city-generation/Game/Assets/Scripts/Primitives/Vector2.cs

using System;
using System.Collections.Generic;
using System.Xml.Serialization;

namespace TransportGame.Primitives
{
    /// <summary>
    /// 2D vector
    /// </summary>
    public struct Vector2
    {
        #region Constant vectors

        /// <summary>
        /// Zero vector
        /// </summary>
        public static readonly Vector2 Zero = new Vector2(0, 0);

        /// <summary>
        /// Unit vector
        /// </summary>
        public static readonly Vector2 Unit = new Vector2(1, 0);

        #endregion

        #region Properties

        /// <summary>
        /// Gets the X component
        /// </summary>
        [XmlAttribute("x")]
        public float X { get; set; }

        /// <summary>
        /// Gets the Y component
        /// </summary>
        [XmlAttribute("y")]
        public float Y { get; set; }

        #endregion

        #region Constructor

        /// <summary>
        /// Initializes a vector2
        /// </summary>
        /// <param name="x">X component</param>
        /// <param name="y">Y component</param>
        public Vector2(float x, float y)
            : this()
        {
            X = x;
            Y = y; 
        }

        /// <summary>
        /// Gets the vector corresponding with specified angle (in radians)
        /// </summary>
        /// <param name="rads">Radians</param>
        /// <returns>Vector</returns>
        public static Vector2 FromRadians(float rads)
        {
            return new Vector2((float)Math.Cos(rads), (float)Math.Sin(rads));
        }

        /// <summary>
        /// Gets the vector corresponding with specified angle (in degrees)
        /// </summary>
        /// <param name="degs">Degrees</param>
        /// <returns>Vector</returns>
        public static Vector2 FromDegrees(float degs)
        {
            float rads = (degs * (float)Math.PI / 180f);
            return FromRadians(rads);
        }

        #endregion

        #region Properties (length, normalized)

        /// <summary>
        /// Gets the length of the vector
        /// </summary>
        public float Length
        {
            get
            {
                return (float)Math.Sqrt(LengthSq);
            }
        }

        /// <summary>
        /// Gets the length of the vector squared
        /// </summary>
        public float LengthSq
        {
            get
            {
                return X * X + Y * Y;
            }
        }

        /// <summary>
        /// Gets the normalized vector
        /// </summary>
        /// <returns>Normalized vector</returns>
        public Vector2 Normalized
        {
            get
            {
                float len = Length;
                return new Vector2(X / len, Y / len);
            }
        }

        /// <summary>
        /// Gets the normalized vector raised to second power
        /// </summary>
        /// <remarks>
        /// This is less computationally expensive (no need to calculate square root).
        /// </remarks>
        /// <returns>Normalized vector</returns>
        public Vector2 NormalizedSq
        {
            get
            {
                float len2 = LengthSq;
                return new Vector2(X * X / len2, Y * Y / len2);
            }
        }

        #endregion

        #region Operations

        /// <summary>
        /// Rotates vector by given number of radians
        /// </summary>
        /// <param name="radians"></param>
        /// <returns></returns>
        public Vector2 Rotate(float radians)
        {
            float sin = (float)Math.Sin(radians);
            float cos = (float)Math.Cos(radians);

            return new Vector2(X * cos - Y * sin, X * sin + Y * cos);
        }

        /// <summary>
        /// Rotates vector by given number of degrees
        /// </summary>
        /// <param name="degrees"></param>
        /// <returns></returns>
        public Vector2 RotateDeg(float degrees)
        {
            return Rotate(degrees * (float)Math.PI / 180f);
        }

        /// <summary>
        /// Sum operator
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>Result of addition</returns>
        public static Vector2 operator +(Vector2 a, Vector2 b)
        {
            return new Vector2(a.X + b.X, a.Y + b.Y);
        }

        /// <summary>
        /// Subtract operator
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>Result of subtraction</returns>
        public static Vector2 operator -(Vector2 a, Vector2 b)
        {
            return new Vector2(a.X - b.X, a.Y - b.Y);
        }

        /// <summary>
        /// Negation operator
        /// </summary>
        /// <param name="a">Vector</param>
        /// <returns>Negated vector</returns>
        public static Vector2 operator -(Vector2 a)
        {
            return new Vector2(-a.X, -a.Y);
        }

        /// <summary>
        /// Multiply by constant
        /// </summary>
        /// <param name="a">Vector</param>
        /// <param name="c">Constant</param>
        /// <returns>Result</returns>
        public static Vector2 operator *(Vector2 a, float c)
        {
            return new Vector2(a.X * c, a.Y * c);
        }

        /// <summary>
        /// Multiply by constant
        /// </summary>
        /// <param name="c">Constant</param>
        /// <param name="a">Vector</param>
        /// <returns>Result</returns>
        public static Vector2 operator *(float c, Vector2 a)
        {
            return new Vector2(a.X * c, a.Y * c);
        }

        /// <summary>
        /// Divide by constant
        /// </summary>
        /// <param name="a">Vector</param>
        /// <param name="c">Constant</param>
        /// <returns>Result</returns>
        public static Vector2 operator /(Vector2 a, float c)
        {
            return new Vector2(a.X / c, a.Y / c);
        }

        /// <summary>
        /// Equality operator
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>True if vectors are equal</returns>
        public static bool operator ==(Vector2 a, Vector2 b)
        {
            return a.X == b.X && a.Y == b.Y;
        }
        /// <summary>
        /// Inequality operator
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>True if vectors are not equal</returns>
        public static bool operator !=(Vector2 a, Vector2 b)
        {
            return a.X != b.X || a.Y != b.Y;
        }

        /// <summary>
        /// Calculates dot product of two vectors
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>Dot product</returns>
        public static float Dot(Vector2 a, Vector2 b)
        {
            return a.X * b.X + a.Y * b.Y;
        }

        /// <summary>
        /// Returns the magnitude of the cross product between the two vectors (z considered 0)
        /// </summary>
        /// <param name="a">First vector</param>
        /// <param name="b">Second vector</param>
        /// <returns>Magnitude of cross product</returns>
        public static float Cross(Vector2 a, Vector2 b)
        {
            return (a.X * b.Y) - (a.Y * b.X);
        }

        /// <summary>
        /// Tests if two vectors are colliniar
        /// </summary>
        /// <param name="a">a</param>
        /// <param name="b">b</param>
        /// <returns>True if vectors are colliniar</returns>
        public static bool AreColliniar(Vector2 a, Vector2 b)
        {
            return Math.Abs(Cross(a, b)) < 1e-12;
        }
        
        #endregion

        #region Object overrides

        /// <summary>
        /// Gets string representation of vector2
        /// </summary>
        /// <returns></returns>
        public override string ToString()
        {
            return String.Format("({0}, {1})", X, Y);
        }

        /// <summary>
        /// Tests if two vectors are equal.
        /// </summary>
        /// <param name="obj"></param>
        /// <returns></returns>
        public override bool Equals(object obj)
        {
            if (obj is Vector2)
            {
                Vector2 other = (Vector2)obj;
                return X == other.X && Y == other.Y;
            }

            return false;
        }

        /// <summary>
        /// Gets hash code of vector2
        /// </summary>
        /// <returns></returns>
        public override int GetHashCode()
        {
            return X.GetHashCode() * 29 + Y.GetHashCode();
        }

        #endregion

        #region Comparers

        private class LengthComparerImpl : IComparer<Vector2>
        {
            public int Compare(Vector2 a, Vector2 b)
            {
                if (a.LengthSq > b.LengthSq)
                    return 1;
                
                if (a.LengthSq < b.LengthSq)
                    return -1;

                return 0;
            }
        }

        private class TrigonometricComparerImpl : IComparer<Vector2>
        {
            private int Quad(Vector2 v)
            {
                if (v.Y >= 0)
                {
                    if (v.X >= 0)
                        return 0;
                    return 1;
                }
                else
                {
                    if (v.X < 0)
                        return 2;
                    return 3;
                }
            }

            public int Compare(Vector2 a, Vector2 b)
            {
                // If vectors are in different quadrants, we can use quadrant number
                int qa = Quad(a), qb = Quad(b);
                
                if (qa != qb)
                {
                    return qa - qb;
                }

                // In same quadrant. Compute cross product which gives us sin(ab)*len(a)*len(b)
                // Vectors are in same quadrant, so angle should be less than 90deg
                float cross = Cross(a, b);
                if (cross < 0)  // Angle > 180 degrees => a > b
                    return 1;
                if (cross > 0)  // Angle < 180 degrees => a < b
                    return -1;

                // Points are on the same line. Use distance
                if (a.LengthSq > b.LengthSq)
                    return 1;
                else if (a.LengthSq < b.LengthSq)
                    return -1;

                // Points are equal
                return 0;
            }
        }

        /// <summary>
        /// Length comparer - compares vectors by length
        /// </summary>
        public static readonly IComparer<Vector2> LengthComparer = new LengthComparerImpl();

        /// <summary>
        /// Trigonometric comparer - compares vectors by angle
        /// </summary>
        public static readonly IComparer<Vector2> TrigonometricComparer = new TrigonometricComparerImpl();

        #endregion
    }
}