sqrid

sqrid provides square grid coordinates and related operations, in a crate with zero dependencies.

It's easier to explain the features of this crate in terms of the types it provides:

• Qa: position, as absolute coordinates in a grid of fixed size. The dimensions of the grid are const generics type parameters; invalid coordinates can't be created.
• Qr: "movement", relative coordinates. These are the cardinal (and intercardinal) directions. Addition is implemented in the form of Qa + Qr = Option<Qa>, which can be None if the result is outside the grid.
• Grid: a Qa-indexed array.
• Gridbool: a bitmap-backed Qa-indexed grid of booleans.
• Sqrid: "factory" type that acts as an entry point to the fundamental types below and to algorithms.

Besides these fundamental types, as also have algorithm modules:

• bf: breadth-first iteration and search.
• astar: A* search that takes a destination Qa.
• ucs: uniform-cost search.

All basic types have the standard iter, iter_mut, extend, as_ref, and conversion operations that should be expected.

Fundamental types

Qa: absolute coordinates, position

The Qa type represents an absolute position in a square grid. The type itself receives the height and width of the grid as const generic parameter.

We should usually create a type alias for the grid size we are using:

use sqrid;

type Qa = sqrid::Qa<6, 7>;

We can only generate Qa instances that are valid - i.e. inside the grid. Some of the ways to create instances:

• Using one of the const associated items: Qa::FIRST and Qa::LAST; Qa::TOP_LEFT, etc.; Qa::CENTER.
• Using try_from with a (i16, i16) tuple or a tuple reference.
• Calling Qa::new, which checks the bounds in const contexts:

  type Qa = sqrid::Qa<6, 7>;
  const MY_FIRST : Qa = Qa::new::<3, 4>();
  

  The following, for instance, doesn't compile:

  type Qa = sqrid::Qa<6, 7>;
  const MY_FIRST : Qa = Qa::new::<12, 4>();
  

Qr: relative coordinates, direction, movement

The Qr type represents a relative movement of one square. It can only be one of the 8 cardinal and intercardinal directions: Qr::N, Qr::NE, Qr::E, Qr::SE, Qr::S, Qr::SW, Qr::W, Qr::NW.

It's a building block for paths, iterating on a Qa neighbors, etc. It effectively represents the edges in a graph where the Qa type represents nodes.

All functions that iterate on Qr values accept a boolean const argument that specifies whether the intercardinal directions (NE, SE, SW, NW) should be considered.

Grid: a Qa-indexed array

A Grid is a generic array that can be indexed by a Qa.

We can create the type from a suitable Sqrid type by using the grid_create macro. We can then interact with specific lines with Grid::line and Grid::line_mut, or with the whole underlying array with as_ref (see std::convert::AsRef) and as_mut (see std::convert::AsMut).

Usage example:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);
type Grid = sqrid::grid_create!(Sqrid, i32);

// The grid create macro above is currently equivalent to:
type Grid2 = sqrid::Grid<i32, { Sqrid::WIDTH }, { Sqrid::HEIGHT },
                              { (Sqrid::WIDTH * Sqrid::HEIGHT) as usize }>;

// We can create grids from iterators via `collect`:
let mut gridnums = (0..9).collect::<Grid>();

// Iterate on their members:
for i in &gridnums {
    println!("i {}", i);
}

// Change the members in a loop:
for i in &mut gridnums {
    *i *= 10;
}

// Iterate on (coordinate, member) tuples:
for (qa, &i) in gridnums.iter_qa() {
    println!("[{}] = {}", qa, i);
}

// And we can always use `as_ref` or `as_mut` to interact with the
// inner array directly. To reverse it, for example, with the
// [`std::slice::reverse`] function:
gridnums.as_mut().reverse();

Gridbool: a bitmap-backed Qa-indexed grid of booleans

The Gridbool is a compact abstraction of a grid of booleans.

The type itself can be created with gridbool_create macro. It's optimized for getting and setting values at specific coordinates, but we can also get all true/false coordinates with suboptimal performance - in this case, the time is proportional to the size of the grid and not to the quantity of true/false values.

Usage example:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);
type Gridbool = sqrid::gridbool_create!(Sqrid);

// We can create a gridbool from a Qa iterator via `collect`:
let mut gb = Qa::iter().filter(|qa| qa.is_corner()).collect::<Gridbool>();

// We can also set values from an iterator:
gb.set_iter_t(Qa::iter().filter(|qa| qa.is_side()));

// Iterate on the true/false values:
for b in gb.iter() {
    println!("{}", b);
}

// Iterate on the true coordinates:
for qa in gb.iter_t() {
    assert!(qa.is_side());
}

// Iterate on (coordinate, bool):
for (qa, b) in gb.iter_qa() {
    println!("[{}] = {}", qa, b);
}

Sqrid: entry point for algorithms

The Qa type and some methods on the Qr type require const generic arguments that usually don't change inside an application. Both Grid and Gridbool also require further arguments that can actually be derived from the width and height of the grid, but that have to be explicitly specified due to some Rust limitations.

To make the creation of these types easier, we provide the Sqrid type, which acumulates all const generic parameters and can be used to create the other types via macros.

Example usage:

type Sqrid = sqrid::sqrid_create!(4, 4, false);
type Qa = sqrid::qa_create!(Sqrid);
type Grid = sqrid::grid_create!(Sqrid, i32);
type Gridbool = sqrid::gridbool_create!(Sqrid);

Algorithms

Breadth-first traversal

The Sqrid::bf_iter function instantiates an iterator struct (BfIterator) that can be used to iterate coordinates in breadth-first order, from a given origin, using a provided function to evaluate a given Qa position + Qr direction into the next Qa position.

Example usage:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);

for (qa, qr) in Sqrid::bf_iter(sqrid::qaqr_eval, &Qa::CENTER)
                .flatten() {
    println!("breadth-first qa {} from {}", qa, qr);
}

Breadth-first search

Sqrid::bfs_path takes an origin, a movement function and a goal function, and figures out the shortest path to a goal by using a breadth-first iteration.

The function returns the Qa that fulfills the goal and a path in the form of a Vec<Qr>.

Example usage:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);

// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok((goal, path)) = Sqrid::bfs_path(
                              sqrid::qaqr_eval, &Qa::TOP_LEFT,
                              |qa| qa == Qa::BOTTOM_RIGHT) {
    println!("goal: {}, path: {:?}", goal, path);
}

A* search

Sqrid::astar_path takes a movement function, an origin and a destination, and figures out the shortest path by using A*.

The function returns path in the form of a Vec<Qr>.

Example usage:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);

// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok(path) = Sqrid::astar_path(sqrid::qaqr_eval, &Qa::TOP_LEFT,
                                    &Qa::BOTTOM_RIGHT) {
    println!("path: {:?}", path);
}

Uniform-cost search

Sqrid::ucs_path takes a movement-cost function, an origin and a destination, and figures out the path with the lowest cost by using uniform-cost search, which is essentially a variation of Dijkstra.

The function returns path in the form of a Vec<Qr>.

Example usage:

type Sqrid = sqrid::sqrid_create!(3, 3, false);
type Qa = sqrid::qa_create!(Sqrid);

fn traverse(position: Qa, direction: sqrid::Qr) -> Option<(Qa, usize)> {
    let next_position = (position + direction)?;
    let cost = 1;
    Some((next_position, cost))
}

// Generate the grid of "came from" directions from bottom-right to
// top-left:
if let Ok(path) = Sqrid::ucs_path(traverse, &Qa::TOP_LEFT,
                                  &Qa::BOTTOM_RIGHT) {
    println!("path: {:?}", path);
}