Rhomb.cs

using System;
using System.Collections.Generic;
using System.Linq;
using RT.Geometry;

namespace RT.Coordinates;

/// <summary>
///     <para>
///         Describes a cell in a <see cref="Grid"/>. Three cells of this kind form a hexagon, which in turn tiles the plane.</para></summary>
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public struct Rhomb : IEquatable<Rhomb>, INeighbor<Rhomb>, INeighbor<object>, IHasSvgGeometry
{
    /// <summary>The underlying hex tile. This rhomb forms one third of that hexagon.</summary>
    public Hex Hex { get; private set; }
    /// <summary>Which of the rhombs within the hexagon this is.</summary>
    public Position Pos { get; private set; }

    /// <summary>
    ///     Constructor.</summary>
    /// <param name="hex">
    ///     A hex tile to construct a rhomb from.</param>
    /// <param name="pos">
    ///     Which of the rhombs within the hexagon to construct.</param>
    public Rhomb(Hex hex, Position pos)
    {
        Hex = hex;
        Pos = pos;
    }

    /// <summary>
    ///     Constructor.</summary>
    /// <param name="q">
    ///     The Q coordinate of the hex tile to construct a rhomb from.</param>
    /// <param name="r">
    ///     The R coordinate of the hex tile to construct a rhomb from.</param>
    /// <param name="pos">
    ///     Which of the rhombs within the hexagon to construct.</param>
    public Rhomb(int q, int r, Position pos)
    {
        Hex = new Hex(q, r);
        Pos = pos;
    }

    /// <summary>Identifies one of the <see cref="Rhomb"/> cells that make up a hexagon.</summary>
    public enum Position
    {
        /// <summary>The rhomb in the top-right of the hexagon.</summary>
        TopRight,
        /// <summary>The rhomb in the bottom-right of the hexagon.</summary>
        BottomRight,
        /// <summary>The rhomb at the left of the hexagon.</summary>
        Left
    }

    /// <inheritdoc/>
    public readonly bool Equals(Rhomb rhomb) => Hex.Equals(rhomb.Hex) && Pos == rhomb.Pos;
    /// <inheritdoc/>
    public override readonly bool Equals(object obj) => obj is Rhomb rhomb && Hex.Equals(rhomb.Hex) && Pos == rhomb.Pos;
    /// <inheritdoc/>
    public override readonly int GetHashCode() => Hex.GetHashCode() * 3 + (int) Pos;

    /// <summary>Compares two <see cref="Rhomb"/> values for equality.</summary>
    public static bool operator ==(Rhomb one, Rhomb two) => one.Hex == two.Hex && one.Pos == two.Pos;
    /// <summary>Compares two <see cref="Rhomb"/> values for inequality.</summary>
    public static bool operator !=(Rhomb one, Rhomb two) => one.Hex != two.Hex || one.Pos != two.Pos;

    /// <inheritdoc/>
    public readonly IEnumerable<Rhomb> Neighbors
    {
        get
        {
            switch (Pos)
            {
                case Position.TopRight:
                    yield return new Rhomb(Hex.Move(Hex.Direction.Up), Position.BottomRight);
                    yield return new Rhomb(Hex.Move(Hex.Direction.UpRight), Position.Left);
                    yield return new Rhomb(Hex, Position.BottomRight);
                    yield return new Rhomb(Hex, Position.Left);
                    break;

                case Position.BottomRight:
                    yield return new Rhomb(Hex, Position.TopRight);
                    yield return new Rhomb(Hex.Move(Hex.Direction.DownRight), Position.Left);
                    yield return new Rhomb(Hex.Move(Hex.Direction.Down), Position.TopRight);
                    yield return new Rhomb(Hex, Position.Left);
                    break;

                case Position.Left:
                    yield return new Rhomb(Hex, Position.TopRight);
                    yield return new Rhomb(Hex, Position.BottomRight);
                    yield return new Rhomb(Hex.Move(Hex.Direction.DownLeft), Position.TopRight);
                    yield return new Rhomb(Hex.Move(Hex.Direction.UpLeft), Position.BottomRight);
                    break;

                default:
                    throw new InvalidOperationException($"{nameof(Pos)} has invalid value {Pos}.");
            }
        }
    }

    readonly IEnumerable<object> INeighbor<object>.Neighbors => Neighbors.Cast<object>();

    /// <inheritdoc/>
    public readonly IEnumerable<Edge> Edges => Vertices.MakeEdges();

    /// <summary>
    ///     Returns the vertices along the perimeter of this <see cref="Rhomb"/>, going clockwise from the vertex at the
    ///     center of <see cref="Hex"/>.</summary>
    public readonly Coordinates.Vertex[] Vertices => Pos switch
    {
        Position.TopRight => [
            new Vertex(Hex, Vertex.Position.Center),
            new Vertex(Hex, Vertex.Position.TopLeft),
            new Vertex(Hex, Vertex.Position.TopRight),
            new Vertex(Hex.Move(Hex.Direction.DownRight), Vertex.Position.TopLeft)
        ],
        Position.BottomRight => [
            new Vertex(Hex, Vertex.Position.Center),
            new Vertex(Hex.Move(Hex.Direction.DownRight), Vertex.Position.TopLeft),
            new Vertex(Hex.Move(Hex.Direction.Down), Vertex.Position.TopRight),
            new Vertex(Hex.Move(Hex.Direction.Down), Vertex.Position.TopLeft)
        ],
        Position.Left => [
            new Vertex(Hex, Vertex.Position.Center),
            new Vertex(Hex.Move(Hex.Direction.Down), Vertex.Position.TopLeft),
            new Vertex(Hex.Move(Hex.Direction.DownLeft), Vertex.Position.TopRight),
            new Vertex(Hex, Vertex.Position.TopLeft)
        ],
        _ => throw new InvalidOperationException($"{nameof(Pos)} has an invalid value of {Pos}.")
    };

    private static readonly PointD[] _ps = [new(.25, -.433012701892220), new(.25, .433012701892220), new(-.5, 0)];

    /// <inheritdoc/>
    public readonly PointD Center => Hex.Center * 2 + _ps[(int) Pos];

    private static readonly Position[] _rhombPositions = (Position[]) Enum.GetValues(typeof(Position));

    /// <summary>
    ///     Returns a collection of <see cref="Rhomb"/> tiles that form a larger hexagonal structure.</summary>
    /// <param name="sideLength">
    ///     Side length of the hexagon structure to produce.</param>
    public static IEnumerable<Rhomb> LargeHexagon(int sideLength) => Hex.LargeHexagon(sideLength).SelectMany(hex => _rhombPositions.Select(pos => new Rhomb(hex, pos)));

    /// <inheritdoc/>
    public override readonly string ToString() => $"R({Hex.Q},{Hex.R})/{(int) Pos}";

    /// <summary>
    ///     Describes a grid structure consisting of <see cref="Rhomb"/> cells that join up in groups of 3 to form hexagons,
    ///     which in turn tile the plane.</summary>
    public class Grid : Structure<Rhomb>
    {
        /// <summary>
        ///     See <see cref="Structure{TCell}.Structure(IEnumerable{TCell}, IEnumerable{Link{TCell}}, Func{TCell,
        ///     IEnumerable{TCell}})"/>.</summary>
        public Grid(IEnumerable<Rhomb> cells, IEnumerable<Link<Rhomb>> links = null, Func<Rhomb, IEnumerable<Rhomb>> getNeighbors = null)
            : base(cells, links, getNeighbors)
        {
        }

        /// <summary>
        ///     Constructs a <see cref="Grid"/> consisting of a hexagonal grid of the specified <paramref name="sideLength"/>.</summary>
        public Grid(int sideLength) : base(LargeHexagon(sideLength))
        {
        }

        /// <inheritdoc/>
        protected override Structure<Rhomb> makeModifiedStructure(IEnumerable<Rhomb> cells, IEnumerable<Link<Rhomb>> traversible) => new Grid(cells, traversible);

        /// <summary>See <see cref="Structure{TCell}.GenerateMaze(Random, MazeBias)"/>.</summary>
        public new Grid GenerateMaze(Random rnd = null, MazeBias bias = MazeBias.Default) => (Grid) base.GenerateMaze(rnd, bias);

        /// <summary>See <see cref="Structure{TCell}.GenerateMaze(Func{int, int, int}, MazeBias)"/>.</summary>
        public new Grid GenerateMaze(Func<int, int, int> rndNext, MazeBias bias = MazeBias.Default) => (Grid) base.GenerateMaze(rndNext, bias);
    }

    /// <summary>Describes one of the vertices of a <see cref="Rhomb"/>.</summary>
    public class Vertex(Hex hex, Vertex.Position pos) : Coordinates.Vertex
    {
        /// <summary>The <see cref="Hex"/> tile that this <see cref="Vertex"/> is within.</summary>
        public Hex Hex { get; private set; } = hex;
        /// <summary>Which position within the <see cref="Hex"/> this vertex is.</summary>
        public Position Pos { get; private set; } = pos;

        /// <summary>
        ///     Describes the position of a <see cref="Vertex"/> in relation to the vertices of its containing <see
        ///     cref="Hex"/>.</summary>
        public enum Position
        {
            /// <summary>Top-left vertex of the hex.</summary>
            TopLeft,
            /// <summary>Top-right vertex of the hex.</summary>
            TopRight,
            /// <summary>Centerpoint of the hex.</summary>
            Center
        }

        /// <inheritdoc/>
        public override bool Equals(object obj) => obj is Vertex rv && Hex.Equals(rv.Hex) && Pos == rv.Pos;
        /// <inheritdoc/>
        public override bool Equals(Coordinates.Vertex vertex) => vertex is Vertex rv && Hex.Equals(rv.Hex) && Pos == rv.Pos;
        /// <inheritdoc/>
        public override int GetHashCode() => Hex.GetHashCode() * 13 + (int) Pos;

        /// <inheritdoc/>
        public override PointD Point => new(
            Hex.Q * 1.5 + (Pos switch { Position.TopLeft => -.5, Position.TopRight => .5, Position.Center => 0, _ => throw new InvalidOperationException($"{nameof(Pos)} has invalid value {Pos}.") }),
            Hex.WidthToHeight * (Hex.Q + Hex.R * 2 + (Pos switch { Position.TopLeft => -1, Position.TopRight => -1, Position.Center => 0, _ => throw new InvalidOperationException($"{nameof(Pos)} has invalid value {Pos}.") })));
    }
}