using System;
using System.Collections.Generic;
using System.Drawing;

namespace BBIWARG.Utility
{
    /// <summary>
    /// Class with represents a vector or a point in 2 dimensional space.
    /// </summary>
    public class Vector2D
    {
        /// <summary>
        /// length of the vector, is initialized with -1 and will only be calculated if needed and only once
        /// </summary>
        private float length = -1;

        /// <summary>
        /// the null vector or origin
        /// </summary>
        public static Vector2D Zero { get { return new Vector2D(0, 0); } }

        /// <summary>
        /// X component as integer
        /// </summary>
        public int IntX { get { return (int)X; } }

        /// <summary>
        /// Y component as integer
        /// </summary>
        public int IntY { get { return (int)Y; } }

        /// <summary>
        /// length of the vector, computed in euclidean distance (2. norm)
        /// </summary>
        public float Length
        {
            get
            {
                if (length == -1)
                    length = (float)Math.Sqrt(X * X + Y * Y);
                return length;
            }
        }

        /// <summary>
        /// X (first) component
        /// </summary>
        public float X { get; private set; }

        /// <summary>
        /// Y (second) component
        /// </summary>
        public float Y { get; private set; }

        /// <summary>
        /// Standard constructor which sets the components.
        /// </summary>
        /// <param name="x">first component</param>
        /// <param name="y">second component</param>
        public Vector2D(float x, float y)
        {
            X = x;
            Y = y;
        }

        /// <summary>
        /// Constructor to create a Vector2D from a Point .
        /// </summary>
        /// <param name="point">a Point</param>
        public Vector2D(Point point)
        {
            X = point.X;
            Y = point.Y;
        }

        /// <summary>
        /// Constructor to create a Vector2D from a PointF.
        /// </summary>
        /// <param name="point">a PointF</param>
        public Vector2D(PointF point)
        {
            X = point.X;
            Y = point.Y;
        }

        /// <summary>
        /// Casts a Vector2D to Point.
        /// </summary>
        /// <param name="vec">a vector</param>
        /// <returns>a Point</returns>
        public static implicit operator Point(Vector2D vec)
        {
            return new Point(vec.IntX, vec.IntY);
        }

        /// <summary>
        /// Casts a Vector2D to PointF.
        /// </summary>
        /// <param name="vec">a vector</param>
        /// <returns>a PointF</returns>
        public static implicit operator PointF(Vector2D vec)
        {
            return new PointF(vec.X, vec.Y);
        }

        /// <summary>
        /// Computes the mean of two vectors.
        /// </summary>
        /// <param name="vectors">second vector</param>
        /// <returns>the mean vector</returns>
        public static Vector2D mean(List<Vector2D> vectors)
        {
            Vector2D sumVector = Vector2D.sum(vectors);
            return sumVector / vectors.Count;
        }

        /// <summary>
        /// Subtracts two vectors (component-by-component).
        /// </summary>
        /// <param name="vector1">the minuend</param>
        /// <param name="vector2">the subtrahend</param>
        /// <returns>the difference of the two vectors</returns>
        public static Vector2D operator -(Vector2D vector1, Vector2D vector2)
        {
            return new Vector2D(vector1.X - vector2.X, vector1.Y - vector2.Y);
        }

        /// <summary>
        /// Multiplies this vector component-by-component with a scalar value.
        /// </summary>
        /// <param name="scalar">the multiplier</param>
        /// <param name="vector">the multiplicand</param>
        /// <returns>multiplied vector (product)</returns>
        public static Vector2D operator *(float scalar, Vector2D vector)
        {
            return new Vector2D(scalar * vector.X, scalar * vector.Y);
        }

        /// <summary>
        /// Multiplies this vector component-by-component with a scalar value.
        /// </summary>
        /// <param name="vector">the multiplicand</param>
        /// <param name="scalar">the multiplier</param>
        /// <returns>multiplied vector (product)</returns>
        public static Vector2D operator *(Vector2D vector, float scalar)
        {
            return new Vector2D(scalar * vector.X, scalar * vector.Y);
        }

        /// <summary>
        /// Divides this vector with a scalar value.
        /// </summary>
        /// <param name="vector">this vector</param>
        /// <param name="scalar">the value</param>
        /// <returns>the divided vector</returns>
        public static Vector2D operator /(Vector2D vector, float scalar)
        {
            return new Vector2D(vector.X / scalar, vector.Y / scalar);
        }

        /// <summary>
        /// Divides on vector with another vector component-by-component.
        /// </summary>
        /// <param name="vector1">the dividend</param>
        /// <param name="vector2">the divisor</param>
        /// <returns>the component divided vector</returns>
        public static Vector2D operator /(Vector2D vector1, Vector2D vector2)
        {
            return new Vector2D(vector1.X / vector2.X, vector1.Y / vector2.Y);
        }

        /// <summary>
        /// Adds two vectors (component-by-component).
        /// </summary>
        /// <param name="vector1">first addend</param>
        /// <param name="vector2">second addend</param>
        /// <returns>sum of the vectors</returns>
        public static Vector2D operator +(Vector2D vector1, Vector2D vector2)
        {
            return new Vector2D(vector1.X + vector2.X, vector1.Y + vector2.Y);
        }

        /// <summary>
        /// Sums a list of vectors (component-by-component).
        /// </summary>
        /// <param name="vectors">a list of vectors</param>
        /// <returns>vector of summed components</returns>
        public static Vector2D sum(List<Vector2D> vectors)
        {
            Vector2D sumVector = new Vector2D(0, 0);
            foreach (Vector2D vector in vectors)
                sumVector += vector;

            return sumVector;
        }

        /// <summary>
        /// Copies this vector (clone).
        /// </summary>
        /// <returns>this vector as new vector</returns>
        public Vector2D copy()
        {
            return new Vector2D(X, Y);
        }

        /// <summary>
        /// Computes the cross product (determinant) of this vector and another vector.
        /// </summary>
        /// <param name="v">the other vector</param>
        /// <returns>cross product of this and v</returns>
        public float crossProduct(Vector2D v)
        {
            return X * v.Y - Y * v.X;
        }

        /// <summary>
        /// Computes the dot product of this vector and another vector.
        /// </summary>
        /// <param name="vector">the other vector</param>
        /// <returns>the dot product</returns>
        public float dotProduct(Vector2D vector)
        {
            return X * vector.X + Y * vector.Y;
        }

        /// <summary>
        /// Computes the absolute vector of this vector.
        /// </summary>
        /// <returns>absolute vector</returns>
        public Vector2D getAbsolute()
        {
            return new Vector2D(Math.Abs(X), Math.Abs(Y));
        }

        /// <summary>
        /// Computes the angle between this vector and another vector in radians.
        /// </summary>
        /// <param name="vector">a vector</param>
        /// <returns>angle in radians</returns>
        public float getAngleBetween(Vector2D vector)
        {
            return (float)Math.Acos(dotProduct(vector) / (Length * vector.Length));
        }

        /// <summary>
        /// Computes the euclidean distance between the point this vector describes and another point described by a Vector.
        /// </summary>
        /// <param name="point">a Point</param>
        /// <returns>euclidean distance</returns>
        public float getDistanceTo(Vector2D point)
        {
            return (this - point).Length;
        }

        /// <summary>
        /// Computes the inverse vector of this vector.
        /// </summary>
        /// <returns>inverse vector</returns>
        public Vector2D getInverse()
        {
            return new Vector2D(-X, -Y);
        }

        /// <summary>
        /// Computes a orthogonal vector of this vector, if side is true the X component will be switched, else the Y component.
        /// </summary>
        /// <param name="side">which vector</param>
        /// <returns>a orthogonal vector</returns>
        public Vector2D getOrthogonal(bool side = true)
        {
            if (side)
                return new Vector2D(Y, -X);
            else
                return new Vector2D(-Y, X);
        }

        /// <summary>
        /// Determines whether a this point is inside the boundaries of a given image or not.
        /// </summary>
        /// <param name="imageSize">a imageSize object</param>
        /// <returns>true iff point is inside the image boundaries</returns>
        public bool isInBound(ImageSize imageSize)
        {
            return isInBound(Vector2D.Zero, imageSize.MaxPixel);
        }

        /// <summary>
        /// Determines whether a point is inside a box. iff bottomRight is higher or more left than topLeft the result is false.
        /// </summary>
        /// <param name="topLeft">top left corner of the box</param>
        /// <param name="bottomRight">bottom right corner of the box</param>
        /// <returns>true iff point is in box</returns>
        public bool isInBound(Vector2D topLeft, Vector2D bottomRight)
        {
            return X >= topLeft.X && X <= bottomRight.X && Y >= topLeft.Y && Y <= bottomRight.Y;
        }

        /// <summary>
        /// Determines whether this point (vector) is inside a given box or not.
        /// </summary>
        /// <param name="corner1">first corner of the box</param>
        /// <param name="corner2">second corner of the box</param>
        /// <returns>true iff point is inside the box</returns>
        public bool isInBox(Vector2D corner1, Vector2D corner2)
        {
            float minX = Math.Min(corner1.X, corner2.X);
            float maxX = Math.Max(corner1.X, corner2.X);
            float minY = Math.Min(corner1.Y, corner2.Y);
            float maxY = Math.Max(corner1.Y, corner2.Y);
            return minX <= X && X <= maxX && minY <= Y && Y <= maxY;
        }

        /// <summary>
        /// Computes whether this vector and another vector point in opposite directions, meaning the smallest angle is between 90° and 180°.
        /// </summary>
        /// <param name="vector">a vector</param>
        /// <returns>true iff the vectors point in opposite directions</returns>
        public bool isInOppositeDirection(Vector2D vector)
        {
            return getAngleBetween(vector) > (Math.PI / 2);
        }

        /// <summary>
        /// Moves this vector along the direction vector factor times inside the imageSize, this point won't leave the image.
        /// </summary>
        /// <param name="imageSize">the size of the image</param>
        /// <param name="direction">the move direction</param>
        /// <param name="factor">the move factor</param>
        /// <returns>a point inside the image</returns>
        public Vector2D moveWithinBound(ImageSize imageSize, Vector2D direction, float factor)
        {
            Vector2D newPosition = this + factor * direction;
            if (!newPosition.isInBound(imageSize))
            {
                Vector2D inverseDirection = direction.getInverse().normalize();
                while (!newPosition.isInBound(imageSize))
                {
                    newPosition += inverseDirection;
                }
            }
            return newPosition;
        }

        /// <summary>
        /// Normalizes this vector with the euclidean norm (2. norm).
        /// </summary>
        /// <returns>normalized vector</returns>
        public Vector2D normalize()
        {
            return new Vector2D(X / Length, Y / Length);
        }

        /// <summary>
        /// Multiplies this vector component-by-component with another vector.
        /// </summary>
        /// <param name="v">the other vector</param>
        /// <returns>the component-by-component multiplied vector</returns>
        public Vector2D scale(Vector2D v)
        {
            return new Vector2D(X * v.X, Y * v.Y);
        }

        /// <summary>
        /// Creates a description of this vector.
        /// </summary>
        /// <returns>a string describing this vector</returns>
        public override string ToString()
        {
            return "(" + X + "|" + Y + ")";
        }
    }
}