checks.

Polygon map

The wxwidgets demo map is loaded from a json file, and looks like

{
  "polygons": [
    "main": [
      [x, y], [x, y], [x,y], ...
    ],
    "hole1": [
      [x, y], [x, y], [x,y], ...
    ],
    "hole2": [
      [x, y], [x, y], [x,y], ...
    ]
  ]
}

The main polygon is the primary walking area - as complex as it needs to be.

Subsequent polygons (not named main) are holes within it.

Polygons don't need to be closed (last [x, y] equals the first), this will be handled internally.

The polygon name isn't used internally, only to decide which polygon is the primary boundary and which are holes.

Graph

The A-star graph doesn't need to be a polygon map. It just needs to be map from node to a list of {node, cost} edges. Node just has to be a term that elixir can use as a map key.

For the 2D map search, it is a map from vertice to a list of {vertice, cost}. This is computed from the polygon map using a set of vertices. This set is composed of;

the main polygon's concave (pointing into the world)
the holes' convex (point out of the hole, into the world)

and PolygonMap.get_vertices/2 creates this.

vertices = [
  {x1, y1}=vertice1,
  {x2, y2}=vertice2,
  {x3, y3}=vertice3,
  ...
]

This is transformed to a graph (PolygonMap.create_graph/4) given the polygon, holes, vertices (from above) and cost function.

Assuming a cost_fun that has type vertice, vertice :: cost, the graph looks like;

graph = %{
  vertice1 => [
    vertice2, cost_fun(vertice1, vertice2),
    vertice3, cost_fun(vertice1, vertice3),
    vertice4, cost_fun(vertice1, vertice4),
  ],
  # When expressed as "vertice = {x, y}"
  {x1, x2} => [
    {{x2, y2}, cost_fun({x1, y2}, {x2, y2})},
    {{x3, y3}, cost_fun({x1, y2}, {x3, y3})},
    ...
  ],
  ...
}

Note: create_graph uses PolygonMap.is_line_of_sight?/3 to determine if two vertices should have an edge. This is currently not configurable or passed as a function.

The default cost_fun and heur_fun is the euclidean distance been the two points. The difference between the two is, cost_fun is used while computing the graph and heur_fun while computing the path. Typically they will be the same but that is dependent on use case.

cost_fun = fn a, b -> Vector.distance(a, b) end

A-star

In the context of A-star, we use the terminology node instead of vertice since we're describing graphs - not strictly polygons. In the example, each node is a polygon vertice (ie. {x, y}).

A node is opaque to the algorithm, it just uses them as keys for it's internal state maps and arguments to heur_fun. indexes.

The A-star algorithm main call is Astar.search/4 and takes.

graph to search. The graph should be constructed as

graph = %{
  node1 => [
    node2, cost_fun(node1, node2),
    node3, cost_fun(node1, node3),
    node4, cost_fun(node1, node4),
  ],
  # When expressed as "node = {x, y}"
  {x1, x2} => [
    {{x2, y2}, cost_fun({x1, y2}, {x2, y2})},
    {{x3, y3}, cost_fun({x1, y2}, {x3, y3})},
    ...
  ],
  ...
}

start and stop, the nodes to find a path between.
heur_fun function node, node :: cost computes the heuristic cost. The default is the euclidian distance.

fn a, b -> Vector.distance(a, b) end

The state it maintains and returns

shortest_path_tree, a map of edges, node_a => node_b, where node_b is the "previous" node from node_a that is the shortest path.
queue priority queue / list [node, node, ...] sorted on the cost (see f_cost below) of the path from start to node to stop.
frontier map of node => node (prev) that have been reached and edges yet to try and have been added to the queue. It's a map, so when we visit a node, we can add how we reached it to shortest_path_tree.
g_cost, map node => cost with the minimal current cost from the start to node. Each iteration compare the current node's g_cost against the value in the map. If it's less, we've found a shorter path to this node and update the g_cost map.
f_cost, map node => cost with the "total cost" of path from start, via node, to stop. This means the computed minimal cost from start to node (g_cost) plus the heuristic cost via heur_fun. This is used to reorder queue.

shortest_path_tree is the most relevant field, and can be converted to a path using Astar.path/1.

Within astar.ex, there's two steps; search & getting the path. search returns the full state, and path could be extended to return the cost along the path if needed. It can fetch this from g_cost.

eskil / scurry