/// <summary>
/// Returns the tangent of the specified complex number.
/// </summary>
/// <param name="value">A complex number.</param>
/// <returns>The tangent of value.</returns>
public static Complex Tan(Complex value)
{
double sa = Functions.Sin(value.A);
double ca = Functions.Cos(value.A);
double shb = Functions.Sinh(value.B);
double cha = Functions.Cosh(value.B);
return((new Complex(sa * cha, ca * shb)) / (new Complex(ca * cha, -sa * shb)));
}
/// <summary>
/// Creates a matrix that rotates around the z-axis.
/// </summary>
/// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
/// <returns>The created rotation matrix.</returns>
public static Matrix2x2f RotationZ(float angle)
{
var cos = Functions.Cos(angle);
var sin = Functions.Sin(angle);
return(new Matrix2x2f(
cos, sin,
-sin, cos
));
}
/// <summary>
/// Creates a matrix that rotates around the z-axis.
/// </summary>
/// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
/// <returns>The created rotation matrix.</returns>
public static Matrix2x2d RotationZ(double angle)
{
var cos = Functions.Cos(angle);
var sin = Functions.Sin(angle);
return(new Matrix2x2d(
cos, sin,
-sin, cos
));
}
/// <summary>
/// Creates a matrix that rotates around the y-axis.
/// </summary>
/// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
/// <returns>The created rotation matrix.</returns>
public static Matrix3x3d RotationY(double angle)
{
var cos = Functions.Cos(angle);
var sin = Functions.Sin(angle);
return(new Matrix3x3d(
cos, 0, -sin,
0, 1, 0,
sin, 0, cos
));
}
/// <summary>
/// Creates a matrix that rotates around the x-axis.
/// </summary>
/// <param name="angle">Angle of rotation in radians. Angles are measured clockwise when looking along the rotation axis toward the origin.</param>
/// <returns>The created rotation matrix.</returns>
public static Matrix3x3f RotationX(float angle)
{
var cos = Functions.Cos(angle);
var sin = Functions.Sin(angle);
return(new Matrix3x3f(
1, 0, 0,
0, cos, sin,
0, -sin, cos
));
}
private static Complex Y(int l, int m, double phi, double theta)
{
return(K(l, m) * Complex.Exp(Complex.I * m * theta) * P(l, m, Functions.Cos(phi)));
}
/// <summary>
/// Creates a complex number from a point's polar coordinates.
/// </summary>
/// <param name="coordinate">The polar coordinate</param>
public static Complex FromPolarCoordinates(Geometry.PolarCoordinate coordinate)
{
return(new Complex(
Functions.Cos(coordinate.Theta) * coordinate.Rho,
Functions.Sin(coordinate.Theta) * coordinate.Rho));
}
/// <summary>
/// Creates a complex number from a point's polar coordinates.
/// </summary>
/// <param name="magnitude">The magnitude, which is the distance from the origin (the intersection of
/// the x-axis and the y-axis) to the number.</param>
/// <param name="phase">The phase, which is the angle from the line to the horizontal axis, measured
/// in radians.</param>
public static Complex FromPolarCoordinates(double magnitude, double phase)
{
return(new Complex(Functions.Cos(phase) * magnitude, Functions.Sin(phase) * magnitude));
}
/// <summary>
/// Returns the sine of the specified complex number.
/// </summary>
/// <param name="value">A complex number.</param>
/// <returns>The sine of value.</returns>
public static Complex Sin(Complex value)
{
return(new Complex(Functions.Sin(value.A) * Functions.Cosh(value.B), Functions.Cos(value.A) * Functions.Sinh(value.B)));
}
/// <summary>
/// Returns e raised to the power specified by a complex number.
/// </summary>
/// <param name="value">A complex number that specifies a power.</param>
/// <returns>The number e raised to the power value.</returns>
public static Complex Exp(Complex value)
{
double e = Functions.Exp(value.A);
return(new Complex(e * Functions.Cos(value.B), e * Functions.Sin(value.B)));
}