Syntriax.Engine/Engine.Core/Vector2D.cs

using System;

namespace Syntriax.Engine.Core;

/// <summary>
/// Represents a two-dimensional vector.
/// </summary>
[System.Diagnostics.DebuggerDisplay("{ToString(),nq}, Length: {Magnitude}, LengthSquared: {MagnitudeSquared}, Normalized: {Normalized.ToString(),nq}")]
public readonly struct Vector2D(float x, float y)
{
    /// <summary>
    /// The X coordinate of the <see cref="Vector2D"/>.
    /// </summary>
    public readonly float X = x;

    /// <summary>
    /// The Y coordinate of the <see cref="Vector2D"/>.
    /// </summary>
    public readonly float Y = y;

    /// <summary>
    /// The magnitude (length) of the <see cref="Vector2D"/>.
    /// </summary>
    public float Magnitude => Length(this);

    /// <summary>
    /// The squared magnitude (length) of the <see cref="Vector2D"/>.
    /// </summary>
    public float MagnitudeSquared => LengthSquared(this);

    /// <summary>
    /// The normalized form of the <see cref="Vector2D"/> (a <see cref="Vector2D"/> with the same direction and a magnitude of 1).
    /// </summary>
    public Vector2D Normalized => Normalize(this);

    /// <summary>
    /// Represents the unit <see cref="Vector2D"/> pointing upwards.
    /// </summary>
    public readonly static Vector2D Up = new(0f, 1f);

    /// <summary>
    /// Represents the unit <see cref="Vector2D"/> pointing downwards.
    /// </summary>
    public readonly static Vector2D Down = new(0f, -1f);

    /// <summary>
    /// Represents the unit <see cref="Vector2D"/> pointing leftwards.
    /// </summary>
    public readonly static Vector2D Left = new(-1f, 0f);

    /// <summary>
    /// Represents the unit <see cref="Vector2D"/> pointing rightwards.
    /// </summary>
    public readonly static Vector2D Right = new(1f, 0f);

    /// <summary>
    /// Represents the zero <see cref="Vector2D"/>.
    /// </summary>
    public readonly static Vector2D Zero = new(0f, 0f);

    /// <summary>
    /// Represents the <see cref="Vector2D"/> with both components equal to 1.
    /// </summary>
    public readonly static Vector2D One = new(1f, 1f);

    public static Vector2D operator -(Vector2D vector) => new(0f - vector.X, 0f - vector.Y);
    public static Vector2D operator +(Vector2D left, Vector2D right) => new(left.X + right.X, left.Y + right.Y);
    public static Vector2D operator -(Vector2D left, Vector2D right) => new(left.X - right.X, left.Y - right.Y);
    public static Vector2D operator *(Vector2D vector, float value) => new(vector.X * value, vector.Y * value);
    public static Vector2D operator *(float value, Vector2D vector) => new(vector.X * value, vector.Y * value);
    public static Vector2D operator /(Vector2D vector, float value) => new(vector.X / value, vector.Y / value);
    public static bool operator ==(Vector2D left, Vector2D right) => left.X == right.X && left.Y == right.Y;
    public static bool operator !=(Vector2D left, Vector2D right) => left.X != right.X || left.Y != right.Y;

    /// <summary>
    /// Calculates the length of the <see cref="Vector2D"/>.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <returns>The length of the <see cref="Vector2D"/>.</returns>
    public static float Length(Vector2D vector) => MathF.Sqrt(LengthSquared(vector));

    /// <summary>
    /// Calculates the squared length of the <see cref="Vector2D"/>.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <returns>The squared length of the <see cref="Vector2D"/>.</returns>
    public static float LengthSquared(Vector2D vector) => vector.X * vector.X + vector.Y * vector.Y;

    /// <summary>
    /// Calculates the distance between two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="from">The start <see cref="Vector2D"/>.</param>
    /// <param name="to">The end <see cref="Vector2D"/>.</param>
    /// <returns>The distance between the two <see cref="Vector2D"/>s.</returns>
    public static float Distance(Vector2D from, Vector2D to) => Length(FromTo(from, to));

    /// <summary>
    /// Inverts the direction of the <see cref="Vector2D"/>.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <returns>The inverted <see cref="Vector2D"/>.</returns>
    public static Vector2D Invert(Vector2D vector) => -vector;

    /// <summary>
    /// Adds two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The sum of the two <see cref="Vector2D"/>s.</returns>
    public static Vector2D Add(Vector2D left, Vector2D right) => left + right;

    /// <summary>
    /// Subtracts one <see cref="Vector2D"/> from another.
    /// </summary>
    /// <param name="left">The <see cref="Vector2D"/> to subtract from.</param>
    /// <param name="right">The <see cref="Vector2D"/> to subtract.</param>
    /// <returns>The result of subtracting the second <see cref="Vector2D"/> from the first.</returns>
    public static Vector2D Subtract(Vector2D left, Vector2D right) => left - right;

    /// <summary>
    /// Multiplies a <see cref="Vector2D"/> by a scalar value.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <param name="value">The scalar value.</param>
    /// <returns>The result of multiplying the <see cref="Vector2D"/> by the scalar value.</returns>
    public static Vector2D Multiply(Vector2D vector, float value) => vector * value;

    /// <summary>
    /// Divides a <see cref="Vector2D"/> by a scalar value.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <param name="value">The scalar value.</param>
    /// <returns>The result of dividing the <see cref="Vector2D"/> by the scalar value.</returns>
    public static Vector2D Divide(Vector2D vector, float value) => vector / value;

    /// <summary>
    /// Calculates the absolute value of each component of the vector.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/>.</param>
    /// <returns>The <see cref="Vector2D"/> with each component's absolute value.</returns>
    public static Vector2D Abs(Vector2D vector) => new(Math.Abs(vector.X), Math.Abs(vector.Y));

    /// <summary>
    /// Normalizes the <see cref="Vector2D"/> (creates a unit <see cref="Vector2D"/> with the same direction).
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/> to normalize.</param>
    /// <returns>The normalized <see cref="Vector2D"/>.</returns>
    public static Vector2D Normalize(Vector2D vector) => vector / Length(vector);

    /// <summary>
    /// Reflects a <see cref="Vector2D"/> off a surface with the specified normal.
    /// </summary>
    /// <param name="vector">The incident <see cref="Vector2D"/>.</param>
    /// <param name="normal">The normal <see cref="Vector2D"/> of the surface.</param>
    /// <returns>The reflected <see cref="Vector2D"/>.</returns>
    public static Vector2D Reflect(Vector2D vector, Vector2D normal) => vector - 2f * Dot(vector, normal) * normal;

    /// <summary>
    /// Calculates the <see cref="Vector2D"/> from one point to another.
    /// </summary>
    /// <param name="from">The starting point.</param>
    /// <param name="to">The ending point.</param>
    /// <returns>The <see cref="Vector2D"/> from the starting point to the ending point.</returns>
    public static Vector2D FromTo(Vector2D from, Vector2D to) => to - from;

    /// <summary>
    /// Scales a <see cref="Vector2D"/> by another <see cref="Vector2D"/> component-wise.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/> to scale.</param>
    /// <param name="scale">The <see cref="Vector2D"/> containing the scaling factors for each component.</param>
    /// <returns>The scaled <see cref="Vector2D"/>.</returns>
    public static Vector2D Scale(Vector2D vector, Vector2D scale) => new(vector.X * scale.X, vector.Y * scale.Y);

    /// <summary>
    /// Calculates a perpendicular <see cref="Vector2D"/> to the given <see cref="Vector2D"/>.
    /// </summary>
    /// <param name="vector">The input <see cref="Vector2D"/>.</param>
    /// <returns>A <see cref="Vector2D"/> perpendicular to the input <see cref="Vector2D"/>.</returns>
    public static Vector2D Perpendicular(Vector2D vector) => new(-vector.Y, vector.X);

    /// <summary>
    /// Rotates a <see cref="Vector2D"/> by the specified angle (in radians).
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/> to rotate.</param>
    /// <param name="angleInRadian">The angle to rotate by, in radians.</param>
    /// <returns>The rotated <see cref="Vector2D"/>.</returns>
    public static Vector2D Rotate(Vector2D vector, float angleInRadian) => new(MathF.Cos(angleInRadian) * vector.X - MathF.Sin(angleInRadian) * vector.Y, MathF.Sin(angleInRadian) * vector.X + MathF.Cos(angleInRadian) * vector.Y);

    /// <summary>
    /// Returns the component-wise minimum of two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The <see cref="Vector2D"/> containing the minimum components from both input <see cref="Vector2D"/>s.</returns>
    public static Vector2D Min(Vector2D left, Vector2D right) => new((left.X < right.X) ? left.X : right.X, (left.Y < right.Y) ? left.Y : right.Y);

    /// <summary>
    /// Returns the component-wise maximum of two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The <see cref="Vector2D"/> containing the maximum components from both input <see cref="Vector2D"/>s.</returns>
    public static Vector2D Max(Vector2D left, Vector2D right) => new((left.X > right.X) ? left.X : right.X, (left.Y > right.Y) ? left.Y : right.Y);

    /// <summary>
    /// Clamps each component of a <see cref="Vector2D"/> between the corresponding component of two other <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="vector">The <see cref="Vector2D"/> to clamp.</param>
    /// <param name="min">The <see cref="Vector2D"/> representing the minimum values for each component.</param>
    /// <param name="max">The <see cref="Vector2D"/> representing the maximum values for each component.</param>
    /// <returns>A <see cref="Vector2D"/> with each component clamped between the corresponding components of the min and max <see cref="Vector2D"/>s.</returns>
    public static Vector2D Clamp(Vector2D vector, Vector2D min, Vector2D max) => new(Math.Clamp(vector.X, min.X, max.X), Math.Clamp(vector.Y, min.Y, max.Y));

    /// <summary>
    /// Performs linear interpolation between two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="from">The starting <see cref="Vector2D"/> (t = 0).</param>
    /// <param name="to">The ending <see cref="Vector2D"/> (t = 1).</param>
    /// <param name="t">The interpolation parameter.</param>
    /// <returns>The interpolated <see cref="Vector2D"/>.</returns>
    public static Vector2D Lerp(Vector2D from, Vector2D to, float t) => from + FromTo(from, to) * t;

    /// <summary>
    /// Calculates the cross product of two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The cross product of the two <see cref="Vector2D"/>s.</returns>
    public static float Cross(Vector2D left, Vector2D right) => left.X * right.Y - left.Y * right.X;

    /// <summary>
    /// Calculates the angle between two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The angle between the two <see cref="Vector2D"/>s in radians.</returns>
    public static float Angle(Vector2D left, Vector2D right) => MathF.Acos(Dot(left, right) / (Length(left) * Length(right)));

    /// <summary>
    /// Calculates the dot product of two <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <returns>The dot product of the two <see cref="Vector2D"/>s.</returns>
    public static float Dot(Vector2D left, Vector2D right) => left.X * right.X + left.Y * right.Y;

    /// <summary>
    /// Determines the orientation of three points represented by <see cref="Vector2D"/>s.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="middle">The second <see cref="Vector2D"/>.</param>
    /// <param name="right">The third <see cref="Vector2D"/>.</param>
    /// <returns>
    /// <para>0 - Collinear.</para>
    /// <para>1 - Clockwise.</para>
    /// <para>2 - Counterclockwise.</para>
    /// </returns>
    public static int Orientation(Vector2D left, Vector2D middle, Vector2D right)
    {
        Vector2D leftToMiddle = left.FromTo(middle);
        Vector2D middleToRight = middle.FromTo(right);

        float value = leftToMiddle.Y * middleToRight.X -
                    leftToMiddle.X * middleToRight.Y;

        if (value > 0) return 1;
        if (value < 0) return 2;
        return 0;
    }

    /// <summary>
    /// Checks if two <see cref="Vector2D"/>s are approximately equal within a specified epsilon range.
    /// </summary>
    /// <param name="left">The first <see cref="Vector2D"/>.</param>
    /// <param name="right">The second <see cref="Vector2D"/>.</param>
    /// <param name="epsilon">The epsilon range.</param>
    /// <returns><see cref="true"/> if the <see cref="Vector2D"/>s are approximately equal; otherwise, <see cref="false"/>.</returns>
    public static bool ApproximatelyEquals(Vector2D left, Vector2D right, float epsilon = float.Epsilon)
        => left.X.ApproximatelyEquals(right.X, epsilon) && left.Y.ApproximatelyEquals(right.Y, epsilon);

    /// <summary>
    /// Converts the <see cref="Vector2D"/> to its string representation.
    /// </summary>
    /// <returns>A string representation of the <see cref="Vector2D"/>.</returns>
    public override string ToString() => $"{nameof(Vector2D)}({X}, {Y})";

    /// <summary>
    /// Determines whether the specified object is equal to the current <see cref="Vector2D"/>.
    /// </summary>
    /// <param name="obj">The object to compare with the current <see cref="Vector2D"/>.</param>
    /// <returns><see cref="true"/> if the specified object is equal to the current <see cref="Vector2D"/>; otherwise, <see cref="false"/>.</returns>
    public override bool Equals(object? obj) => obj is Vector2D objVec && X.Equals(objVec.X) && Y.Equals(objVec.Y);

    /// <summary>
    /// Generates a hash code for the <see cref="Vector2D"/>.
    /// </summary>
    /// <returns>A hash code for the <see cref="Vector2D"/>.</returns>
    public override int GetHashCode() => HashCode.Combine(X, Y);
}