# [−][src]Struct nalgebra::base::Unit

```#[repr(transparent)]
pub struct Unit<T> { /* fields omitted */ }```

A wrapper that ensures the underlying algebraic entity has a unit norm.

Use `.as_ref()` or `.into_inner()` to obtain the underlying value by-reference or by-move.

## Methods

### `impl<N: RealField, D: Dim, S: Storage<N, D>> Unit<Vector<N, D, S>>`[src]

#### `pub fn slerp<S2: Storage<N, D>>(    &self,     rhs: &Unit<Vector<N, D, S2>>,     t: N) -> Unit<VectorN<N, D>> where    DefaultAllocator: Allocator<N, D>, `[src]

Computes the spherical linear interpolation between two unit vectors.

# Examples:

```
let v1 = Unit::new_normalize(Vector2::new(1.0, 2.0));
let v2 = Unit::new_normalize(Vector2::new(2.0, -3.0));

let v = v1.slerp(&v2, 1.0);

assert_eq!(v, v2);```

#### `pub fn try_slerp<S2: Storage<N, D>>(    &self,     rhs: &Unit<Vector<N, D, S2>>,     t: N,     epsilon: N) -> Option<Unit<VectorN<N, D>>> where    DefaultAllocator: Allocator<N, D>, `[src]

Computes the spherical linear interpolation between two unit vectors.

Returns `None` if the two vectors are almost collinear and with opposite direction (in this case, there is an infinity of possible results).

### `impl<T: NormedSpace> Unit<T>`[src]

#### `pub fn new_normalize(value: T) -> Self`[src]

Normalize the given value and return it wrapped on a `Unit` structure.

#### `pub fn try_new(value: T, min_norm: T::RealField) -> Option<Self>`[src]

Attempts to normalize the given value and return it wrapped on a `Unit` structure.

Returns `None` if the norm was smaller or equal to `min_norm`.

#### `pub fn new_and_get(value: T) -> (Self, T::RealField)`[src]

Normalize the given value and return it wrapped on a `Unit` structure and its norm.

#### `pub fn try_new_and_get(    value: T,     min_norm: T::RealField) -> Option<(Self, T::RealField)>`[src]

Normalize the given value and return it wrapped on a `Unit` structure and its norm.

Returns `None` if the norm was smaller or equal to `min_norm`.

#### `pub fn renormalize(&mut self) -> T::RealField`[src]

Normalizes this value again. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

Returns the norm before re-normalization. See `.renormalize_fast` for a faster alternative that may be slightly less accurate if `self` drifted significantly from having a unit length.

#### `pub fn renormalize_fast(&mut self)`[src]

Normalizes this value again using a first-order Taylor approximation. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

### `impl<T> Unit<T>`[src]

#### `pub fn new_unchecked(value: T) -> Self`[src]

Wraps the given value, assuming it is already normalized.

#### `pub fn from_ref_unchecked<'a>(value: &'a T) -> &'a Self`[src]

Wraps the given reference, assuming it is already normalized.

#### `pub fn into_inner(self) -> T`[src]

Retrieves the underlying value.

#### `pub fn unwrap(self) -> T`[src]

Deprecated:

use `.into_inner()` instead

Retrieves the underlying value. Deprecated: use Unit::into_inner instead.

#### `pub fn as_mut_unchecked(&mut self) -> &mut T`[src]

Returns a mutable reference to the underlying value. This is `_unchecked` because modifying the underlying value in such a way that it no longer has unit length may lead to unexpected results.

### `impl<N: RealField> Unit<Quaternion<N>>`[src]

#### `pub fn into_owned(self) -> Self`[src]

Deprecated:

This method is unnecessary and will be removed in a future release. Use `.clone()` instead.

Moves this unit quaternion into one that owns its data.

#### `pub fn clone_owned(&self) -> Self`[src]

Deprecated:

This method is unnecessary and will be removed in a future release. Use `.clone()` instead.

Clones this unit quaternion into one that owns its data.

#### `pub fn angle(&self) -> N`[src]

The rotation angle in [0; pi] of this unit quaternion.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
assert_eq!(rot.angle(), 1.78);```

#### `pub fn quaternion(&self) -> &Quaternion<N>`[src]

The underlying quaternion.

Same as `self.as_ref()`.

# Example

```let axis = UnitQuaternion::identity();
assert_eq!(*axis.quaternion(), Quaternion::new(1.0, 0.0, 0.0, 0.0));```

#### ```#[must_use = "Did you mean to use conjugate_mut()?"] pub fn conjugate(&self) -> Self```[src]

Compute the conjugate of this unit quaternion.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
let conj = rot.conjugate();
assert_eq!(conj, UnitQuaternion::from_axis_angle(&-axis, 1.78));```

#### ```#[must_use = "Did you mean to use inverse_mut()?"] pub fn inverse(&self) -> Self```[src]

Inverts this quaternion if it is not zero.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
let inv = rot.inverse();
assert_eq!(rot * inv, UnitQuaternion::identity());
assert_eq!(inv * rot, UnitQuaternion::identity());```

#### `pub fn angle_to(&self, other: &Self) -> N`[src]

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

# Example

```let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);```

#### `pub fn rotation_to(&self, other: &Self) -> Self`[src]

The unit quaternion needed to make `self` and `other` coincide.

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

# Example

```let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
let rot_to = rot1.rotation_to(&rot2);
assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);```

#### `pub fn lerp(&self, other: &Self, t: N) -> Quaternion<N>`[src]

Linear interpolation between two unit quaternions.

The result is not normalized.

# Example

```let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(0.9, 0.1, 0.0, 0.0));```

#### `pub fn nlerp(&self, other: &Self, t: N) -> Self`[src]

Normalized linear interpolation between two unit quaternions.

This is the same as `self.lerp` except that the result is normalized.

# Example

```let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
assert_eq!(q1.nlerp(&q2, 0.1), UnitQuaternion::new_normalize(Quaternion::new(0.9, 0.1, 0.0, 0.0)));```

#### `pub fn slerp(&self, other: &Self, t: N) -> Self`[src]

Spherical linear interpolation between two unit quaternions.

Panics if the angle between both quaternion is 180 degrees (in which case the interpolation is not well-defined). Use `.try_slerp` instead to avoid the panic.

# Examples:

```
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);

let q = q1.slerp(&q2, 1.0 / 3.0);

assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));```

#### `pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self>`[src]

Computes the spherical linear interpolation between two unit quaternions or returns `None` if both quaternions are approximately 180 degrees apart (in which case the interpolation is not well-defined).

# Arguments

• `self`: the first quaternion to interpolate from.
• `other`: the second quaternion to interpolate toward.
• `t`: the interpolation parameter. Should be between 0 and 1.
• `epsilon`: the value below which the sinus of the angle separating both quaternion must be to return `None`.

#### `pub fn conjugate_mut(&mut self)`[src]

Compute the conjugate of this unit quaternion in-place.

#### `pub fn inverse_mut(&mut self)`[src]

Inverts this quaternion if it is not zero.

# Example

```let axisangle = Vector3::new(0.1, 0.2, 0.3);
let mut rot = UnitQuaternion::new(axisangle);
rot.inverse_mut();
assert_relative_eq!(rot * UnitQuaternion::new(axisangle), UnitQuaternion::identity());
assert_relative_eq!(UnitQuaternion::new(axisangle) * rot, UnitQuaternion::identity());```

#### `pub fn axis(&self) -> Option<Unit<Vector3<N>>>`[src]

The rotation axis of this unit quaternion or `None` if the rotation is zero.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = UnitQuaternion::from_axis_angle(&axis, angle);
assert_eq!(rot.axis(), Some(axis));

// Case with a zero angle.
let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
assert!(rot.axis().is_none());```

#### `pub fn scaled_axis(&self) -> Vector3<N>`[src]

The rotation axis of this unit quaternion multiplied by the rotation angle.

# Example

```let axisangle = Vector3::new(0.1, 0.2, 0.3);
let rot = UnitQuaternion::new(axisangle);
assert_relative_eq!(rot.scaled_axis(), axisangle, epsilon = 1.0e-6);```

#### `pub fn axis_angle(&self) -> Option<(Unit<Vector3<N>>, N)>`[src]

The rotation axis and angle in ]0, pi] of this unit quaternion.

Returns `None` if the angle is zero.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = UnitQuaternion::from_axis_angle(&axis, angle);
assert_eq!(rot.axis_angle(), Some((axis, angle)));

// Case with a zero angle.
let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
assert!(rot.axis_angle().is_none());```

#### `pub fn exp(&self) -> Quaternion<N>`[src]

Compute the exponential of a quaternion.

Note that this function yields a `Quaternion<N>` because it loses the unit property.

#### `pub fn ln(&self) -> Quaternion<N>`[src]

Compute the natural logarithm of a quaternion.

Note that this function yields a `Quaternion<N>` because it loses the unit property. The vector part of the return value corresponds to the axis-angle representation (divided by 2.0) of this unit quaternion.

# Example

```let axisangle = Vector3::new(0.1, 0.2, 0.3);
let q = UnitQuaternion::new(axisangle);
assert_relative_eq!(q.ln().vector().into_owned(), axisangle, epsilon = 1.0e-6);```

#### `pub fn powf(&self, n: N) -> Self`[src]

Raise the quaternion to a given floating power.

This returns the unit quaternion that identifies a rotation with axis `self.axis()` and angle `self.angle() × n`.

# Example

```let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = UnitQuaternion::from_axis_angle(&axis, angle);
let pow = rot.powf(2.0);
assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
assert_eq!(pow.angle(), 2.4);```

#### `pub fn to_rotation_matrix(&self) -> Rotation<N, U3>`[src]

Builds a rotation matrix from this unit quaternion.

# Example

```let q = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let rot = q.to_rotation_matrix();
let expected = Matrix3::new(0.8660254, -0.5,      0.0,
0.5,       0.8660254, 0.0,
0.0,       0.0,       1.0);

assert_relative_eq!(*rot.matrix(), expected, epsilon = 1.0e-6);```

#### `pub fn to_euler_angles(&self) -> (N, N, N)`[src]

Deprecated:

This is renamed to use `.euler_angles()`.

Converts this unit quaternion into its equivalent Euler angles.

The angles are produced in the form (roll, pitch, yaw).

#### `pub fn euler_angles(&self) -> (N, N, N)`[src]

Retrieves the euler angles corresponding to this unit quaternion.

The angles are produced in the form (roll, pitch, yaw).

# Example

```let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
let euler = rot.euler_angles();
assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);```

#### `pub fn to_homogeneous(&self) -> Matrix4<N>`[src]

Converts this unit quaternion into its equivalent homogeneous transformation matrix.

# Example

```let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
let expected = Matrix4::new(0.8660254, -0.5,      0.0, 0.0,
0.5,       0.8660254, 0.0, 0.0,
0.0,       0.0,       1.0, 0.0,
0.0,       0.0,       0.0, 1.0);

assert_relative_eq!(rot.to_homogeneous(), expected, epsilon = 1.0e-6);```

#### `pub fn transform_point(&self, pt: &Point3<N>) -> Point3<N>`[src]

Rotate a point by this unit quaternion.

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

# Example

```let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
let transformed_point = rot.transform_point(&Point3::new(1.0, 2.0, 3.0));

assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);```

#### `pub fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N>`[src]

Rotate a vector by this unit quaternion.

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

# Example

```let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
let transformed_vector = rot.transform_vector(&Vector3::new(1.0, 2.0, 3.0));

assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);```

#### `pub fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N>`[src]

Rotate a point by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the point.

# Example

```let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
let transformed_point = rot.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));

assert_relative_eq!(transformed_point, Point3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);```

#### `pub fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N>`[src]

Rotate a vector by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the vector.

# Example

```let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
let transformed_vector = rot.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));

assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);```

### `impl<N: RealField> Unit<Quaternion<N>>`[src]

#### `pub fn identity() -> Self`[src]

The rotation identity.

# Example

```let q = UnitQuaternion::identity();
let q2 = UnitQuaternion::new(Vector3::new(1.0, 2.0, 3.0));
let v = Vector3::new_random();
let p = Point3::from(v);

assert_eq!(q * q2, q2);
assert_eq!(q2 * q, q2);
assert_eq!(q * v, v);
assert_eq!(q * p, p);```

#### `pub fn from_axis_angle<SB>(axis: &Unit<Vector<N, U3, SB>>, angle: N) -> Self where    SB: Storage<N, U3>, `[src]

Creates a new quaternion from a unit vector (the rotation axis) and an angle (the rotation angle).

# Example

```let axis = Vector3::y_axis();
let angle = f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::from_axis_angle(&axis, angle);

assert_eq!(q.axis().unwrap(), axis);
assert_eq!(q.angle(), angle);
assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// A zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());```

#### `pub fn from_quaternion(q: Quaternion<N>) -> Self`[src]

Creates a new unit quaternion from a quaternion.

The input quaternion will be normalized.

#### `pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Self`[src]

Creates a new unit quaternion from Euler angles.

The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.

# Example

```let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
let euler = rot.euler_angles();
assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);```

#### `pub fn from_rotation_matrix(rotmat: &Rotation3<N>) -> Self`[src]

Builds an unit quaternion from a rotation matrix.

# Example

```let axis = Vector3::y_axis();
let angle = 0.1;
let rot = Rotation3::from_axis_angle(&axis, angle);
let q = UnitQuaternion::from_rotation_matrix(&rot);
assert_relative_eq!(q.to_rotation_matrix(), rot, epsilon = 1.0e-6);
assert_relative_eq!(q.axis().unwrap(), rot.axis().unwrap(), epsilon = 1.0e-6);
assert_relative_eq!(q.angle(), rot.angle(), epsilon = 1.0e-6);```

#### `pub fn from_matrix(m: &Matrix3<N>) -> Self`[src]

Builds an unit quaternion 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.

#### `pub fn from_matrix_eps(    m: &Matrix3<N>,     eps: N,     max_iter: usize,     guess: Self) -> Self`[src]

Builds an unit quaternion 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.

#### `pub fn rotation_between<SB, SC>(    a: &Vector<N, U3, SB>,     b: &Vector<N, U3, SC>) -> Option<Self> where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

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

# Example

```let a = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
assert_relative_eq!(q * a, b);
assert_relative_eq!(q.inverse() * b, a);```

#### `pub fn scaled_rotation_between<SB, SC>(    a: &Vector<N, U3, SB>,     b: &Vector<N, U3, SC>,     s: N) -> Option<Self> where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

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

# Example

```let a = Vector3::new(1.0, 2.0, 3.0);
let b = Vector3::new(3.0, 1.0, 2.0);
let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);```

#### `pub fn rotation_between_axis<SB, SC>(    a: &Unit<Vector<N, U3, SB>>,     b: &Unit<Vector<N, U3, SC>>) -> Option<Self> where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

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

# Example

```let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
assert_relative_eq!(q * a, b);
assert_relative_eq!(q.inverse() * b, a);```

#### `pub fn scaled_rotation_between_axis<SB, SC>(    na: &Unit<Vector<N, U3, SB>>,     nb: &Unit<Vector<N, U3, SC>>,     s: N) -> Option<Self> where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

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(Vector3::new(1.0, 2.0, 3.0));
let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);```

#### `pub fn face_towards<SB, SC>(    dir: &Vector<N, U3, SB>,     up: &Vector<N, U3, SC>) -> Self where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

Creates an unit quaternion that corresponds to the local frame of an observer standing at the origin and looking toward `dir`.

It maps the `z` axis to the direction `dir`.

# Arguments

• dir - The look direction. It does not need to be normalized.
• up - The vertical direction. It does not need to be normalized. The only requirement of this parameter is to not be collinear to `dir`. Non-collinearity is not checked.

# Example

```let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();

let q = UnitQuaternion::face_towards(&dir, &up);
assert_relative_eq!(q * Vector3::z(), dir.normalize());```

#### `pub fn new_observer_frames<SB, SC>(    dir: &Vector<N, U3, SB>,     up: &Vector<N, U3, SC>) -> Self where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

Deprecated:

renamed to `face_towards`

#### `pub fn look_at_rh<SB, SC>(    dir: &Vector<N, U3, SB>,     up: &Vector<N, U3, SC>) -> Self where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

Builds a right-handed look-at view matrix without translation.

It maps the view direction `dir` to the negative `z` axis. This conforms to the common notion of right handed look-at matrix from the computer graphics community.

# Arguments

• dir − The view direction. It does not need to be normalized.
• up - A vector approximately aligned with required the vertical axis. It does not need to be normalized. The only requirement of this parameter is to not be collinear to `dir`.

# Example

```let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();

let q = UnitQuaternion::look_at_rh(&dir, &up);
assert_relative_eq!(q * dir.normalize(), -Vector3::z());```

#### `pub fn look_at_lh<SB, SC>(    dir: &Vector<N, U3, SB>,     up: &Vector<N, U3, SC>) -> Self where    SB: Storage<N, U3>,    SC: Storage<N, U3>, `[src]

Builds a left-handed look-at view matrix without translation.

It maps the view direction `dir` to the positive `z` axis. This conforms to the common notion of left handed look-at matrix from the computer graphics community.

# Arguments

• dir − The view direction. It does not need to be normalized.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to `dir`.

# Example

```let dir = Vector3::new(1.0, 2.0, 3.0);
let up = Vector3::y();

let q = UnitQuaternion::look_at_lh(&dir, &up);
assert_relative_eq!(q * dir.normalize(), Vector3::z());```

#### `pub fn new<SB>(axisangle: Vector<N, U3, SB>) -> Self where    SB: Storage<N, U3>, `[src]

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `N::default_epsilon()`, this returns the identity rotation.

# Example

```let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::new(axisangle);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// A zero vector yields an identity.
assert_eq!(UnitQuaternion::new(Vector3::<f32>::zeros()), UnitQuaternion::identity());```

#### `pub fn new_eps<SB>(axisangle: Vector<N, U3, SB>, eps: N) -> Self where    SB: Storage<N, U3>, `[src]

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation.

# Example

```let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::new_eps(axisangle, 1.0e-6);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// An almost zero vector yields an identity.
assert_eq!(UnitQuaternion::new_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());```

#### `pub fn from_scaled_axis<SB>(axisangle: Vector<N, U3, SB>) -> Self where    SB: Storage<N, U3>, `[src]

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `N::default_epsilon()`, this returns the identity rotation. Same as `Self::new(axisangle)`.

# Example

```let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::from_scaled_axis(axisangle);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// A zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());```

#### `pub fn from_scaled_axis_eps<SB>(axisangle: Vector<N, U3, SB>, eps: N) -> Self where    SB: Storage<N, U3>, `[src]

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation. Same as `Self::new_eps(axisangle, eps)`.

# Example

```let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);
let q = UnitQuaternion::from_scaled_axis_eps(axisangle, 1.0e-6);

assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// An almost zero vector yields an identity.
assert_eq!(UnitQuaternion::from_scaled_axis_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());```

#### `pub fn mean_of(unit_quaternions: impl IntoIterator<Item = Self>) -> Self`[src]

Create the mean unit quaternion from a data structure implementing IntoIterator returning unit quaternions.

The method will panic if the iterator does not return any quaternions.

Algorithm from: Oshman, Yaakov, and Avishy Carmi. "Attitude estimation from vector observations using a genetic-algorithm-embedded quaternion particle filter." Journal of Guidance, Control, and Dynamics 29.4 (2006): 879-891.

# Example

```let q1 = UnitQuaternion::from_euler_angles(0.0, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-0.1, 0.0, 0.0);
let q3 = UnitQuaternion::from_euler_angles(0.1, 0.0, 0.0);

let quat_vec = vec![q1, q2, q3];
let q_mean = UnitQuaternion::mean_of(quat_vec);

let euler_angles_mean = q_mean.euler_angles();
assert_relative_eq!(euler_angles_mean.0, 0.0, epsilon = 1.0e-7)```

### `impl<N: RealField> Unit<Complex<N>>`[src]

#### `pub fn angle(&self) -> N`[src]

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

# Example

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

#### `pub fn sin_angle(&self) -> N`[src]

The sine of the rotation angle.

# Example

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

#### `pub fn cos_angle(&self) -> N`[src]

The cosine of the rotation angle.

# Example

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

#### `pub fn scaled_axis(&self) -> Vector1<N>`[src]

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.

#### `pub fn axis_angle(&self) -> Option<(Unit<Vector1<N>>, N)>`[src]

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.

#### `pub fn complex(&self) -> &Complex<N>`[src]

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()));```

#### ```#[must_use = "Did you mean to use conjugate_mut()?"] pub fn conjugate(&self) -> Self```[src]

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);```

#### ```#[must_use = "Did you mean to use inverse_mut()?"] pub fn inverse(&self) -> Self```[src]

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);```

#### `pub fn angle_to(&self, other: &Self) -> N`[src]

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);```

#### `pub fn rotation_to(&self, other: &Self) -> Self`[src]

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);```

#### `pub fn conjugate_mut(&mut self)`[src]

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);```

#### `pub fn inverse_mut(&mut self)`[src]

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());```

#### `pub fn powf(&self, n: N) -> Self`[src]

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);```

#### `pub fn to_rotation_matrix(&self) -> Rotation2<N>`[src]

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);```

#### `pub fn to_homogeneous(&self) -> Matrix3<N>`[src]

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);```

#### `pub fn transform_point(&self, pt: &Point2<N>) -> Point2<N>`[src]

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);```

#### `pub fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N>`[src]

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);```

#### `pub fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N>`[src]

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);```

#### `pub fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N>`[src]

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);```

### `impl<N: RealField> Unit<Complex<N>>`[src]

#### `pub fn identity() -> Self`[src]

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);```

#### `pub fn new(angle: N) -> Self`[src]

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));```

#### `pub fn from_angle(angle: N) -> Self`[src]

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));```

#### `pub fn from_cos_sin_unchecked(cos: N, sin: N) -> Self`[src]

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));```

#### `pub fn from_scaled_axis<SB: Storage<N, U1>>(    axisangle: Vector<N, U1, SB>) -> Self`[src]

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.

#### `pub fn from_complex(q: Complex<N>) -> Self`[src]

Creates a new unit complex number from a complex number.

The input complex number will be normalized.

#### `pub fn from_complex_and_get(q: Complex<N>) -> (Self, N)`[src]

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.

#### `pub fn from_rotation_matrix(rotmat: &Rotation2<N>) -> Self`[src]

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));```

#### `pub fn from_matrix(m: &Matrix2<N>) -> Self`[src]

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.

#### `pub fn from_matrix_eps(    m: &Matrix2<N>,     eps: N,     max_iter: usize,     guess: Self) -> Self`[src]

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.

#### `pub fn rotation_between<SB, SC>(    a: &Vector<N, U2, SB>,     b: &Vector<N, U2, SC>) -> Self where    SB: Storage<N, U2>,    SC: Storage<N, U2>, `[src]

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);```

#### `pub fn scaled_rotation_between<SB, SC>(    a: &Vector<N, U2, SB>,     b: &Vector<N, U2, SC>,     s: N) -> Self where    SB: Storage<N, U2>,    SC: Storage<N, U2>, `[src]

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);```

#### `pub fn rotation_between_axis<SB, SC>(    a: &Unit<Vector<N, U2, SB>>,     b: &Unit<Vector<N, U2, SC>>) -> Self where    SB: Storage<N, U2>,    SC: Storage<N, U2>, `[src]

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);```

#### `pub fn scaled_rotation_between_axis<SB, SC>(    na: &Unit<Vector<N, U2, SB>>,     nb: &Unit<Vector<N, U2, SC>>,     s: N) -> Self where    SB: Storage<N, U2>,    SC: Storage<N, U2>, `[src]

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

### `impl<N: RealField> AbsDiffEq<Unit<Complex<N>>> for UnitComplex<N>`[src]

#### `type Epsilon = N`

Used for specifying relative comparisons.

### `impl<N, R: Dim, C: Dim, S> AbsDiffEq<Unit<Matrix<N, R, C, S>>> for Unit<Matrix<N, R, C, S>> where    N: Scalar + AbsDiffEq,    S: Storage<N, R, C>,    N::Epsilon: Copy, `[src]

#### `type Epsilon = N::Epsilon`

Used for specifying relative comparisons.

### `impl<N: RealField + AbsDiffEq<Epsilon = N>> AbsDiffEq<Unit<Quaternion<N>>> for UnitQuaternion<N>`[src]

#### `type Epsilon = N`

Used for specifying relative comparisons.

### `impl<T> Deref for Unit<T>`[src]

#### `type Target = T`

The resulting type after dereferencing.

### `impl<N: RealField> Distribution<Unit<Complex<N>>> for Standard where    OpenClosed01: Distribution<N>, `[src]

#### `fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> UnitComplex<N>`[src]

Generate a uniformly distributed random `UnitComplex`.

### `impl<N: RealField, D: DimName> Distribution<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Standard where    DefaultAllocator: Allocator<N, D>,    StandardNormal: Distribution<N>, `[src]

#### `fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Unit<VectorN<N, D>>`[src]

Generate a uniformly distributed random unit vector.

### `impl<N: RealField> Distribution<Unit<Quaternion<N>>> for Standard where    OpenClosed01: Distribution<N>, `[src]

#### `fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> UnitQuaternion<N>`[src]

Generate a uniformly distributed random rotation quaternion.

### `impl<'b, N: RealField> Div<&'b Unit<Complex<N>>> for UnitComplex<N>`[src]

#### `type Output = Self`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, N: RealField> Div<&'b Unit<Complex<N>>> for &'a UnitComplex<N>`[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<'b, N: RealField> Div<&'b Unit<Complex<N>>> for Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, N: RealField> Div<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, N: RealField> Div<&'b Unit<Quaternion<N>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<'b, N: RealField> Div<&'b Unit<Quaternion<N>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, N: RealField> Div<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<'b, N: RealField> Div<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<'b, N, C: TCategoryMul<TAffine>> Div<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `/` operator.

### `impl<'a, 'b, N, C: TCategoryMul<TAffine>> Div<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `/` operator.

### `impl<N: RealField> Div<Unit<Complex<N>>> for UnitComplex<N>`[src]

#### `type Output = Self`

The resulting type after applying the `/` operator.

### `impl<'a, N: RealField> Div<Unit<Complex<N>>> for &'a UnitComplex<N>`[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<N: RealField> Div<Unit<Complex<N>>> for Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<'a, N: RealField> Div<Unit<Complex<N>>> for &'a Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `/` operator.

### `impl<'a, N: RealField> Div<Unit<Quaternion<N>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<N: RealField> Div<Unit<Quaternion<N>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<'a, N: RealField> Div<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<N: RealField> Div<Unit<Quaternion<N>>> for Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `/` operator.

### `impl<N, C: TCategoryMul<TAffine>> Div<Unit<Quaternion<N>>> for Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `/` operator.

### `impl<'a, N, C: TCategoryMul<TAffine>> Div<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `/` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Complex<N>>> for UnitComplex<N>`[src]

#### `type Output = Self`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Complex<N>>> for &'a UnitComplex<N>`[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Complex<N>>> for Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Complex<N>>> for Translation<N, U2> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Isometry<N, U2, UnitComplex<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Complex<N>>> for &'a Translation<N, U2> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Isometry<N, U2, UnitComplex<N>>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField, D: DimName, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where    R: AlgaRotation<Point<N, D>>,    DefaultAllocator: Allocator<N, D>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField, D: DimName, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where    R: AlgaRotation<Point<N, D>>,    DefaultAllocator: Allocator<N, D>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'b, N, D: DimName, S: Storage<N, D>> Mul<&'b Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul,    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,    DefaultAllocator: Allocator<N, D>,    ShapeConstraint: AreMultipliable<D, D, D, U1>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N, D: DimName, S: Storage<N, D>> Mul<&'b Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul,    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,    DefaultAllocator: Allocator<N, D>,    ShapeConstraint: AreMultipliable<D, D, D, U1>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField, S: Storage<N, U2>> Mul<&'b Unit<Matrix<N, U2, U1, S>>> for UnitComplex<N> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Unit<Vector2<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField, S: Storage<N, U2>> Mul<&'b Unit<Matrix<N, U2, U1, S>>> for &'a UnitComplex<N> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Unit<Vector2<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField, SB: Storage<N, U3>> Mul<&'b Unit<Matrix<N, U3, U1, SB>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Unit<Vector3<N>>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField, SB: Storage<N, U3>> Mul<&'b Unit<Matrix<N, U3, U1, SB>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Unit<Vector3<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for Translation<N, U3> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Isometry<N, U3, UnitQuaternion<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N: RealField> Mul<&'b Unit<Quaternion<N>>> for &'a Translation<N, U3> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Isometry<N, U3, UnitQuaternion<N>>`

The resulting type after applying the `*` operator.

### `impl<'b, N, C: TCategoryMul<TAffine>> Mul<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `*` operator.

### `impl<'a, 'b, N, C: TCategoryMul<TAffine>> Mul<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Complex<N>>> for UnitComplex<N>`[src]

#### `type Output = Self`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Complex<N>>> for &'a UnitComplex<N>`[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Complex<N>>> for Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Complex<N>>> for &'a Rotation<N, U2> where    DefaultAllocator: Allocator<N, U2, U2>, `[src]

#### `type Output = UnitComplex<N>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Complex<N>>> for Translation<N, U2> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Isometry<N, U2, UnitComplex<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Complex<N>>> for &'a Translation<N, U2> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Isometry<N, U2, UnitComplex<N>>`

The resulting type after applying the `*` operator.

### `impl<N: RealField, D: DimName, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where    R: AlgaRotation<Point<N, D>>,    DefaultAllocator: Allocator<N, D>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField, D: DimName, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where    R: AlgaRotation<Point<N, D>>,    DefaultAllocator: Allocator<N, D>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<N, D: DimName, S: Storage<N, D>> Mul<Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul,    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,    DefaultAllocator: Allocator<N, D>,    ShapeConstraint: AreMultipliable<D, D, D, U1>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<'a, N, D: DimName, S: Storage<N, D>> Mul<Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul,    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,    DefaultAllocator: Allocator<N, D>,    ShapeConstraint: AreMultipliable<D, D, D, U1>, `[src]

#### `type Output = Unit<VectorN<N, D>>`

The resulting type after applying the `*` operator.

### `impl<N: RealField, S: Storage<N, U2>> Mul<Unit<Matrix<N, U2, U1, S>>> for UnitComplex<N> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Unit<Vector2<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField, S: Storage<N, U2>> Mul<Unit<Matrix<N, U2, U1, S>>> for &'a UnitComplex<N> where    DefaultAllocator: Allocator<N, U2, U1>, `[src]

#### `type Output = Unit<Vector2<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField, SB: Storage<N, U3>> Mul<Unit<Matrix<N, U3, U1, SB>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Unit<Vector3<N>>`

The resulting type after applying the `*` operator.

### `impl<N: RealField, SB: Storage<N, U3>> Mul<Unit<Matrix<N, U3, U1, SB>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Unit<Vector3<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Quaternion<N>>> for &'a UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Quaternion<N>>> for UnitQuaternion<N> where    DefaultAllocator: Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Quaternion<N>>> for Rotation<N, U3> where    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, `[src]

#### `type Output = UnitQuaternion<N>`

The resulting type after applying the `*` operator.

### `impl<N: RealField> Mul<Unit<Quaternion<N>>> for Translation<N, U3> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Isometry<N, U3, UnitQuaternion<N>>`

The resulting type after applying the `*` operator.

### `impl<'a, N: RealField> Mul<Unit<Quaternion<N>>> for &'a Translation<N, U3> where    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, `[src]

#### `type Output = Isometry<N, U3, UnitQuaternion<N>>`

The resulting type after applying the `*` operator.

### `impl<N, C: TCategoryMul<TAffine>> Mul<Unit<Quaternion<N>>> for Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `*` operator.

### `impl<'a, N, C: TCategoryMul<TAffine>> Mul<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,    DefaultAllocator: Allocator<N, U4, U4> + Allocator<N, U4, U1>, `[src]

#### `type Output = Transform<N, U3, C::Representative>`

The resulting type after applying the `*` operator.

### `impl<T: Neg> Neg for Unit<T>`[src]

#### `type Output = Unit<T::Output>`

The resulting type after applying the `-` operator.

## Blanket Implementations

### `impl<R, E> AffineTransformation<E> for R where    E: EuclideanSpace<RealField = R>,    R: RealField,    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,    <E as EuclideanSpace>::Coordinates: ClosedNeg, `

#### `type Rotation = Id<Multiplicative>`

Type of the first rotation to be applied.

#### `type NonUniformScaling = R`

Type of the non-uniform scaling to be applied.

#### `type Translation = Id<Multiplicative>`

The type of the pure translation part of this affine transformation.

### `impl<T> Same<T> for T`

#### `type Output = T`

Should always be `Self`

### `impl<R, E> Similarity<E> for R where    E: EuclideanSpace<RealField = R>,    R: RealField + SubsetOf<R>,    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,    <E as EuclideanSpace>::Coordinates: ClosedNeg, `

#### `type Scaling = R`

The type of the pure (uniform) scaling part of this similarity transformation.

### `impl<T> ToOwned for T where    T: Clone, `[src]

#### `type Owned = T`

The resulting type after obtaining ownership.

### `impl<T, U> TryFrom<U> for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto<U> for T where    U: TryFrom<T>, `[src]

#### `type Error = <U as TryFrom<T>>::Error`

The type returned in the event of a conversion error.