Vector2.cs

// Unity C# reference source
// Copyright (c) Unity Technologies. For terms of use, see
// https://unity3d.com/legal/licenses/Unity_Reference_Only_License

using System;
using System.Runtime.InteropServices;

// Representation of 2D vectors and points.
[StructLayout(LayoutKind.Sequential)]
public struct Vector2 : IEquatable<Vector2>
{
    // X component of the vector.
    public float x;
    // Y component of the vector.
    public float y;

    // Access the /x/ or /y/ component using [0] or [1] respectively.
    public float this[int index]
    {
        get
        {
            switch (index)
            {
                case 0: return x;
                case 1: return y;
                default:
                    throw new IndexOutOfRangeException("Invalid Vector2 index!");
            }
        }

        set
        {
            switch (index)
            {
                case 0: x = value; break;
                case 1: y = value; break;
                default:
                    throw new IndexOutOfRangeException("Invalid Vector2 index!");
            }
        }
    }

    // Constructs a new vector with given x, y components.
    public Vector2(float x, float y) { this.x = x; this.y = y; }

    // Set x and y components of an existing Vector2.
    public void Set(float newX, float newY) { x = newX; y = newY; }

    // Linearly interpolates between two vectors.
    public static Vector2 Lerp(Vector2 a, Vector2 b, float t)
    {
        t = Mathf.Clamp01(t);
        return new Vector2(
            a.x + (b.x - a.x) * t,
            a.y + (b.y - a.y) * t
        );
    }

    // Linearly interpolates between two vectors without clamping the interpolant
    public static Vector2 LerpUnclamped(Vector2 a, Vector2 b, float t)
    {
        return new Vector2(
            a.x + (b.x - a.x) * t,
            a.y + (b.y - a.y) * t
        );
    }

    // Moves a point /current/ towards /target/.
    public static Vector2 MoveTowards(Vector2 current, Vector2 target, float maxDistanceDelta)
    {
        Vector2 toVector = target - current;
        float dist = toVector.magnitude;
        if (dist <= maxDistanceDelta || dist == 0)
            return target;
        return current + toVector / dist * maxDistanceDelta;
    }

    // Multiplies two vectors component-wise.
    public static Vector2 Scale(Vector2 a, Vector2 b) { return new Vector2(a.x * b.x, a.y * b.y); }

    // Multiplies every component of this vector by the same component of /scale/.
    public void Scale(Vector2 scale) { x *= scale.x; y *= scale.y; }

    // Makes this vector have a ::ref::magnitude of 1.
    public void Normalize()
    {
        float mag = magnitude;
        if (mag > kEpsilon)
            this = this / mag;
        else
            this = zero;
    }

    // Returns this vector with a ::ref::magnitude of 1 (RO).
    public Vector2 normalized
    {
        get
        {
            Vector2 v = new Vector2(x, y);
            v.Normalize();
            return v;
        }
    }

    /// *listonly*
    public override string ToString() { return string.Format("({0:F1}, {1:F1})", x, y); }
    // Returns a nicely formatted string for this vector.
    public string ToString(string format)
    {
        return string.Format("({0}, {1})", x.ToString(format), y.ToString(format));
    }

    // used to allow Vector2s to be used as keys in hash tables
    public override int GetHashCode()
    {
        return x.GetHashCode() ^ (y.GetHashCode() << 2);
    }

    // also required for being able to use Vector2s as keys in hash tables
    public override bool Equals(object other)
    {
        if (!(other is Vector2)) return false;

        return Equals((Vector2)other);
    }

    public bool Equals(Vector2 other)
    {
        return x.Equals(other.x) && y.Equals(other.y);
    }

    public static Vector2 Reflect(Vector2 inDirection, Vector2 inNormal)
    {
        return -2F * Dot(inNormal, inDirection) * inNormal + inDirection;
    }

    public static Vector2 Perpendicular(Vector2 inDirection)
    {
        return new Vector2(-inDirection.y, inDirection.x);
    }

    // Dot Product of two vectors.
    public static float Dot(Vector2 lhs, Vector2 rhs) { return lhs.x * rhs.x + lhs.y * rhs.y; }

    // Returns the length of this vector (RO).
    public float magnitude { get { return Mathf.Sqrt(x * x + y * y); } }
    // Returns the squared length of this vector (RO).
    public float sqrMagnitude { get { return x * x + y * y; } }

    // Returns the angle in degrees between /from/ and /to/.
    public static float Angle(Vector2 from, Vector2 to)
    {
        // sqrt(a) * sqrt(b) = sqrt(a * b) -- valid for real numbers
        float denominator = Mathf.Sqrt(from.sqrMagnitude * to.sqrMagnitude);
        if (denominator < kEpsilonNormalSqrt)
            return 0F;

        float dot = Mathf.Clamp(Dot(from, to) / denominator, -1F, 1F);
        return Mathf.Acos(dot) * Mathf.Rad2Deg;
    }

    // Returns the signed angle in degrees between /from/ and /to/. Always returns the smallest possible angle
    public static float SignedAngle(Vector2 from, Vector2 to)
    {
        float unsigned_angle = Angle(from, to);
        float sign = Mathf.Sign(from.x * to.y - from.y * to.x);
        return unsigned_angle * sign;
    }

    // Returns the distance between /a/ and /b/.
    public static float Distance(Vector2 a, Vector2 b) { return (a - b).magnitude; }

    // Returns a copy of /vector/ with its magnitude clamped to /maxLength/.
    public static Vector2 ClampMagnitude(Vector2 vector, float maxLength)
    {
        if (vector.sqrMagnitude > maxLength * maxLength)
            return vector.normalized * maxLength;
        return vector;
    }

    // Returns a vector that is made from the smallest components of two vectors.
    public static Vector2 Min(Vector2 lhs, Vector2 rhs) { return new Vector2(Mathf.Min(lhs.x, rhs.x), Mathf.Min(lhs.y, rhs.y)); }

    // Returns a vector that is made from the largest components of two vectors.
    public static Vector2 Max(Vector2 lhs, Vector2 rhs) { return new Vector2(Mathf.Max(lhs.x, rhs.x), Mathf.Max(lhs.y, rhs.y)); }

    public static Vector2 SmoothDamp(Vector2 current, Vector2 target, ref Vector2 currentVelocity, float smoothTime, float maxSpeed)
    {
        float deltaTime = Time.deltaTime;
        return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, deltaTime);
    }

    public static Vector2 SmoothDamp(Vector2 current, Vector2 target, ref Vector2 currentVelocity, float smoothTime)
    {
        float deltaTime = Time.deltaTime;
        float maxSpeed = Mathf.Infinity;
        return SmoothDamp(current, target, ref currentVelocity, smoothTime, maxSpeed, deltaTime);
    }

    public static Vector2 SmoothDamp(Vector2 current, Vector2 target, ref Vector2 currentVelocity, float smoothTime, float maxSpeed, float deltaTime)
    {
        // Based on Game Programming Gems 4 Chapter 1.10
        smoothTime = Mathf.Max(0.0001F, smoothTime);
        float omega = 2F / smoothTime;

        float x = omega * deltaTime;
        float exp = 1F / (1F + x + 0.48F * x * x + 0.235F * x * x * x);
        Vector2 change = current - target;
        Vector2 originalTo = target;

        // Clamp maximum speed
        float maxChange = maxSpeed * smoothTime;
        change = ClampMagnitude(change, maxChange);
        target = current - change;

        Vector2 temp = (currentVelocity + omega * change) * deltaTime;
        currentVelocity = (currentVelocity - omega * temp) * exp;
        Vector2 output = target + (change + temp) * exp;

        // Prevent overshooting
        if (Dot(originalTo - current, output - originalTo) > 0)
        {
            output = originalTo;
            currentVelocity = (output - originalTo) / deltaTime;
        }

        return output;
    }

    // Adds two vectors.
    public static Vector2 operator+(Vector2 a, Vector2 b) { return new Vector2(a.x + b.x, a.y + b.y); }
    // Subtracts one vector from another.
    public static Vector2 operator-(Vector2 a, Vector2 b) { return new Vector2(a.x - b.x, a.y - b.y); }
    // Multiplies one vector by another.
    public static Vector2 operator*(Vector2 a, Vector2 b) { return new Vector2(a.x * b.x, a.y * b.y); }
    // Divides one vector over another.
    public static Vector2 operator/(Vector2 a, Vector2 b) { return new Vector2(a.x / b.x, a.y / b.y); }
    // Negates a vector.
    public static Vector2 operator-(Vector2 a) { return new Vector2(-a.x, -a.y); }
    // Multiplies a vector by a number.
    public static Vector2 operator*(Vector2 a, float d) { return new Vector2(a.x * d, a.y * d); }
    // Multiplies a vector by a number.
    public static Vector2 operator*(float d, Vector2 a) { return new Vector2(a.x * d, a.y * d); }
    // Divides a vector by a number.
    public static Vector2 operator/(Vector2 a, float d) { return new Vector2(a.x / d, a.y / d); }
    // Returns true if the vectors are equal.
    public static bool operator==(Vector2 lhs, Vector2 rhs)
    {
        // Returns false in the presence of NaN values.
        return (lhs - rhs).sqrMagnitude < kEpsilon * kEpsilon;
    }

    // Returns true if vectors are different.
    public static bool operator!=(Vector2 lhs, Vector2 rhs)
    {
        // Returns true in the presence of NaN values.
        return !(lhs == rhs);
    }

    // Converts a [[Vector3]] to a Vector2.
    public static implicit operator Vector2(Vector3 v)
    {
        return new Vector2(v.x, v.y);
    }

    // Converts a Vector2 to a [[Vector3]].
    public static implicit operator Vector3(Vector2 v)
    {
        return new Vector3(v.x, v.y, 0);
    }

    static readonly Vector2 zeroVector = new Vector2(0F, 0F);
    static readonly Vector2 oneVector = new Vector2(1F, 1F);
    static readonly Vector2 upVector = new Vector2(0F, 1F);
    static readonly Vector2 downVector = new Vector2(0F, -1F);
    static readonly Vector2 leftVector = new Vector2(-1F, 0F);
    static readonly Vector2 rightVector = new Vector2(1F, 0F);
    static readonly Vector2 positiveInfinityVector = new Vector2(float.PositiveInfinity, float.PositiveInfinity);
    static readonly Vector2 negativeInfinityVector = new Vector2(float.NegativeInfinity, float.NegativeInfinity);


    // Shorthand for writing @@Vector2(0, 0)@@
    public static Vector2 zero { get { return zeroVector; } }
    // Shorthand for writing @@Vector2(1, 1)@@
    public static Vector2 one { get { return oneVector; }   }
    // Shorthand for writing @@Vector2(0, 1)@@
    public static Vector2 up { get { return upVector; } }
    // Shorthand for writing @@Vector2(0, -1)@@
    public static Vector2 down { get { return downVector; } }
    // Shorthand for writing @@Vector2(-1, 0)@@
    public static Vector2 left { get { return leftVector; } }
    // Shorthand for writing @@Vector2(1, 0)@@
    public static Vector2 right { get { return rightVector; } }
    // Shorthand for writing @@Vector2(float.PositiveInfinity, float.PositiveInfinity)@@
    public static Vector2 positiveInfinity { get { return positiveInfinityVector; } }
    // Shorthand for writing @@Vector2(float.NegativeInfinity, float.NegativeInfinity)@@
    public static Vector2 negativeInfinity { get { return negativeInfinityVector; } }

    // *Undocumented*
    public const float kEpsilon = 0.00001F;
    // *Undocumented*
    public const float kEpsilonNormalSqrt = 1e-15f;
}