Shaker/Veldrid/Agg/VectorMath/Vector3.cs

#region --- License ---

/*
Copyright (c) 2006 - 2008 The Open Toolkit library.

Permission is hereby granted, free of charge, to any person obtaining a copy of
this software and associated documentation files (the "Software"), to deal in
the Software without restriction, including without limitation the rights to
use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
of the Software, and to permit persons to whom the Software is furnished to do
so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

#endregion --- License ---

using System;
using System.Runtime.InteropServices;
using System.Linq;

using System.Collections.Generic;

namespace MatterHackers.VectorMath
{
	/// <summary>
	/// Represents a 3D vector using three double-precision floating-point numbers.
	/// </summary>
	
	[Serializable]
	[StructLayout(LayoutKind.Sequential)]
	public struct Vector3 : IEquatable<Vector3>
	{
		#region Fields

		/// <summary>
		/// The X component of the Vector3.
		/// </summary>
		public double X;

		/// <summary>
		/// The Y component of the Vector3.
		/// </summary>
		public double Y;

		/// <summary>
		/// The Z component of the Vector3.
		/// </summary>
		public double Z;

		#endregion Fields

		#region Constructors

		/// <summary>
		/// Constructs a new Vector3.
		/// </summary>
		/// <param name="x">The x component of the Vector3.</param>
		/// <param name="y">The y component of the Vector3.</param>
		/// <param name="z">The z component of the Vector3.</param>
		public Vector3(double x, double y, double z)
		{
			this.X = x;
			this.Y = y;
			this.Z = z;
		}

		/// <summary>
		/// Constructs a new instance from the given Vector2d.
		/// </summary>
		/// <param name="v">The Vector2d to copy components from.</param>
		public Vector3(Vector2 v, double z = 0)
		{
			X = v.X;
			Y = v.Y;
			this.Z = z;
		}

		/// <summary>
		/// Constructs a new instance from the given Vector3d.
		/// </summary>
		/// <param name="v">The Vector3d to copy components from.</param>
		public Vector3(Vector3 v)
		{
			X = v.X;
			Y = v.Y;
			Z = v.Z;
		}

		public Vector3(Vector3Float v)
		{
			X = v.X;
			Y = v.Y;
			Z = v.Z;
		}

		public Vector3(double[] doubleArray)
		{
			X = doubleArray[0];
			Y = doubleArray[1];
			Z = doubleArray[2];
		}

		/// <summary>
		/// Constructs a new instance from the given Vector4d.
		/// </summary>
		/// <param name="v">The Vector4d to copy components from.</param>
		public Vector3(Vector4 v)
		{
			X = v.X;
			Y = v.Y;
			Z = v.Z;
		}



		#endregion Constructors

		#region Properties

		public double this[int index]
		{
			get
			{
				switch (index)
				{
					case 0:
						return X;

					case 1:
						return Y;

					case 2:
						return Z;

					default:
						return 0;
				}
			}

			set
			{
				switch (index)
				{
					case 0:
						X = value;
						break;

					case 1:
						Y = value;
						break;

					case 2:
						Z = value;
						break;

					default:
						throw new Exception();
				}
			}
		}

		public void Set(double x, double y, double z)
		{
			X = x;
			Y = y;
			Z = z;
		}

		#endregion Properties

		#region Public Members

		#region Instance

		#region public double Length

		/// <summary>
		/// Gets the length (magnitude) of the vector.
		/// </summary>
		/// <see cref="LengthFast"/>
		/// <seealso cref="LengthSquared"/>
		
		public double Length
		{
			get
			{
				return System.Math.Sqrt(X * X + Y * Y + Z * Z);
			}
		}

		public double DistanceToSegment(Vector3 start, Vector3 end)
		{
			var segmentDelta = end - start;
			var segmentLength = segmentDelta.Length;
			var segmentNormal = segmentDelta.GetNormal();
			var deltaToStart = this - start;
			var distanceFromStart = segmentNormal.Dot(deltaToStart);
			if (distanceFromStart >= 0 && distanceFromStart < segmentLength)
			{
				var perpendicular = segmentNormal.GetPerpendicular(new Vector3(0, 0, 1));
				var distanceFromLine = Math.Abs(deltaToStart.Dot(perpendicular));
				return distanceFromLine;
			}
			
			if (distanceFromStart < 0)
			{
				return deltaToStart.Length;
			}

			var deltaToEnd = this - end;
			return deltaToEnd.Length;
		}


		#endregion public double Length

		#region public double LengthSquared

		/// <summary>
		/// Gets the square of the vector length (magnitude).
		/// </summary>
		/// <remarks>
		/// This property avoids the costly square root operation required by the Length property. This makes it more suitable
		/// for comparisons.
		/// </remarks>
		/// <see cref="Length"/>
		/// <seealso cref="LengthFast"/>
		
		public double LengthSquared
		{
			get
			{
				return X * X + Y * Y + Z * Z;
			}
		}

		#endregion public double LengthSquared

		#region public void Normalize()

		/// <summary>
		/// Returns a normalized Vector of this.
		/// </summary>
		/// <returns></returns>
		public Vector3 GetNormal()
		{
			Vector3 temp = this;
			temp.Normalize();
			return temp;
		}

		/// <summary>
		/// Scales the Vector3d to unit length.
		/// </summary>
		public void Normalize()
		{
			double length = this.Length;
			if (length != 0)
			{
				double scale = 1.0 / this.Length;
				X *= scale;
				Y *= scale;
				Z *= scale;
			}
		}

		#endregion public void Normalize()

		public bool IsValid()
		{
			if (double.IsNaN(X) || double.IsInfinity(X)
				|| double.IsNaN(Y) || double.IsInfinity(Y)
				|| double.IsNaN(Z) || double.IsInfinity(Z))
			{
				return false;
			}

			return true;
		}

		#region public double[] ToArray()

		public double[] ToArray()
		{
			return new double[] { X, Y, Z };
		}

		#endregion public double[] ToArray()

		#endregion Instance

		#region Static

		#region Fields

		/// <summary>
		/// Defines a unit-length Vector3d that points towards the X-axis.
		/// </summary>
		public static readonly Vector3 UnitX = new Vector3(1, 0, 0);

		/// <summary>
		/// Defines a unit-length Vector3d that points towards the Y-axis.
		/// </summary>
		public static readonly Vector3 UnitY = new Vector3(0, 1, 0);

		/// <summary>
		/// /// Defines a unit-length Vector3d that points towards the Z-axis.
		/// </summary>
		public static readonly Vector3 UnitZ = new Vector3(0, 0, 1);

		/// <summary>
		/// Defines a zero-length Vector3.
		/// </summary>
		public static readonly Vector3 Zero = new Vector3(0, 0, 0);

		/// <summary>
		/// Defines an instance with all components set to 1.
		/// </summary>
		public static readonly Vector3 One = new Vector3(1, 1, 1);

		/// <summary>
		/// Defines an instance with all components set to positive infinity.
		/// </summary>
		public static readonly Vector3 PositiveInfinity = new Vector3(double.PositiveInfinity, double.PositiveInfinity, double.PositiveInfinity);

		/// <summary>
		/// Defines an instance with all components set to negative infinity.
		/// </summary>
		public static readonly Vector3 NegativeInfinity = new Vector3(double.NegativeInfinity, double.NegativeInfinity, double.NegativeInfinity);

		/// <summary>
		/// Defines the size of the Vector3d struct in bytes.
		/// </summary>
		public static readonly int SizeInBytes = Marshal.SizeOf(new Vector3());

		#endregion Fields

		#region Add

		/// <summary>
		/// Adds two vectors.
		/// </summary>
		/// <param name="a">Left operand.</param>
		/// <param name="b">Right operand.</param>
		/// <returns>Result of operation.</returns>
		public static Vector3 Add(Vector3 a, Vector3 b)
		{
			Add(ref a, ref b, out a);
			return a;
		}

		/// <summary>
		/// Adds two vectors.
		/// </summary>
		/// <param name="a">Left operand.</param>
		/// <param name="b">Right operand.</param>
		/// <param name="result">Result of operation.</param>
		public static void Add(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result = new Vector3(a.X + b.X, a.Y + b.Y, a.Z + b.Z);
		}

		#endregion Add

		#region Subtract

		/// <summary>
		/// Subtract one Vector from another
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <returns>Result of subtraction</returns>
		public static Vector3 Subtract(Vector3 a, Vector3 b)
		{
			Subtract(ref a, ref b, out a);
			return a;
		}

		/// <summary>
		/// Subtract one Vector from another
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <param name="result">Result of subtraction</param>
		public static void Subtract(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result = new Vector3(a.X - b.X, a.Y - b.Y, a.Z - b.Z);
		}

		#endregion Subtract

		#region Multiply

		/// <summary>
		/// Multiplies a vector by a scalar.
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <returns>Result of the operation.</returns>
		public static Vector3 Multiply(Vector3 vector, double scale)
		{
			Multiply(ref vector, scale, out vector);
			return vector;
		}

		/// <summary>
		/// Multiplies a vector by a scalar.
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <param name="result">Result of the operation.</param>
		public static void Multiply(ref Vector3 vector, double scale, out Vector3 result)
		{
			result = new Vector3(vector.X * scale, vector.Y * scale, vector.Z * scale);
		}

		/// <summary>
		/// Multiplies a vector by the components a vector (scale).
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <returns>Result of the operation.</returns>
		public static Vector3 Multiply(Vector3 vector, Vector3 scale)
		{
			Multiply(ref vector, ref scale, out vector);
			return vector;
		}

		/// <summary>
		/// Multiplies a vector by the components of a vector (scale).
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <param name="result">Result of the operation.</param>
		public static void Multiply(ref Vector3 vector, ref Vector3 scale, out Vector3 result)
		{
			result = new Vector3(vector.X * scale.X, vector.Y * scale.Y, vector.Z * scale.Z);
		}

		#endregion Multiply

		#region Divide

		/// <summary>
		/// Divides a vector by a scalar.
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <returns>Result of the operation.</returns>
		public static Vector3 Divide(Vector3 vector, double scale)
		{
			Divide(ref vector, scale, out vector);
			return vector;
		}

		/// <summary>
		/// Divides a vector by a scalar.
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <param name="result">Result of the operation.</param>
		public static void Divide(ref Vector3 vector, double scale, out Vector3 result)
		{
			Multiply(ref vector, 1 / scale, out result);
		}

		/// <summary>
		/// Divides a vector by the components of a vector (scale).
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <returns>Result of the operation.</returns>
		public static Vector3 Divide(Vector3 vector, Vector3 scale)
		{
			Divide(ref vector, ref scale, out vector);
			return vector;
		}

		/// <summary>
		/// Divide a vector by the components of a vector (scale).
		/// </summary>
		/// <param name="vector">Left operand.</param>
		/// <param name="scale">Right operand.</param>
		/// <param name="result">Result of the operation.</param>
		public static void Divide(ref Vector3 vector, ref Vector3 scale, out Vector3 result)
		{
			result = new Vector3(vector.X / scale.X, vector.Y / scale.Y, vector.Z / scale.Z);
		}

		#endregion Divide

		#region ComponentMin

		/// <summary>
		/// Calculate the component-wise minimum of two vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <returns>The component-wise minimum</returns>
		public static Vector3 ComponentMin(Vector3 a, Vector3 b)
		{
			a.X = a.X < b.X ? a.X : b.X;
			a.Y = a.Y < b.Y ? a.Y : b.Y;
			a.Z = a.Z < b.Z ? a.Z : b.Z;
			return a;
		}

		public static Vector3 Parse(string s)
		{
			var result = Vector3.Zero;

			var values = s.Split(',').Select(sValue =>
			{
				double.TryParse(sValue, out double number);
				return number;
			}).ToArray();

			for (int i = 0; i < Math.Min(3, values.Length); i++)
			{
				result[i] = values[i];
			}

			return result;
		}

		/// <summary>
		/// Calculate the component-wise minimum of two vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <param name="result">The component-wise minimum</param>
		public static void ComponentMin(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result.X = a.X < b.X ? a.X : b.X;
			result.Y = a.Y < b.Y ? a.Y : b.Y;
			result.Z = a.Z < b.Z ? a.Z : b.Z;
		}

		#endregion ComponentMin

		#region ComponentMax

		/// <summary>
		/// Calculate the component-wise maximum of two vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <returns>The component-wise maximum</returns>
		public static Vector3 ComponentMax(Vector3 a, Vector3 b)
		{
			a.X = a.X > b.X ? a.X : b.X;
			a.Y = a.Y > b.Y ? a.Y : b.Y;
			a.Z = a.Z > b.Z ? a.Z : b.Z;
			return a;
		}

		public static Vector3 ComponentMax(Vector3 a, double b)
		{
			a.X = a.X > b ? a.X : b;
			a.Y = a.Y > b ? a.Y : b;
			a.Z = a.Z > b ? a.Z : b;

			return a;
		}

		/// <summary>
		/// Calculate the component-wise maximum of two vectors
		/// </summary>
		/// <param name="a">First operand</param>
		/// <param name="b">Second operand</param>
		/// <param name="result">The component-wise maximum</param>
		public static void ComponentMax(ref Vector3 a, ref Vector3 b, out Vector3 result)
		{
			result.X = a.X > b.X ? a.X : b.X;
			result.Y = a.Y > b.Y ? a.Y : b.Y;
			result.Z = a.Z > b.Z ? a.Z : b.Z;
		}

		#endregion ComponentMax

		#region Min

		/// <summary>
		/// Returns the Vector3d with the minimum magnitude
		/// </summary>
		/// <param name="left">Left operand</param>
		/// <param name="right">Right operand</param>
		/// <returns>The minimum Vector3</returns>
		public static Vector3 Min(Vector3 left, Vector3 right)
		{
			return left.LengthSquared < right.LengthSquared ? left : right;
		}

		#endregion Min

		#region Max

		/// <summary>
		/// Returns the Vector3d with the minimum magnitude
		/// </summary>
		/// <param name="left">Left operand</param>
		/// <param name="right">Right operand</param>
		/// <returns>The minimum Vector3</returns>
		public static Vector3 Max(Vector3 left, Vector3 right)
		{
			return left.LengthSquared >= right.LengthSquared ? left : right;
		}

		#endregion Max

		#region Clamp

		/// <summary>
		/// Clamp a vector to the given minimum and maximum vectors
		/// </summary>
		/// <param name="vec">Input vector</param>
		/// <param name="min">Minimum vector</param>
		/// <param name="max">Maximum vector</param>
		/// <returns>The clamped vector</returns>
		public static Vector3 Clamp(Vector3 vec, Vector3 min, Vector3 max)
		{
			vec.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
			vec.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
			vec.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
			return vec;
		}

		/// <summary>
		/// Clamp a vector to the given minimum and maximum vectors
		/// </summary>
		/// <param name="vec">Input vector</param>
		/// <param name="min">Minimum vector</param>
		/// <param name="max">Maximum vector</param>
		/// <param name="result">The clamped vector</param>
		public static void Clamp(ref Vector3 vec, ref Vector3 min, ref Vector3 max, out Vector3 result)
		{
			result.X = vec.X < min.X ? min.X : vec.X > max.X ? max.X : vec.X;
			result.Y = vec.Y < min.Y ? min.Y : vec.Y > max.Y ? max.Y : vec.Y;
			result.Z = vec.Z < min.Z ? min.Z : vec.Z > max.Z ? max.Z : vec.Z;
		}

		#endregion Clamp

		#region Normalize

		/// <summary>
		/// Scale a vector to unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <returns>The normalized vector</returns>
		public static Vector3 Normalize(Vector3 vec)
		{
			double scale = 1.0 / vec.Length;
			vec.X *= scale;
			vec.Y *= scale;
			vec.Z *= scale;
			return vec;
		}

		/// <summary>
		/// Scale a vector to unit length
		/// </summary>
		/// <param name="vec">The input vector</param>
		/// <param name="result">The normalized vector</param>
		public static void Normalize(ref Vector3 vec, out Vector3 result)
		{
			double scale = 1.0 / vec.Length;
			result.X = vec.X * scale;
			result.Y = vec.Y * scale;
			result.Z = vec.Z * scale;
		}

		#endregion Normalize

		#region Utility

		/// <summary>
		/// Checks if 3 points are collinear (all lie on the same line).
		/// </summary>
		/// <param name="a"></param>
		/// <param name="b"></param>
		/// <param name="c"></param>
		/// <param name="epsilon"></param>
		/// <returns></returns>
		public static bool Collinear(Vector3 a, Vector3 b, Vector3 c, double epsilon = .000001)
		{
			// Return true if a, b, and c all lie on the same line.
			return Math.Abs((b - a).Cross(c - a).Length) < epsilon;
		}

		public static Vector3 Abs(Vector3 a)
		{
			return new Vector3(Math.Abs(a.X), Math.Abs(a.Y), Math.Abs(a.Z));
		}

		/// <summary>
		/// Given an arbitrary vector find a perpendicular from the infinite perpendiculars that are available
		/// </summary>
		/// <param name="a">The vector to find a perpendicular for</param>
		/// <returns>A perpendicular vector to a</returns>
		public Vector3 GetPerpendicular()
		{
			if (this.X != 0)
			{
				return new Vector3(-(this.Y + this.Z) / this.X, 1, 1);
			}
			else if (this.Y != 0)
			{
				return new Vector3(1, -(this.X + this.Z) / this.Y, 1);
			}
			else if (this.Z != 0)
			{
				return new Vector3(1, 1, -(this.X + this.Y) / this.Z);
			}

			// the input vector has no length (no vector is perpendicular to it)
			return default(Vector3);
		}

		public Vector3 GetPerpendicular(Vector3 b)
		{
			return GetPerpendicular(this, b);
		}

		public static Vector3 GetPerpendicular(Vector3 a, Vector3 b)
		{
			if (!Collinear(a, b, Zero))
			{
				return a.Cross(b);
			}
			else
			{
				Vector3 zOne = new Vector3(0, 0, 100000);
				if (!Collinear(a, b, zOne))
				{
					return Vector3Ex.Cross(a - zOne, b - zOne);
				}
				else
				{
					Vector3 xOne = new Vector3(1000000, 0, 0);
					return Vector3Ex.Cross(a - xOne, b - xOne);
				}
			}
		}

		#endregion Utility

		#region Lerp

		/// <summary>
		/// Returns a new Vector that is the linear blend of the 2 given Vectors
		/// </summary>
		/// <param name="a">First input vector</param>
		/// <param name="b">Second input vector</param>
		/// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
		/// <returns>a when blend=0, b when blend=1, and a linear combination otherwise</returns>
		public static Vector3 Lerp(Vector3 a, Vector3 b, double blend)
		{
			if (blend == 0)
			{
				return a;
			}
			if (blend == 1)
			{
				return b;
			}
			a.X = blend * (b.X - a.X) + a.X;
			a.Y = blend * (b.Y - a.Y) + a.Y;
			a.Z = blend * (b.Z - a.Z) + a.Z;
			return a;
		}

		/// <summary>
		/// Returns a new Vector that is the linear blend of the 2 given Vectors
		/// </summary>
		/// <param name="a">First input vector</param>
		/// <param name="b">Second input vector</param>
		/// <param name="blend">The blend factor. a when blend=0, b when blend=1.</param>
		/// <param name="result">a when blend=0, b when blend=1, and a linear combination otherwise</param>
		public static void Lerp(ref Vector3 a, ref Vector3 b, double blend, out Vector3 result)
		{
			result.X = blend * (b.X - a.X) + a.X;
			result.Y = blend * (b.Y - a.Y) + a.Y;
			result.Z = blend * (b.Z - a.Z) + a.Z;
		}

		#endregion Lerp

		#region Barycentric

		/// <summary>
		/// Interpolate 3 Vectors using Barycentric coordinates
		/// </summary>
		/// <param name="a">First input Vector</param>
		/// <param name="b">Second input Vector</param>
		/// <param name="c">Third input Vector</param>
		/// <param name="u">First Barycentric Coordinate</param>
		/// <param name="v">Second Barycentric Coordinate</param>
		/// <returns>a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise</returns>
		public static Vector3 BaryCentric(Vector3 a, Vector3 b, Vector3 c, double u, double v)
		{
			return a + u * (b - a) + v * (c - a);
		}

		/// <summary>Interpolate 3 Vectors using Barycentric coordinates</summary>
		/// <param name="a">First input Vector.</param>
		/// <param name="b">Second input Vector.</param>
		/// <param name="c">Third input Vector.</param>
		/// <param name="u">First Barycentric Coordinate.</param>
		/// <param name="v">Second Barycentric Coordinate.</param>
		/// <param name="result">Output Vector. a when u=v=0, b when u=1,v=0, c when u=0,v=1, and a linear combination of a,b,c otherwise</param>
		public static void BaryCentric(ref Vector3 a, ref Vector3 b, ref Vector3 c, double u, double v, out Vector3 result)
		{
			result = a; // copy

			Vector3 temp = b; // copy
			Subtract(ref temp, ref a, out temp);
			Multiply(ref temp, u, out temp);
			Add(ref result, ref temp, out result);

			temp = c; // copy
			Subtract(ref temp, ref a, out temp);
			Multiply(ref temp, v, out temp);
			Add(ref result, ref temp, out result);
		}

		#endregion Barycentric

		#region CalculateAngle

		/// <summary>
		/// Calculates the angle (in radians) between two vectors.
		/// </summary>
		/// <param name="first">The first vector.</param>
		/// <param name="second">The second vector.</param>
		/// <returns>Angle (in radians) between the vectors.</returns>
		/// <remarks>Note that the returned angle is never bigger than the constant Pi.</remarks>
		public static double CalculateAngle(Vector3 first, Vector3 second)
		{
			return System.Math.Acos((first.Dot(second)) / (first.Length * second.Length));
		}

		/// <summary>Calculates the angle (in radians) between two vectors.</summary>
		/// <param name="first">The first vector.</param>
		/// <param name="second">The second vector.</param>
		/// <param name="result">Angle (in radians) between the vectors.</param>
		/// <remarks>Note that the returned angle is never bigger than the constant Pi.</remarks>
		public static void CalculateAngle(ref Vector3 first, ref Vector3 second, out double result)
		{
			double temp;
			first.Dot(ref second, out temp);
			result = System.Math.Acos(temp / (first.Length * second.Length));
		}

		#endregion CalculateAngle

		#endregion Static

		#region Swizzle

		/// <summary>
		/// Gets or sets an OpenTK.Vector2d with the X and Y components of this instance.
		/// </summary>
		
		public Vector2 Xy { get { return new Vector2(X, Y); } set { X = value.X; Y = value.Y; } }

		#endregion Swizzle

		#region Operators

		/// <summary>
		/// Adds two instances.
		/// </summary>
		/// <param name="left">The first instance.</param>
		/// <param name="right">The second instance.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator +(Vector3 left, Vector3 right)
		{
			left.X += right.X;
			left.Y += right.Y;
			left.Z += right.Z;
			return left;
		}

		/// <summary>
		/// Subtracts two instances.
		/// </summary>
		/// <param name="left">The first instance.</param>
		/// <param name="right">The second instance.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator -(Vector3 left, Vector3 right)
		{
			left.X -= right.X;
			left.Y -= right.Y;
			left.Z -= right.Z;
			return left;
		}

		/// <summary>
		/// Negates an instance.
		/// </summary>
		/// <param name="vec">The instance.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator -(Vector3 vec)
		{
			vec.X = -vec.X;
			vec.Y = -vec.Y;
			vec.Z = -vec.Z;
			return vec;
		}

		/// <summary>
		/// Component wise multiply two vectors together, x*x, y*y, z*z.
		/// </summary>
		/// <param name="vecA"></param>
		/// <param name="vecB"></param>
		/// <returns></returns>
		public static Vector3 operator *(Vector3 vecA, Vector3 vecB)
		{
			vecA.X *= vecB.X;
			vecA.Y *= vecB.Y;
			vecA.Z *= vecB.Z;
			return vecA;
		}

		/// <summary>
		/// Multiplies an instance by a scalar.
		/// </summary>
		/// <param name="vec">The instance.</param>
		/// <param name="scale">The scalar.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator *(Vector3 vec, double scale)
		{
			vec.X *= scale;
			vec.Y *= scale;
			vec.Z *= scale;
			return vec;
		}

		/// <summary>
		/// Multiplies an instance by a scalar.
		/// </summary>
		/// <param name="scale">The scalar.</param>
		/// <param name="vec">The instance.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator *(double scale, Vector3 vec)
		{
			vec.X *= scale;
			vec.Y *= scale;
			vec.Z *= scale;
			return vec;
		}

		/// <summary>
		/// Creates a new vector which is the numerator divide by each component of the vector.
		/// </summary>
		/// <param name="numerator"></param>
		/// <param name="vec"></param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator /(double numerator, Vector3 vec)
		{
			return new Vector3((numerator / vec.X), (numerator / vec.Y), (numerator / vec.Z));
		}

		/// <summary>
		/// Divides an instance by a scalar.
		/// </summary>
		/// <param name="vec">The instance.</param>
		/// <param name="scale">The scalar.</param>
		/// <returns>The result of the calculation.</returns>
		public static Vector3 operator /(Vector3 vec, double scale)
		{
			double mult = 1 / scale;
			vec.X *= mult;
			vec.Y *= mult;
			vec.Z *= mult;
			return vec;
		}

		/// <summary>
		/// Compares two instances for equality.
		/// </summary>
		/// <param name="left">The first instance.</param>
		/// <param name="right">The second instance.</param>
		/// <returns>True, if left equals right; false otherwise.</returns>
		public static bool operator ==(Vector3 left, Vector3 right)
		{
			return left.Equals(right);
		}

		/// <summary>
		/// Compares two instances for inequality.
		/// </summary>
		/// <param name="left">The first instance.</param>
		/// <param name="right">The second instance.</param>
		/// <returns>True, if left does not equa lright; false otherwise.</returns>
		public static bool operator !=(Vector3 left, Vector3 right)
		{
			return !left.Equals(right);
		}

		#endregion Operators

		#region Overrides

		#region public override string ToString()

		/// <summary>
		/// Returns a System.String that represents the current Vector3.
		/// </summary>
		/// <returns></returns>
		public override string ToString()
		{
			return String.Format($"[{X:0.####}, {Y:0.####}, {Z:0.####}]");
		}

		#endregion public override string ToString()

		#region public override int GetHashCode()

		/// <summary>
		/// Returns the hashcode for this instance.
		/// </summary>
		/// <returns>A System.Int32 containing the unique hashcode for this instance.</returns>
		public override int GetHashCode()
		{
			return new { X, Y, Z }.GetHashCode();
		}

		/// <summary>
		/// return a 64 bit hash code proposed by Jon Skeet
		// http://stackoverflow.com/questions/8094867/good-gethashcode-override-for-list-of-foo-objects-respecting-the-order
		/// </summary>
		/// <returns></returns>
		public ulong GetLongHashCode(ulong hash = 14695981039346656037)
		{
			hash = Vector4.GetLongHashCode(X, hash);
			hash = Vector4.GetLongHashCode(Y, hash);
			hash = Vector4.GetLongHashCode(Z, hash);

			return hash;
		}

		#endregion public override int GetHashCode()

		#region public override bool Equals(object obj)

		/// <summary>
		/// Indicates whether this instance and a specified object are equal.
		/// </summary>
		/// <param name="obj">The object to compare to.</param>
		/// <returns>True if the instances are equal; false otherwise.</returns>
		public override bool Equals(object obj)
		{
			if (!(obj is Vector3))
				return false;

			return this.Equals((Vector3)obj);
		}

		/// <summary>
		/// Indicates whether this instance and a specified object are equal within an error range.
		/// </summary>
		/// <param name="OtherVector"></param>
		/// <param name="ErrorValue"></param>
		/// <returns>True if the instances are equal; false otherwise.</returns>
		public bool Equals(Vector3 OtherVector, double ErrorValue)
		{
			if ((X < OtherVector.X + ErrorValue && X > OtherVector.X - ErrorValue) &&
				(Y < OtherVector.Y + ErrorValue && Y > OtherVector.Y - ErrorValue) &&
				(Z < OtherVector.Z + ErrorValue && Z > OtherVector.Z - ErrorValue))
			{
				return true;
			}

			return false;
		}

		#endregion public override bool Equals(object obj)

		#endregion Overrides

		#endregion Public Members

		#region IEquatable<Vector3> Members

		/// <summary>Indicates whether the current vector is equal to another vector.</summary>
		/// <param name="other">A vector to compare with this vector.</param>
		/// <returns>true if the current vector is equal to the vector parameter; otherwise, false.</returns>
		public bool Equals(Vector3 other)
		{
			return
				X == other.X &&
				Y == other.Y &&
				Z == other.Z;
		}

		#endregion IEquatable<Vector3> Members

		#region IConvertable
		public TypeCode GetTypeCode()
		{
			throw new NotImplementedException();
		}

		public bool ToBoolean(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public char ToChar(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public sbyte ToSByte(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public byte ToByte(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public short ToInt16(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public ushort ToUInt16(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public int ToInt32(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public uint ToUInt32(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public long ToInt64(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public ulong ToUInt64(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public float ToSingle(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public double ToDouble(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public decimal ToDecimal(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public DateTime ToDateTime(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public string ToString(IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		public object ToType(Type conversionType, IFormatProvider provider)
		{
			throw new NotImplementedException();
		}

		#endregion IConvertable

		public static double ComponentMax(Vector3 vector3)
		{
			return Math.Max(vector3.X, Math.Max(vector3.Y, vector3.Z));
		}

		public static double ComponentMin(Vector3 vector3)
		{
			return Math.Min(vector3.X, Math.Min(vector3.Y, vector3.Z));
		}
	}

	public static class Vector3Ex
	{
		#region Dot

		/// <summary>
		/// Calculate the dot (scalar) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The dot product of the two inputs</returns>
		public static double Dot(this Vector3 left, Vector3 right)
		{
			return left.X * right.X + left.Y * right.Y + left.Z * right.Z;
		}

		public static float[] ToFloatArray(this List<Vector3> list)
        {
			var array = new float[list.Count * 3];

			for (var i=0; i<list.Count; i++)
            {
				array[i * 3 + 0] = (float)list[i].X;
				array[i * 3 + 1] = (float)list[i].Y;
				array[i * 3 + 2] = (float)list[i].Z;
            }

			return array;
        }

		/// <summary>
		/// Calculate the dot (scalar) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <param name="result">The dot product of the two inputs</param>
		public static void Dot(this Vector3 left, ref Vector3 right, out double result)
		{
			result = left.X * right.X + left.Y * right.Y + left.Z * right.Z;
		}

		#endregion Dot

		#region Cross

		/// <summary>
		/// Calculate the cross (vector) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The cross product of the two inputs</returns>
		public static Vector3 Cross(this Vector3 left, Vector3 right)
		{
			Vector3 result;
			left.Cross(ref right, out result);
			return result;
		}

		/// <summary>
		/// Calculate the cross (vector) product of two vectors
		/// </summary>
		/// <param name="left">First operand</param>
		/// <param name="right">Second operand</param>
		/// <returns>The cross product of the two inputs</returns>
		/// <param name="result">The cross product of the two inputs</param>
		public static void Cross(this Vector3 left, ref Vector3 right, out Vector3 result)
		{
			result = new Vector3(left.Y * right.Z - left.Z * right.Y,
				left.Z * right.X - left.X * right.Z,
				left.X * right.Y - left.Y * right.X);
		}

		#endregion Cross

		#region Transform

		/// <summary>Transform a direction vector by the given Matrix
		/// Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored.
		/// </summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector3 TransformVector(this Vector3 vec, Matrix4X4 mat)
		{
			return new Vector3(
				vec.Dot(new Vector3(mat.Column0)),
				vec.Dot(new Vector3(mat.Column1)),
				vec.Dot(new Vector3(mat.Column2)));
		}

		/// <summary>Transform a direction vector by the given Matrix
		/// Assumes the matrix has a bottom row of (0,0,0,1), that is the translation part is ignored.
		/// </summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <param name="result">The transformed vector</param>
		public static void TransformVector(this Vector3 vec, ref Matrix4X4 mat, out Vector3 result)
		{
			result.X = vec.X * mat.Row0.X +
					   vec.Y * mat.Row1.X +
					   vec.Z * mat.Row2.X;

			result.Y = vec.X * mat.Row0.Y +
					   vec.Y * mat.Row1.Y +
					   vec.Z * mat.Row2.Y;

			result.Z = vec.X * mat.Row0.Z +
					   vec.Y * mat.Row1.Z +
					   vec.Z * mat.Row2.Z;
		}

		/// This calculates the inverse of the given matrix, use TransformNormalInverse if you
		/// already have the inverse to avoid this extra calculation
		/// <param name="normal">The normal to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed normal</returns>
		public static Vector3 TransformNormal(this Vector3 normal, Matrix4X4 mat)
		{
			Vector3 result;
			TransformNormal(normal, ref mat, out result);
			return result;
		}

		/// <summary>Transform a Normal by the given Matrix</summary>
		/// <remarks>
		/// This calculates the inverse of the given matrix, use TransformNormal if you have
		/// a point on the plane (fastest) or TransformNormalInverse if you
		/// have the inverse but not a point on the plane - to avoid this extra calculation
		/// </remarks>
		/// <param name="normal">The normal to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <param name="result">The transformed normal</param>
		public static void TransformNormal(this Vector3 normal, ref Matrix4X4 mat, out Vector3 result)
		{
			Matrix4X4 Inverse = Matrix4X4.Invert(mat);
			TransformNormalInverse(normal, ref Inverse, out result);
		}

		/// <summary>Transform a Normal by the (transpose of the) given Matrix</summary>
		/// <remarks>
		/// This version doesn't calculate the inverse matrix.
		/// Use this version if you already have the inverse of the desired transform to hand
		/// </remarks>
		/// <param name="normal">The normal to transform</param>
		/// <param name="invMat">The inverse of the desired transformation</param>
		/// <returns>The transformed normal</returns>
		public static Vector3 TransformNormalInverse(this Vector3 normal, Matrix4X4 invMat)
		{
			return new Vector3(
				normal.Dot(new Vector3(invMat.Row0)),
				normal.Dot(new Vector3(invMat.Row1)),
				normal.Dot(new Vector3(invMat.Row2)));
		}

		/// <summary>Transform a Normal by the (transpose of the) given Matrix</summary>
		/// <remarks>
		/// This version doesn't calculate the inverse matrix.
		/// Use this version if you already have the inverse of the desired transform to hand
		/// </remarks>
		/// <param name="normal">The normal to transform</param>
		/// <param name="invMat">The inverse of the desired transformation</param>
		/// <param name="result">The transformed normal</param>
		public static void TransformNormalInverse(this Vector3 normal, ref Matrix4X4 invMat, out Vector3 result)
		{
			result.X = normal.X * invMat.Row0.X +
					   normal.Y * invMat.Row0.Y +
					   normal.Z * invMat.Row0.Z;

			result.Y = normal.X * invMat.Row1.X +
					   normal.Y * invMat.Row1.Y +
					   normal.Z * invMat.Row1.Z;

			result.Z = normal.X * invMat.Row2.X +
					   normal.Y * invMat.Row2.Y +
					   normal.Z * invMat.Row2.Z;
		}

		/// <summary>Transform a Position by the given Matrix</summary>
		/// <param name="pos">The position to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed position</returns>
		public static Vector3 TransformPosition(this Vector3 pos, Matrix4X4 mat)
		{
			return new Vector3(
				pos.Dot(new Vector3(mat.Column0)) + mat.Row3.X,
				pos.Dot(new Vector3(mat.Column1)) + mat.Row3.Y,
				pos.Dot(new Vector3(mat.Column2)) + mat.Row3.Z);
		}

		/// <summary>Transform a Position by the given Matrix</summary>
		/// <param name="pos">The position to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <param name="result">The transformed position</param>
		public static void TransformPosition(this Vector3 pos, ref Matrix4X4 mat, out Vector3 result)
		{
			result.X = pos.X * mat.Row0.X +
					   pos.Y * mat.Row1.X +
					   pos.Z * mat.Row2.X +
					   mat.Row3.X;

			result.Y = pos.X * mat.Row0.Y +
					   pos.Y * mat.Row1.Y +
					   pos.Z * mat.Row2.Y +
					   mat.Row3.Y;

			result.Z = pos.X * mat.Row0.Z +
					   pos.Y * mat.Row1.Z +
					   pos.Z * mat.Row2.Z +
					   mat.Row3.Z;
		}

		/// <summary>
		/// Transform all the vectors in the array by the given Matrix.
		/// </summary>
		/// <param name="boundsVerts"></param>
		/// <param name="rotationQuaternion"></param>
		public static void Transform(this Vector3[] vecArray, Matrix4X4 mat)
		{
			for (int i = 0; i < vecArray.Length; i++)
			{
				vecArray[i] = Transform(vecArray[i], mat);
			}
		}

		/// <summary>Transform a Vector by the given Matrix</summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector3 Transform(this Vector3 vec, Matrix4X4 mat)
		{
			return new Vector3(
				vec.X * mat.Row0.X + vec.Y * mat.Row1.X + vec.Z * mat.Row2.X + mat.Row3.X,
				vec.X * mat.Row0.Y + vec.Y * mat.Row1.Y + vec.Z * mat.Row2.Y + mat.Row3.Y,
				vec.X * mat.Row0.Z + vec.Y * mat.Row1.Z + vec.Z * mat.Row2.Z + mat.Row3.Z);
		}

		/// <summary>Transform a Vector by the given Matrix</summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <param name="result">The transformed vector</param>
		public static void Transform(this Vector3 vec, ref Matrix4X4 mat, out Vector3 result)
		{
			result = new Vector3(
				vec.X * mat.Row0.X + vec.Y * mat.Row1.X + vec.Z * mat.Row2.X + mat.Row3.X,
				vec.X * mat.Row0.Y + vec.Y * mat.Row1.Y + vec.Z * mat.Row2.Y + mat.Row3.Y,
				vec.X * mat.Row0.Z + vec.Y * mat.Row1.Z + vec.Z * mat.Row2.Z + mat.Row3.Z);
		}

		/// <summary>
		/// Transforms a vector by a quaternion rotation.
		/// </summary>
		/// <param name="vec">The vector to transform.</param>
		/// <param name="quat">The quaternion to rotate the vector by.</param>
		/// <returns>The result of the operation.</returns>
		public static Vector3 Transform(this Vector3 vec, Quaternion quat)
		{
			Vector3 result;
			Transform(vec, ref quat, out result);
			return result;
		}

		/// <summary>
		/// Transforms a vector by a quaternion rotation.
		/// </summary>
		/// <param name="vec">The vector to transform.</param>
		/// <param name="quat">The quaternion to rotate the vector by.</param>
		/// <param name="result">The result of the operation.</param>
		public static void Transform(this Vector3 vec, ref Quaternion quat, out Vector3 result)
		{
			// Since vec.W == 0, we can optimize quat * vec * quat^-1 as follows:
			// vec + 2.0 * cross(quat.xyz, cross(quat.xyz, vec) + quat.w * vec)
			Vector3 xyz = quat.Xyz, temp, temp2;
			xyz.Cross(ref vec, out temp);
			Vector3.Multiply(ref vec, quat.W, out temp2);
			Vector3.Add(ref temp, ref temp2, out temp);
			xyz.Cross(ref temp, out temp);
			Vector3.Multiply(ref temp, 2, out temp);
			Vector3.Add(ref vec, ref temp, out result);
		}

		/// <summary>
		/// Transform all the vectors in the array by the quaternion rotation.
		/// </summary>
		/// <param name="boundsVerts"></param>
		/// <param name="rotationQuaternion"></param>
		public static void Transform(this Vector3[] vecArray, Quaternion rotationQuaternion)
		{
			for (int i = 0; i < vecArray.Length; i++)
			{
				vecArray[i] = Transform(vecArray[i], rotationQuaternion);
			}
		}

		/// <summary>
		/// Transform a Vector3d by the given Matrix, and project the resulting Vector4 back to a Vector3
		/// </summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <returns>The transformed vector</returns>
		public static Vector3 TransformPerspective(this Vector3 vec, Matrix4X4 mat)
		{
			Vector3 result;
			TransformPerspective(vec, ref mat, out result);
			return result;
		}

		/// <summary>Transform a Vector3d by the given Matrix, and project the resulting Vector4d back to a Vector3d</summary>
		/// <param name="vec">The vector to transform</param>
		/// <param name="mat">The desired transformation</param>
		/// <param name="result">The transformed vector</param>
		public static void TransformPerspective(this Vector3 vec, ref Matrix4X4 mat, out Vector3 result)
		{
			Vector4 v = new Vector4(vec);
			Vector4.Transform(v, ref mat, out v);
			result.X = v.X / v.W;
			result.Y = v.Y / v.W;
			result.Z = v.Z / v.W;
		}

		#endregion Transform

		public static Vector3 Abs(this Vector3 a)
		{
			return Vector3.Abs(a);
		}
	}
}