/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
public static QuaternionD operator +(QuaternionD left, QuaternionD right)
{
return(QuaternionD.Add(left, right));
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/>.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> containing the result.</returns>
public static QuaternionD operator *(QuaternionD left, QuaternionD right)
{
return(QuaternionD.Multiply(left, right));
}
/// <summary>
/// Divides a scalar by a quaternion.
/// </summary>
/// <param name="q">A <see cref="QuaternionD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator /(double s, QuaternionD q)
{
return(QuaternionD.Multiply(q, 1 / s));
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
public static QuaternionD Subtract(QuaternionD left, QuaternionD right)
{
return(new QuaternionD(left.W - right.W, left.X - right.X, left.Y - right.Y, left.Z - right.Z));
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
public static QuaternionD operator -(QuaternionD a, QuaternionD b)
{
return(QuaternionD.Subtract(a, b));
}
/// <summary>
/// Multiplies a quaternion by a scalar.
/// </summary>
/// <param name="q">A <see cref="QuaternionD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator *(QuaternionD q, double s)
{
return(QuaternionD.Multiply(q, s));
}
/// <summary>
/// Multiplies a quaternion by a scalar.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD Multiply(QuaternionD quaternion, double scalar)
{
QuaternionD result = new QuaternionD(quaternion);
result.W *= scalar;
result.X *= scalar;
result.Y *= scalar;
result.Z *= scalar;
return result;
}
/// <summary>
/// Calculates the dot product of two quaternions.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>The dot product value.</returns>
public static double DotProduct(QuaternionD a, QuaternionD b)
{
return(a.W * b.W + a.X * b.X + a.Y * b.Y + a.Z * b.Z);
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/>.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> containing the result.</returns>
public static QuaternionD Multiply(QuaternionD left, QuaternionD right)
{
QuaternionD result = new QuaternionD();
result.W = left.W * right.W - left.X * right.X - left.Y * right.Y - left.Z * right.Z;
result.X = left.W * right.X + left.X * right.W + left.Y * right.Z - left.Z * right.Y;
result.Y = left.W * right.Y + left.Y * right.W + left.Z * right.X - left.X * right.Z;
result.Z = left.W * right.Z + left.Z * right.W + left.X * right.Y - left.Y * right.X;
return result;
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/> and put the result in a third quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <param name="result">A <see cref="QuaternionD"/> instance to hold the result.</param>
public static void Multiply(QuaternionD left, QuaternionD right, ref QuaternionD result)
{
result.W = left.W * right.W - left.X * right.X - left.Y * right.Y - left.Z * right.Z;
result.X = left.W * right.X + left.X * right.W + left.Y * right.Z - left.Z * right.Y;
result.Y = left.W * right.Y + left.Y * right.W + left.Z * right.X - left.X * right.Z;
result.Z = left.W * right.Z + left.Z * right.W + left.X * right.Y - left.Y * right.X;
}
/// <summary>
/// Subtracts a quaternion from a quaternion and puts the result into a third quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <param name="result">A <see cref="QuaternionD"/> instance to hold the result.</param>
public static void Subtract(QuaternionD left, QuaternionD right, ref QuaternionD result)
{
result.W = left.W - right.W;
result.X = left.X - right.X;
result.Y = left.Y - right.Y;
result.Z = left.Z - right.Z;
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
public static QuaternionD Subtract(QuaternionD left, QuaternionD right)
{
return new QuaternionD(left.W - right.W, left.X - right.X, left.Y - right.Y, left.Z - right.Z);
}
/// <summary>
/// Adds two quaternions and put the result in the third quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <param name="result">A <see cref="QuaternionD"/> instance to hold the result.</param>
public static void Add(QuaternionD left, QuaternionD right, ref QuaternionD result)
{
result.W = left.W + right.W;
result.X = left.X + right.X;
result.Y = left.Y + right.Y;
result.Z = left.Z + right.Z;
}
/// <summary>
/// Divides a quaternion by a scalar.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator /(QuaternionD quaternion, double scalar)
{
return(QuaternionD.Divide(quaternion, scalar));
}
/// <summary>
/// Multiplies a quaternion by a scalar and put the result in a third quaternion.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <param name="result">A <see cref="QuaternionD"/> instance to hold the result.</param>
public static void Multiply(QuaternionD quaternion, double scalar, ref QuaternionD result)
{
result.W = quaternion.W * scalar;
result.X = quaternion.X * scalar;
result.Y = quaternion.Y * scalar;
result.Z = quaternion.Z * scalar;
}
/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
public static QuaternionD Add(QuaternionD left, QuaternionD right)
{
return new QuaternionD(left.W + right.W, left.X + right.X, left.Y + right.Y, left.Z + right.Z);
}
/// <summary>
/// Divides a quaternion by a scalar.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD Divide(QuaternionD quaternion, double scalar)
{
if (scalar == 0)
{
throw new DivideByZeroException("Dividing quaternion by zero");
}
QuaternionD result = new QuaternionD(quaternion);
result.W /= scalar;
result.X /= scalar;
result.Y /= scalar;
result.Z /= scalar;
return result;
}
/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
public static QuaternionD operator +(QuaternionD a, QuaternionD b)
{
return(QuaternionD.Add(a, b));
}
/// <summary>
/// Divides a quaternion by a scalar and put the result in a third quaternion.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <param name="result">A <see cref="QuaternionD"/> instance to hold the result.</param>
public static void Divide(QuaternionD quaternion, double scalar, ref QuaternionD result)
{
if (scalar == 0)
{
throw new DivideByZeroException("Dividing quaternion by zero");
}
result.W = quaternion.W / scalar;
result.X = quaternion.X / scalar;
result.Y = quaternion.Y / scalar;
result.Z = quaternion.Z / scalar;
}
/// <summary>
/// Multiplies quaternion <paramref name="a"/> by quaternion <paramref name="b"/>.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> containing the result.</returns>
public static QuaternionD operator *(QuaternionD a, QuaternionD b)
{
return(QuaternionD.Multiply(a, b));
}
/// <summary>
/// Calculates the dot product of two quaternions.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>The dot product value.</returns>
public static double DotProduct(QuaternionD left, QuaternionD right)
{
return left.W * right.W + left.X * right.X + left.Y * right.Y + left.Z * right.Z;
}
/// <summary>
/// Divides a quaternion by a scalar.
/// </summary>
/// <param name="q">A <see cref="QuaternionD"/> instance.</param>
/// <param name="s">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator /(QuaternionD q, double s)
{
return(QuaternionD.Divide(q, s));
}
/// <summary>
/// Calculates the logarithm of a given quaternion.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <returns>The quaternion's logarithm.</returns>
public static QuaternionD Log(QuaternionD quaternion)
{
QuaternionD result = new QuaternionD(0, 0, 0, 0);
if (MathFunctions.Abs(quaternion.W) < 1.0)
{
double angle = System.Math.Acos(quaternion.W);
double sin = System.Math.Sin(angle);
if (MathFunctions.Abs(sin) >= 0)
{
double coeff = angle / sin;
result.X = coeff * quaternion.X;
result.Y = coeff * quaternion.Y;
result.Z = coeff * quaternion.Z;
}
else
{
result.X = quaternion.X;
result.Y = quaternion.Y;
result.Z = quaternion.Z;
}
}
return result;
}
/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
public static QuaternionD Add(QuaternionD left, QuaternionD right)
{
return(new QuaternionD(left.W + right.W, left.X + right.X, left.Y + right.Y, left.Z + right.Z));
}
/// <summary>
/// Calculates the exponent of a quaternion.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <returns>The quaternion's exponent.</returns>
public QuaternionD Exp(QuaternionD quaternion)
{
QuaternionD result = new QuaternionD(0, 0, 0, 0);
double angle = System.Math.Sqrt(quaternion.X * quaternion.X + quaternion.Y * quaternion.Y + quaternion.Z * quaternion.Z);
double sin = System.Math.Sin(angle);
if (MathFunctions.Abs(sin) > 0)
{
double coeff = angle / sin;
result.X = coeff * quaternion.X;
result.Y = coeff * quaternion.Y;
result.Z = coeff * quaternion.Z;
}
else
{
result.X = quaternion.X;
result.Y = quaternion.Y;
result.Z = quaternion.Z;
}
return result;
}
/// <summary>
/// Calculates the dot product of two quaternions.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>The dot product value.</returns>
public static double DotProduct(QuaternionD left, QuaternionD right)
{
return(left.W * right.W + left.X * right.X + left.Y * right.Y + left.Z * right.Z);
}
/// <summary>
/// Initializes a new instance of the <see cref="QuaternionD"/> class using coordinates from a given <see cref="QuaternionD"/> instance.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance to copy the coordinates from.</param>
public QuaternionD(QuaternionD quaternion)
{
_w = quaternion.W;
_x = quaternion.X;
_y = quaternion.Y;
_z = quaternion.Z;
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="left">A <see cref="QuaternionD"/> instance.</param>
/// <param name="right">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
public static QuaternionD operator -(QuaternionD left, QuaternionD right)
{
return(QuaternionD.Subtract(left, right));
}
/// <summary>
/// Adds two quaternions.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the sum.</returns>
public static QuaternionD Add(QuaternionD a, QuaternionD b)
{
return(new QuaternionD(a.W + b.W, a.X + b.X, a.Y + b.Y, a.Z + b.Z));
}
/// <summary>
/// Multiplies a quaternion by a scalar.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator *(QuaternionD quaternion, double scalar)
{
return(QuaternionD.Multiply(quaternion, scalar));
}
/// <summary>
/// Subtracts a quaternion from a quaternion.
/// </summary>
/// <param name="a">A <see cref="QuaternionD"/> instance.</param>
/// <param name="b">A <see cref="QuaternionD"/> instance.</param>
/// <returns>A new <see cref="QuaternionD"/> instance containing the difference.</returns>
public static QuaternionD Subtract(QuaternionD a, QuaternionD b)
{
return(new QuaternionD(a.W - b.W, a.X - b.X, a.Y - b.Y, a.Z - b.Z));
}
/// <summary>
/// Divides a scalar by a quaternion.
/// </summary>
/// <param name="quaternion">A <see cref="QuaternionD"/> instance.</param>
/// <param name="scalar">A scalar.</param>
/// <returns>A <see cref="QuaternionD"/> instance to hold the result.</returns>
public static QuaternionD operator /(double scalar, QuaternionD quaternion)
{
return(QuaternionD.Multiply(quaternion, (1.0 / scalar)));
}
/// <summary>
/// Converts the specified string to its <see cref="QuaternionD"/> equivalent.
/// A return value indicates whether the conversion succeeded or failed.
/// </summary>
/// <param name="value">A string representation of a <see cref="QuaternionD"/>.</param>
/// <param name="result">
/// When this method returns, if the conversion succeeded,
/// contains a <see cref="QuaternionD"/> representing the vector specified by <paramref name="value"/>.
/// </param>
/// <returns><see langword="true"/> if value was converted successfully; otherwise, <see langword="false"/>.</returns>
public static bool TryParse(string value, out QuaternionD result)
{
Regex r = new Regex(@"\((?<w>.*),(?<x>.*),(?<y>.*),(?<z>.*)\)", RegexOptions.None);
Match m = r.Match(value);
if (m.Success)
{
result = new QuaternionD(
double.Parse(m.Result("${x}")),
double.Parse(m.Result("${y}")),
double.Parse(m.Result("${z}")),
double.Parse(m.Result("${w}"))
);
return true;
}
result = QuaternionD.Zero;
return false;
}
