public static Vector3d Transform(Vector3d vector, Quaterniond rotation)
{
var v = rotation * new Quaterniond(vector.X, vector.Y, vector.Z, 0) * Conjugate(rotation);
return(new Vector3d(v.A, v.B, v.C));
}
/// <summary>
/// Computes the argument of a quaternion and returns the result.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The argument of value.</returns>
public static double Argument(Quaterniond value)
{
return(Functions.Atan2(Absolute(Imaginary(value)), value.A));
}
/// <summary>
/// Calculates the dot product (inner product) of two quaternions.
/// </summary>
/// <param name="left">First source quaternion.</param>
/// <param name="right">Second source quaternion.</param>
/// <returns>The dot product of the two quaternions.</returns>
public static double Dot(Quaterniond left, Quaterniond right)
{
return(left.A * right.A + left.B * right.B + left.C * right.C + left.D * right.D);
}
/// <summary>
/// Computes the absolute value (or modulus or magnitude) of a quaternion and returns the result.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The absolute value of value.</returns>
public static double Absolute(Quaterniond value)
{
return(Functions.Sqrt(value.A * value.A + value.B * value.B + value.C * value.C + value.D * value.D));
}
/// <summary>
/// Computes the conjugate of a quaternion and returns the result.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The conjugate of value.</returns>
public static Quaterniond Conjugate(Quaterniond value)
{
return(new Quaterniond(value.A, -value.B, -value.C, -value.D));
}
/// <summary>
/// Return imaginary part of a quaternion.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The imaginary part of a quaternion.</returns>
public static Quaterniond Imaginary(Quaterniond value)
{
return(new Quaterniond(0, value.B, value.C, value.D));
}
/// <summary>
/// Computes the absolute squared value of a quaternion and returns the result.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The absolute squared value of value.</returns>
public static double AbsoluteSquared(Quaterniond value)
{
return(value.A * value.A + value.B * value.B + value.C * value.C + value.D * value.D);
}
/// <summary>
/// Determines whether any components of a quaternion satisfy a condition.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <param name="predicate">A function to test each component for a condition.</param>
/// <returns>true if any component of the quaternion passes the test in the specified
/// predicate; otherwise, false.</returns>
public static bool Any(Quaterniond value, Predicate <double> predicate)
{
return(predicate(value.A) || predicate(value.B) || predicate(value.C) || predicate(value.D));
}
/// <summary>
/// Return real part of a quaternion.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The real part of a quaternion.</returns>
public static Quaterniond Real(Quaterniond value)
{
return(new Quaterniond(value.A, 0, 0, 0));
}
/// <summary>
/// Determines whether all components of a quaternion satisfy a condition.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <param name="predicate">A function to test each component for a condition.</param>
/// <returns>true if every component of the quaternion passes the test in the specified
/// predicate; otherwise, false.</returns>
public static bool All(Quaterniond value, Predicate <double> predicate)
{
return(predicate(value.A) && predicate(value.B) && predicate(value.C) && predicate(value.D));
}
/// <summary>
/// Determines whether any component of a quaternion is non-zero.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>true if any components are non-zero; false otherwise.</returns>
public static bool Any(Quaterniond value)
{
return(value.A != 0 || value.B != 0 || value.C != 0 || value.D != 0);
}
/// <summary>
/// Determines whether all components of a quaternion are non-zero.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>true if all components are non-zero; false otherwise.</returns>
public static bool All(Quaterniond value)
{
return(value.A != 0 && value.B != 0 && value.C != 0 && value.D != 0);
}
/// <summary>
/// Returns a value that indicates whether two quaternions are equal.
/// </summary>
/// <param name="left">The first quaternion to compare.</param>
/// <param name="right">The second quaternion to compare.</param>
/// <returns>true if the left and right are equal; otherwise, false.</returns>
public static bool Equals(Quaterniond left, Quaterniond right)
{
return(left == right);
}
/// <summary>
/// Subtracts one quaternion from another and returns the result.
/// </summary>
/// <param name="left">The value to subtract from (the minuend).</param>
/// <param name="right">The value to subtract (the subtrahend).</param>
/// <returns>The result of subtracting right from left (the difference).</returns>
public static Quaterniond Subtract(Quaterniond left, Quaterniond right)
{
return(new Quaterniond(left.A - right.A, left.B - right.B, left.C - right.C, left.D - right.D));
}
/// <summary>
/// Adds two quaternions and returns the result.
/// </summary>
/// <param name="left">The first value to add.</param>
/// <param name="right">The second value to add.</param>
/// <returns>The sum of left and right.</returns>
public static Quaterniond Add(Quaterniond left, Quaterniond right)
{
return(new Quaterniond(left.A + right.A, left.B + right.B, left.C + right.C, left.D + right.D));
}
/// <summary>
/// Returns the additive inverse of a quaternion.
/// </summary>
/// <param name="value">A quaternion.</param>
/// <returns>The negative of value.</returns>
public static Quaterniond Negative(Quaterniond value)
{
return(new Quaterniond(-value.A, -value.B, -value.C, -value.D));
}