Balanced Directions

Balanced Directions is a Rust crate for modeling directions and movements in a 3x3 grid using a balanced ternary-inspired logic. It can be viewed as a 2D ternary digit.

It provides tools to manipulate positions, paths, and directions on a grid-based structure, making it useful in scenarios requiring discrete grid movement, coordinated navigation, or 2D spatial logic.

Features

• Enum Representation (Balance):
  Represents positions in a 3x3 grid with easy access to their 2D vector representation.
• Grid Navigation:
  Convenient methods for grid-based movement operations (up, down, left, right) as well as rotations, flips, and vector transformations.
• Path Manipulation:
  A Path structure for modeling sequences of movements, offering utilities to normalize, reverse, and transform paths.
• Ternary Integration (Optional, active by default):
  Balanced-ternary-based coordinates when integrating with the balanced-ternary crate.
  Adds double balanced-ternary logic operations.
• #![no_std] Compatibility:
  A lightweight design for use in embedded or low-level systems.

Examples

Position Representation and Movement

The core Balance enum represents positions in a 3x3 grid. For example, you can easily identify positions such as TopLeft or Center. Use movement methods to perform grid operations.

use balanced_directions::Balance;

fn example_usage() {
    let position = Balance::TopLeft;
    assert_eq!(position.to_vector(), (-1, -1));

    let moved = position.right();
    assert_eq!(moved, Balance::Top);

    let rotated = moved.rotate_left();
    assert_eq!(rotated, Balance::Left);
    assert_eq!(rotated.to_angle(), Balance::WEST);
}

Path Representation and Manipulation

The Path structure enables you to work with sequences of grid movements.

use balanced_directions::{Balance, Path};

fn path_example() {
    let movements = vec![Balance::Top, Balance::Right, Balance::Bottom];
    let path = Path::new(movements);

    assert_eq!(path.len(), 3);
    assert_eq!(path.to_vector(), (1, 0)); // Cumulative movement: right by 1

    let movements = vec![Balance::Top, Balance::Top, Balance::Top, Balance::Bottom];
    let path = Path::new(movements);
    assert_eq!(path.to_vector(), (0, -2)); // Cumulative movement: top by 2
    let normalized_path = path.normalized();
    assert_eq!(normalized_path.to_vector(), (0, -2));
    assert_eq!(normalized_path.len(), 2);
}

Integration with Balanced Ternary

With the feature "ternary", you can convert grid positions to and from balanced ternary representations.

use balanced_directions::Balance;
use balanced_ternary::Digit;

fn ternary_example() {
    let position = Balance::Top;
    let ternary_pair = position.to_ternary_pair();
    assert_eq!(ternary_pair, (Digit::Zero, Digit::Neg)); // Top is represented as (0, -1)

    let recreated_position = Balance::from_ternary_pair(Digit::Zero, Digit::Neg);
    assert_eq!(recreated_position, Balance::Top);
    let possibly = recreated_position.possibly();
    assert_eq!(possibly, Balance::TopRight);
}

API Overview

Balance

The Balance enum represents nine positions of a 3x3 grid	As a 2D ternary digit its cases can be viewed as False/Unknown/True on 2 dimensions

Balance enum cases:

• TopLeft, Top, TopRight
• Left, Center, Right
• BottomLeft, Bottom, BottomRight

Operations:

A lot of operation can be performed with one (unary operations) or two (binary operations) Balance(s).

Below, the operation table of all Balance operations.

Unary directions

Moves with bounds (up, right, down, left) or wraps around (up_wrap, right_wrap, down_wrap, left_wrap).

Unary operations

Performs some useful transformations on a Balance (flip_h, neg, flip_v, not (transpose), rotate_left, rotate_right,center_h, center_v).

Double balanced-ternary logic

Shorthands for Digit operations :

• possibly, necessary, contingently,
• absolute_positive, positive, not_negative,
• not_positive, negative, absolute_negative,
• ht_not, post, pre.

Binary operations

Combines two Balances into one (add, mul, sub, and with the ternary feature : bitand, bitor, bitxor, k3_imply, ht_imply).

Path

A collection of Balance movements stored as steps in a sequence. Paths can be created, traversed, and normalized for efficient representation of cumulative movement.

Key Methods:

• Construction: new(), from_vector()
• Traversal: iter(), iter_mut()
• Transformation: normalized(), reversed(), each(), each_zip()

Cases

1. Grid-based Movement in Games Simulate and manipulate movements within 3x3 environments for character navigation, AI paths, or puzzle logic.
2. Embedded Robotics Applications Represent grid movements for sensor or actuator navigation without relying on the standard library.
3. Spatial Modeling or Math-based Algorithms Perform 2D spatial computations with a high-level abstraction for vector-based movements.

Documentation

The complete API documentation is available on docs.rs. It contains details on each type, method, and their use cases.

Related Libraries

• balanced-ternary: Provides balanced ternary number manipulations used for optional integration.

License

Copyright (c) 2025 Sébastien GELDREICH
Balanced Direction is licensed under the MIT License.