[][src]Type Definition nalgebra::geometry::UnitQuaternion

type UnitQuaternion<N> = Unit<Quaternion<N>>;

A unit quaternions. May be used to represent a rotation.

Methods

impl<N: RealField> UnitQuaternion<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));

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));

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.

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> UnitQuaternion<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

Deprecated: Use [UnitQuaternion::face_towards] instead.

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());

Trait Implementations

impl<N: RealField> From<Rotation<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> Into<Quaternion<N>> for UnitQuaternion<N>[src]

impl<N: RealField + Display> Display for UnitQuaternion<N>[src]

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

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

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

type Output = Vector3<N>

The resulting type after applying the * operator.

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

type Output = Vector3<N>

The resulting type after applying the * operator.

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

type Output = Vector3<N>

The resulting type after applying the * operator.

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

type Output = Vector3<N>

The resulting type after applying the * operator.

impl<'a, 'b, N: RealField> Mul<&'b Point<N, U3>> for &'a UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 
[src]

type Output = Point3<N>

The resulting type after applying the * operator.

impl<'a, N: RealField> Mul<Point<N, U3>> for &'a UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 
[src]

type Output = Point3<N>

The resulting type after applying the * operator.

impl<'b, N: RealField> Mul<&'b Point<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 
[src]

type Output = Point3<N>

The resulting type after applying the * operator.

impl<N: RealField> Mul<Point<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 
[src]

type Output = Point3<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<'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<'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<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<N: RealField> Mul<Translation<N, U3>> for UnitQuaternion<N> 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<Translation<N, U3>> for &'a UnitQuaternion<N> 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: RealField> Mul<&'b Translation<N, U3>> for UnitQuaternion<N> 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 Translation<N, U3>> for &'a UnitQuaternion<N> 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: RealField> Mul<Isometry<N, U3, Unit<Quaternion<N>>>> for UnitQuaternion<N> 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<Isometry<N, U3, Unit<Quaternion<N>>>> for &'a UnitQuaternion<N> 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: RealField> Mul<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for UnitQuaternion<N> 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 Isometry<N, U3, Unit<Quaternion<N>>>> for &'a UnitQuaternion<N> 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: RealField> Mul<Similarity<N, U3, Unit<Quaternion<N>>>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 
[src]

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

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> + 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 UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + 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> + 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> + Allocator<N, U4, U1>, 
[src]

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

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

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

impl<N: RealField> MulAssign<Unit<Quaternion<N>>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 
[src]

impl<'b, N: RealField> MulAssign<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 
[src]

impl<N: RealField> MulAssign<Rotation<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 
[src]

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

impl<N: RealField> DivAssign<Unit<Quaternion<N>>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U4, U1>, 
[src]

impl<'b, N: RealField> DivAssign<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 
[src]

impl<N: RealField> DivAssign<Rotation<N, U3>> for UnitQuaternion<N> where
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 
[src]

impl<N: RealField + Arbitrary> Arbitrary for UnitQuaternion<N> where
    Owned<N, U4>: Send,
    Owned<N, U3>: Send
[src]

default fn shrink(&self) -> Box<dyn Iterator<Item = Self> + 'static>

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

type Epsilon = N

Used for specifying relative comparisons.

default fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of ApproxEq::abs_diff_eq.

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

default fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

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

default fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of ApproxEq::ulps_eq.

impl<N: RealField> One for UnitQuaternion<N>[src]

default fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 
[src]

Returns true if self is equal to the multiplicative identity. Read more

impl<N: RealField> AbstractMagma<Multiplicative> for UnitQuaternion<N>[src]

default fn op(&self, O, lhs: &Self) -> Self

Performs specific operation.

impl<N: RealField> AbstractQuasigroup<Multiplicative> for UnitQuaternion<N>[src]

default fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more

default fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq

Returns true if latin squareness holds for the given arguments. Read more

impl<N: RealField> AbstractSemigroup<Multiplicative> for UnitQuaternion<N>[src]

default fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

default fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq

Returns true if associativity holds for the given arguments.

impl<N: RealField> AbstractLoop<Multiplicative> for UnitQuaternion<N>[src]

impl<N: RealField> AbstractMonoid<Multiplicative> for UnitQuaternion<N>[src]

default fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

default fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq

Checks whether operating with the identity element is a no-op for the given argument. Read more

impl<N: RealField> AbstractGroup<Multiplicative> for UnitQuaternion<N>[src]

impl<N: RealField> TwoSidedInverse<Multiplicative> for UnitQuaternion<N>[src]

impl<N: RealField> Identity<Multiplicative> for UnitQuaternion<N>[src]

default fn id(O) -> Self

Specific identity.

impl<N1, N2> SubsetOf<Unit<Quaternion<N2>>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N1, N2> SubsetOf<Rotation<N2, U3>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>, 
[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>, 
[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>, 
[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N1: RealField, N2: RealField + SupersetOf<N1>> SubsetOf<Matrix<N2, U4, U4, <DefaultAllocator as Allocator<N2, U4, U4>>::Buffer>> for UnitQuaternion<N1>[src]

default fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<N: RealField> Transformation<Point<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> ProjectiveTransformation<Point<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> AffineTransformation<Point<N, U3>> for UnitQuaternion<N>[src]

type Rotation = Self

Type of the first rotation to be applied.

type NonUniformScaling = Id

Type of the non-uniform scaling to be applied.

type Translation = Id

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

default fn append_rotation_wrt_point(
    &self,
    r: &Self::Rotation,
    p: &E
) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant. Read more

impl<N: RealField> Similarity<Point<N, U3>> for UnitQuaternion<N>[src]

type Scaling = Id

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

default fn translate_point(&self, pt: &E) -> E

Applies this transformation's pure translational part to a point.

default fn rotate_point(&self, pt: &E) -> E

Applies this transformation's pure rotational part to a point.

default fn scale_point(&self, pt: &E) -> E

Applies this transformation's pure scaling part to a point.

default fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation's pure rotational part to a vector.

default fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation's pure scaling part to a vector.

default fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse's pure translational part to a point.

default fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse's pure rotational part to a point.

default fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse's pure scaling part to a point.

default fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse's pure rotational part to a vector.

default fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse's pure scaling part to a vector.

impl<N: RealField> Isometry<Point<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> DirectIsometry<Point<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> OrthogonalTransformation<Point<N, U3>> for UnitQuaternion<N>[src]

impl<N: RealField> Rotation<Point<N, U3>> for UnitQuaternion<N>[src]