UnitComplex in nalgebra::geometry - Rust
Description: A 2D rotation represented as a complex number with magnitude 1.
Keywords: rust, rustlang, rust-lang, UnitComplex

# Type Definition nalgebra::geometry::UnitComplex

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    pub type UnitComplex<T> = Unit<Complex<T>>;

Expand description

A 2D rotation represented as a complex number with magnitude 1.

All the methods specific `UnitComplex` are listed here. You may also read the documentation of the `Complex` type which is used internally and accessible with `unit_complex.complex()`.

## Construction

- Identity `identity`
- From a 2D rotation angle `new`, `from_cos_sin_unchecked`…
- From an existing 2D matrix or complex number `from_matrix`, `rotation_to`, `powf`…
- From two vectors `rotation_between`, `scaled_rotation_between_axis`…

## Transformation and composition

- Angle extraction `angle`, `angle_to`…
- Transformation of a vector or a point `transform_vector`, `inverse_transform_point`…
- Conjugation and inversion `conjugate`, `inverse_mut`…
- Interpolation `slerp`…

## Conversion

- Conversion to a matrix `to_rotation_matrix`, `to_homogeneous`…

## Implementations§

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Angle extraction

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#### pub fn angle(&self) -> T

The rotation angle in `]-pi; pi]` of this unit complex number.

##### Example

    let rot = UnitComplex::new(1.78);
    assert_eq!(rot.angle(), 1.78);

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#### pub fn sin_angle(&self) -> T

The sine of the rotation angle.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(rot.sin_angle(), angle.sin());

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#### pub fn cos_angle(&self) -> T

The cosine of the rotation angle.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(rot.cos_angle(),angle.cos());

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#### pub fn scaled_axis(&self) -> Vector1<T>

The rotation angle returned as a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `.angle()` method instead is more common.

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#### pub fn axis_angle(&self) -> Option<(Unit<Vector1<T>>, T)>where
T: RealField,

The rotation axis and angle in (0, pi] of this complex number.

This is generally used in the context of generic programming. Using the `.angle()` method instead is more common. Returns `None` if the angle is zero.

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#### pub fn angle_to(&self, other: &Self) -> T

The rotation angle needed to make `self` and `other` coincide.

##### Example

    let rot1 = UnitComplex::new(0.1);
    let rot2 = UnitComplex::new(1.7);
    assert_relative_eq!(rot1.angle_to(&rot2), 1.6);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Conjugation and inversion

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#### pub fn conjugate(&self) -> Self

Compute the conjugate of this unit complex number.

##### Example

    let rot = UnitComplex::new(1.78);
    let conj = rot.conjugate();
    assert_eq!(rot.complex().im, -conj.complex().im);
    assert_eq!(rot.complex().re, conj.complex().re);

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#### pub fn inverse(&self) -> Self

Inverts this complex number if it is not zero.

##### Example

    let rot = UnitComplex::new(1.2);
    let inv = rot.inverse();
    assert_relative_eq!(rot * inv, UnitComplex::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, UnitComplex::identity(), epsilon = 1.0e-6);

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#### pub fn conjugate_mut(&mut self)

Compute in-place the conjugate of this unit complex number.

##### Example

    let angle = 1.7;
    let rot = UnitComplex::new(angle);
    let mut conj = UnitComplex::new(angle);
    conj.conjugate_mut();
    assert_eq!(rot.complex().im, -conj.complex().im);
    assert_eq!(rot.complex().re, conj.complex().re);

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#### pub fn inverse_mut(&mut self)

Inverts in-place this unit complex number.

##### Example

    let angle = 1.7;
    let mut rot = UnitComplex::new(angle);
    rot.inverse_mut();
    assert_relative_eq!(rot * UnitComplex::new(angle), UnitComplex::identity());
    assert_relative_eq!(UnitComplex::new(angle) * rot, UnitComplex::identity());

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Conversion to a matrix

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#### pub fn to_rotation_matrix(self) -> Rotation2<T>

Builds the rotation matrix corresponding to this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
    let expected = Rotation2::new(f32::consts::FRAC_PI_6);
    assert_eq!(rot.to_rotation_matrix(), expected);

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#### pub fn to_homogeneous(self) -> Matrix3<T>

Converts this unit complex number into its equivalent homogeneous transformation matrix.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
    let expected = Matrix3::new(0.8660254, -0.5,      0.0,
                                0.5,       0.8660254, 0.0,
                                0.0,       0.0,       1.0);
    assert_eq!(rot.to_homogeneous(), expected);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Transformation of a vector or a point

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#### pub fn transform_point(&self, pt: &Point2<T>) -> Point2<T>

Rotate the given point by this unit complex number.

This is the same as the multiplication `self * pt`.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_point = rot.transform_point(&Point2::new(1.0, 2.0));
    assert_relative_eq!(transformed_point, Point2::new(-2.0, 1.0), epsilon = 1.0e-6);

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#### pub fn transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

Rotate the given vector by this unit complex number.

This is the same as the multiplication `self * v`.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.transform_vector(&Vector2::new(1.0, 2.0));
    assert_relative_eq!(transformed_vector, Vector2::new(-2.0, 1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_point(&self, pt: &Point2<T>) -> Point2<T>

Rotate the given point by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_point = rot.inverse_transform_point(&Point2::new(1.0, 2.0));
    assert_relative_eq!(transformed_point, Point2::new(2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

Rotate the given vector by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_vector(&Vector2::new(1.0, 2.0));
    assert_relative_eq!(transformed_vector, Vector2::new(2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_unit_vector(
&self,
v: &Unit<Vector2<T>>
) -> Unit<Vector2<T>>

Rotate the given vector by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_unit_vector(&Vector2::x_axis());
    assert_relative_eq!(transformed_vector, -Vector2::y_axis(), epsilon = 1.0e-6);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Interpolation

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#### pub fn slerp(&self, other: &Self, t: T) -> Self

Spherical linear interpolation between two rotations represented as unit complex numbers.

##### Examples:

    let rot1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
    let rot2 = UnitComplex::new(-std::f32::consts::PI);

    let rot = rot1.slerp(&rot2, 1.0 / 3.0);

    assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Identity

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#### pub fn identity() -> Self

The unit complex number multiplicative identity.

##### Example

    let rot1 = UnitComplex::identity();
    let rot2 = UnitComplex::new(1.7);

    assert_eq!(rot1 * rot2, rot2);
    assert_eq!(rot2 * rot1, rot2);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Construction from a 2D rotation angle

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#### pub fn new(angle: T) -> Self

Builds the unit complex number corresponding to the rotation with the given angle.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

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#### pub fn from_angle(angle: T) -> Self

Builds the unit complex number corresponding to the rotation with the angle.

Same as `Self::new(angle)`.

##### Example

    let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

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#### pub fn from_cos_sin_unchecked(cos: T, sin: T) -> Self

Builds the unit complex number from the sinus and cosinus of the rotation angle.

The input values are not checked to actually be cosines and sine of the same value. Is is generally preferable to use the `::new(angle)` constructor instead.

##### Example

    let angle = f32::consts::FRAC_PI_2;
    let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

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#### pub fn from_scaled_axis<SB: Storage<T, U1>>(
axisangle: Vector<T, U1, SB>
) -> Self

Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `::new(angle)` method instead is more common.

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Construction from an existing 2D matrix or complex number

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#### pub fn cast<To: Scalar>(self) -> UnitComplex<To>where
UnitComplex<To>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    #[macro_use] extern crate approx;
    let c = UnitComplex::new(1.0f64);
    let c2 = c.cast::<f32>();
    assert_relative_eq!(c2, UnitComplex::new(1.0f32));

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#### pub fn complex(&self) -> &Complex<T>

The underlying complex number.

Same as `self.as_ref()`.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));

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#### pub fn from_complex(q: Complex<T>) -> Self

Creates a new unit complex number from a complex number.

The input complex number will be normalized.

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#### pub fn from_complex_and_get(q: Complex<T>) -> (Self, T)

Creates a new unit complex number from a complex number.

The input complex number will be normalized. Returns the norm of the complex number as well.

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#### pub fn from_rotation_matrix(rotmat: &Rotation2<T>) -> Self

Builds the unit complex number from the corresponding 2D rotation matrix.

##### Example

    let rot = Rotation2::new(1.7);
    let complex = UnitComplex::from_rotation_matrix(&rot);
    assert_eq!(complex, UnitComplex::new(1.7));

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#### pub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

In order to get a valid unit-quaternion, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

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#### pub fn from_matrix(m: &Matrix2<T>) -> Selfwhere
T: RealField,

Builds an unit complex by extracting the rotation part of the given transformation `m`.

This is an iterative method. See `.from_matrix_eps` to provide mover convergence parameters and starting solution. This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

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#### pub fn from_matrix_eps(
m: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,

Builds an unit complex by extracting the rotation part of the given transformation `m`.

This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

##### Parameters

- `m`: the matrix from which the rotational part is to be extracted.
- `eps`: the angular errors tolerated between the current rotation and the optimal one.
- `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
- `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other guesses come to mind.

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#### pub fn rotation_to(&self, other: &Self) -> Self

The unit complex number needed to make `self` and `other` coincide.

The result is such that: `self.rotation_to(other) * self == other`.

##### Example

    let rot1 = UnitComplex::new(0.1);
    let rot2 = UnitComplex::new(1.7);
    let rot_to = rot1.rotation_to(&rot2);

    assert_relative_eq!(rot_to * rot1, rot2);
    assert_relative_eq!(rot_to.inverse() * rot2, rot1);

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#### pub fn powf(&self, n: T) -> Self

Raise this unit complex number to a given floating power.

This returns the unit complex number that identifies a rotation angle equal to `self.angle() × n`.

##### Example

    let rot = UnitComplex::new(0.78);
    let pow = rot.powf(2.0);
    assert_relative_eq!(pow.angle(), 2.0 * 0.78);

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### impl<T: SimdRealField> UnitComplex<T>where
T::Element: SimdRealField,

#### Construction from two vectors

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#### pub fn rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The unit complex needed to make `a` and `b` be collinear and point toward the same direction.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot = UnitComplex::rotation_between(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

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#### pub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>,
s: T
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot2 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
    let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
    assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

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#### pub fn rotation_between_axis<SB, SC>(
a: &Unit<Vector<T, U2, SB>>,
b: &Unit<Vector<T, U2, SC>>
) -> Selfwhere
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The unit complex needed to make `a` and `b` be collinear and point toward the same direction.

##### Example

    let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
    let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
    let rot = UnitComplex::rotation_between_axis(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

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#### pub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Vector<T, U2, SB>>,
nb: &Unit<Vector<T, U2, SC>>,
s: T
) -> Selfwhere
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
    let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
    let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
    let rot5 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.5);
    assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

## Trait Implementations§

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### impl<T: RealField> AbsDiffEq<Unit<Complex<T>>> for UnitComplex<T>

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#### type Epsilon = T

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T: SimdRealField> AbstractRotation<T, 2> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn identity() -> Self

The rotation identity.
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#### fn inverse(&self) -> Self

The rotation inverse.
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#### fn inverse_mut(&mut self)

Change `self` to its inverse.
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#### fn transform_vector(&self, v: &SVector<T, 2>) -> SVector<T, 2>

Apply the rotation to the given vector.
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#### fn transform_point(&self, p: &Point<T, 2>) -> Point<T, 2>

Apply the rotation to the given point.
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#### fn inverse_transform_vector(&self, v: &SVector<T, 2>) -> SVector<T, 2>

Apply the inverse rotation to the given vector.
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#### fn inverse_transform_point(&self, p: &Point<T, 2>) -> Point<T, 2>

Apply the inverse rotation to the given point.
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#### fn inverse_transform_unit_vector(
&self,
v: &Unit<SVector<T, D>>
) -> Unit<SVector<T, D>>

Apply the inverse rotation to the given unit vector.
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### impl<T: SimdRealField> Default for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn default() -> Self

Returns the “default value” for a type. Read more
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### impl<T: RealField + Display> Display for UnitComplex<T>

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#### fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<Rotation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Self) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: &'b Rotation<T, 2>)

Performs the `/=` operation. Read more
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### impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: Rotation<T, 2>)

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
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### impl<T> From<[Unit<Complex<<T as SimdValue>::Element>>; 16]> for UnitComplex<T>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + Copy + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [UnitComplex<T::Element>; 16]) -> Self

Converts to this type from the input type.
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### impl<T> From<[Unit<Complex<<T as SimdValue>::Element>>; 2]> for UnitComplex<T>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + Copy + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [UnitComplex<T::Element>; 2]) -> Self

Converts to this type from the input type.
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### impl<T> From<[Unit<Complex<<T as SimdValue>::Element>>; 4]> for UnitComplex<T>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + Copy + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [UnitComplex<T::Element>; 4]) -> Self

Converts to this type from the input type.
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### impl<T> From<[Unit<Complex<<T as SimdValue>::Element>>; 8]> for UnitComplex<T>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + Copy + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [UnitComplex<T::Element>; 8]) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn from(q: Rotation2<T>) -> Self

Converts to this type from the input type.
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Vector<T, Const<2>, S>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Matrix<T, Const<2>, Const<1>, S>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Vector<T, Const<2>, S>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b OPoint<T, Const<2>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = OPoint<T, Const<2>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Point2<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b OPoint<T, Const<2>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = OPoint<T, Const<2>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Point2<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 2>> for &'a UnitComplex<T>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Transform<T, C, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, C> Mul<&'b Transform<T, C, 2>> for UnitComplex<T>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Transform<T, C, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Translation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Translation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Translation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Isometry<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Matrix<T, Const<2>, Const<1>, S>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Vector<T, Const<2>, S>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Matrix<T, Const<2>, Const<1>, S>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Vector<T, Const<2>, S>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<OPoint<T, Const<2>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = OPoint<T, Const<2>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Point2<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<OPoint<T, Const<2>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = OPoint<T, Const<2>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Point2<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Rotation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, C> Mul<Transform<T, C, 2>> for &'a UnitComplex<T>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Transform<T, C, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, C> Mul<Transform<T, C, 2>> for UnitComplex<T>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Transform<T, C, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Translation<T, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Translation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Translation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Translation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for UnitComplex<T>

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Self) -> Self

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, 2>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: Rotation<T, 2>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> One for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn one() -> Self

Returns the multiplicative identity element of `Self`, `1`. Read more
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#### fn set_one(&mut self)

Sets `self` to the multiplicative identity element of `Self`, `1`.
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#### fn is_one(&self) -> bool where
Self: PartialEq<Self>,

Returns `true` if `self` is equal to the multiplicative identity. Read more
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### impl<T: Scalar + PartialEq> PartialEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn eq(&self, rhs: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
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#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: RealField> RelativeEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T: SimdRealField> SimdValue for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Element = Unit<Complex<<T as SimdValue>::Element>>

The type of the elements of each lane of this SIMD value.
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#### type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like `self`.
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#### fn lanes() -> usize

The number of lanes of this SIMD value.
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#### fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to `val`.
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#### fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self`. Read more
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#### unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self` without bound-checking.
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#### fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val`. Read more
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#### unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val` without bound-checking.
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#### fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges `self` and `other` depending on the lanes of `cond`. Read more
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#### fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self`. Read more
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#### fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self` paired with the corresponding lane of `b`. Read more
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### impl<T1, T2, R> SubsetOf<Isometry<T2, R, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 2> + SupersetOf<Self>,

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#### fn to_superset(&self) -> Isometry<T2, R, 2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(iso: &Isometry<T2, R, 2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(iso: &Isometry<T2, R, 2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1: RealField, T2: RealField + SupersetOf<T1>> SubsetOf<Matrix<T2, Const<3>, Const<3>, ArrayStorage<T2, 3, 3>>> for UnitComplex<T1>

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#### fn to_superset(&self) -> Matrix3<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(m: &Matrix3<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(m: &Matrix3<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Rotation<T2, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> Rotation2<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(rot: &Rotation2<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(rot: &Rotation2<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2, R> SubsetOf<Similarity<T2, R, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 2> + SupersetOf<Self>,

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#### fn to_superset(&self) -> Similarity<T2, R, 2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(sim: &Similarity<T2, R, 2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(sim: &Similarity<T2, R, 2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2, C> SubsetOf<Transform<T2, C, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,

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#### fn to_superset(&self) -> Transform<T2, C, 2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(t: &Transform<T2, C, 2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(t: &Transform<T2, C, 2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(uq: &UnitComplex<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(uq: &UnitComplex<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T: RealField> UlpsEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: Scalar + Eq> Eq for UnitComplex<T>