#[repr(transparent)]pub struct Quat(_);
Expand description
A quaternion representing an orientation.
This quaternion is intended to be of unit length but may denormalize due to floating point “error creep” which can occur when successive quaternion operations are applied.
This type is 16 byte aligned.
Implementations
sourceimpl Quat
impl Quat
sourcepub const IDENTITY: Quat = Self(InnerF32::W)
pub const IDENTITY: Quat = Self(InnerF32::W)
The identity quaternion. Corresponds to no rotation.
sourcepub fn from_xyzw(x: f32, y: f32, z: f32, w: f32) -> Quat
pub fn from_xyzw(x: f32, y: f32, z: f32, w: f32) -> Quat
Creates a new rotation quaternion.
This should generally not be called manually unless you know what you are doing.
Use one of the other constructors instead such as identity
or from_axis_angle
.
from_xyzw
is mostly used by unit tests and serde
deserialization.
pub const fn identity() -> Quat
use Quat::IDENTITY instead
sourcepub fn from_slice_unaligned(slice: &[f32]) -> Quat
pub fn from_slice_unaligned(slice: &[f32]) -> Quat
Creates a rotation quaternion from an unaligned slice.
Preconditions
The resulting quaternion is expected to be of unit length.
Panics
Panics if slice
length is less than 4.
sourcepub fn write_to_slice_unaligned(self, slice: &mut [f32])
pub fn write_to_slice_unaligned(self, slice: &mut [f32])
sourcepub fn from_axis_angle(axis: Vec3, angle: f32) -> Quat
pub fn from_axis_angle(axis: Vec3, angle: f32) -> Quat
Create a quaternion for a normalized rotation axis
and angle
(in radians).
The axis must be normalized (unit-length).
sourcepub fn from_scaled_axis(v: Vec3) -> Quat
pub fn from_scaled_axis(v: Vec3) -> Quat
Create a quaternion that rotates v.length()
radians around v.normalize()
.
from_scaled_axis(Vec3::ZERO)
results in the identity quaternion.
sourcepub fn from_rotation_x(angle: f32) -> Quat
pub fn from_rotation_x(angle: f32) -> Quat
Creates a quaternion from the angle
(in radians) around the x axis.
sourcepub fn from_rotation_y(angle: f32) -> Quat
pub fn from_rotation_y(angle: f32) -> Quat
Creates a quaternion from the angle
(in radians) around the y axis.
sourcepub fn from_rotation_z(angle: f32) -> Quat
pub fn from_rotation_z(angle: f32) -> Quat
Creates a quaternion from the angle
(in radians) around the z axis.
sourcepub fn from_rotation_ypr(yaw: f32, pitch: f32, roll: f32) -> Quat
pub fn from_rotation_ypr(yaw: f32, pitch: f32, roll: f32) -> Quat
Create a quaternion from the given yaw (around y), pitch (around x) and roll (around z) in radians.
sourcepub fn from_rotation_mat3(mat: &Mat3) -> Quat
pub fn from_rotation_mat3(mat: &Mat3) -> Quat
Creates a quaternion from a 3x3 rotation matrix.
sourcepub fn from_rotation_mat4(mat: &Mat4) -> Quat
pub fn from_rotation_mat4(mat: &Mat4) -> Quat
Creates a quaternion from a 3x3 rotation matrix inside a homogeneous 4x4 matrix.
sourcepub fn from_rotation_arc(from: Vec3, to: Vec3) -> Quat
pub fn from_rotation_arc(from: Vec3, to: Vec3) -> Quat
Gets the minimal rotation for transforming from
to to
.
The rotation is in the plane spanned by the two vectors.
Will rotate at most 180 degrees.
The input vectors must be normalized (unit-length).
from_rotation_arc(from, to) * from ≈ to
.
For near-singular cases (from≈to and from≈-to) the current implementation
is only accurate to about 0.001 (for f32
).
sourcepub fn from_rotation_arc_colinear(from: Vec3, to: Vec3) -> Quat
pub fn from_rotation_arc_colinear(from: Vec3, to: Vec3) -> Quat
Gets the minimal rotation for transforming from
to either to
or -to
.
This means that the resulting quaternion will rotate from
so that it is colinear with to
.
The rotation is in the plane spanned by the two vectors. Will rotate at most 90 degrees.
The input vectors must be normalized (unit-length).
to.dot(from_rotation_arc_colinear(from, to) * from).abs() ≈ 1
.
sourcepub fn to_axis_angle(self) -> (Vec3, f32)
pub fn to_axis_angle(self) -> (Vec3, f32)
Returns the rotation axis and angle (in radians) of self
.
sourcepub fn to_scaled_axis(self) -> Vec3
pub fn to_scaled_axis(self) -> Vec3
Returns the rotation axis scaled by the rotation in radians.
sourcepub fn conjugate(self) -> Quat
pub fn conjugate(self) -> Quat
Returns the quaternion conjugate of self
. For a unit quaternion the
conjugate is also the inverse.
sourcepub fn inverse(self) -> Quat
pub fn inverse(self) -> Quat
Returns the inverse of a normalized quaternion.
Typically quaternion inverse returns the conjugate of a normalized quaternion.
Because self
is assumed to already be unit length this method does not normalize
before returning the conjugate.
sourcepub fn dot(self, other: Quat) -> f32
pub fn dot(self, other: Quat) -> f32
Computes the dot product of self
and other
. The dot product is
equal to the the cosine of the angle between two quaternion rotations.
sourcepub fn length_squared(self) -> f32
pub fn length_squared(self) -> f32
Computes the squared length of self
.
This is generally faster than length()
as it avoids a square
root operation.
sourcepub fn length_recip(self) -> f32
pub fn length_recip(self) -> f32
Computes 1.0 / length()
.
For valid results, self
must not be of length zero.
sourcepub fn normalize(self) -> Quat
pub fn normalize(self) -> Quat
Returns self
normalized to length 1.0.
For valid results, self
must not be of length zero.
sourcepub fn is_finite(self) -> bool
pub fn is_finite(self) -> bool
Returns true
if, and only if, all elements are finite.
If any element is either NaN
, positive or negative infinity, this will return false
.
pub fn is_nan(self) -> bool
sourcepub fn is_normalized(self) -> bool
pub fn is_normalized(self) -> bool
Returns whether self
of length 1.0
or not.
Uses a precision threshold of 1e-6
.
pub fn is_near_identity(self) -> bool
sourcepub fn angle_between(self, other: Quat) -> f32
pub fn angle_between(self, other: Quat) -> f32
Returns the angle (in radians) for the minimal rotation for transforming this quaternion into another.
Both quaternions must be normalized.
sourcepub fn abs_diff_eq(self, other: Quat, max_abs_diff: f32) -> bool
pub fn abs_diff_eq(self, other: Quat, max_abs_diff: f32) -> bool
Returns true if the absolute difference of all elements between self
and other
is less than or equal to max_abs_diff
.
This can be used to compare if two quaternions contain similar elements. It works
best when comparing with a known value. The max_abs_diff
that should be used used
depends on the values being compared against.
For more see comparing floating point numbers.
sourcepub fn lerp(self, end: Quat, s: f32) -> Quat
pub fn lerp(self, end: Quat, s: f32) -> Quat
Performs a linear interpolation between self
and other
based on
the value s
.
When s
is 0.0
, the result will be equal to self
. When s
is 1.0
, the result will be equal to other
.
sourcepub fn slerp(self, end: Quat, s: f32) -> Quat
pub fn slerp(self, end: Quat, s: f32) -> Quat
Performs a spherical linear interpolation between self
and end
based on the value s
.
When s
is 0.0
, the result will be equal to self
. When s
is 1.0
, the result will be equal to end
.
Note that a rotation can be represented by two quaternions: q
and
-q
. The slerp path between q
and end
will be different from the
path between -q
and end
. One path will take the long way around and
one will take the short way. In order to correct for this, the dot
product between self
and end
should be positive. If the dot
product is negative, slerp between -self
and end
.
sourcepub fn mul_vec3(self, other: Vec3) -> Vec3
pub fn mul_vec3(self, other: Vec3) -> Vec3
Multiplies a quaternion and a 3D vector, returning the rotated vector.
sourcepub fn mul_quat(self, other: Quat) -> Quat
pub fn mul_quat(self, other: Quat) -> Quat
Multiplies two quaternions. If they each represent a rotation, the result will represent the combined rotation. Note that due to floating point rounding the result may not be perfectly normalized.
sourcepub fn mul_vec3a(self, other: Vec3A) -> Vec3A
pub fn mul_vec3a(self, other: Vec3A) -> Vec3A
Multiplies a quaternion and a 3D vector, returning the rotated vector.
pub fn as_f64(self) -> DQuat
Trait Implementations
sourceimpl Add<Quat> for Quat
impl Add<Quat> for Quat
sourceimpl MulAssign<Quat> for Quat
impl MulAssign<Quat> for Quat
sourcefn mul_assign(&mut self, other: Quat)
fn mul_assign(&mut self, other: Quat)
Performs the *=
operation. Read more
sourceimpl PartialOrd<Quat> for Quat
impl PartialOrd<Quat> for Quat
sourcefn partial_cmp(&self, other: &Quat) -> Option<Ordering>
fn partial_cmp(&self, other: &Quat) -> Option<Ordering>
This method returns an ordering between self
and other
values if one exists. Read more
1.0.0 · sourcefn lt(&self, other: &Rhs) -> bool
fn lt(&self, other: &Rhs) -> bool
This method tests less than (for self
and other
) and is used by the <
operator. Read more
1.0.0 · sourcefn le(&self, other: &Rhs) -> bool
fn le(&self, other: &Rhs) -> bool
This method tests less than or equal to (for self
and other
) and is used by the <=
operator. Read more
impl Copy for Quat
Auto Trait Implementations
impl RefUnwindSafe for Quat
impl Send for Quat
impl Sync for Quat
impl Unpin for Quat
impl UnwindSafe for Quat
Blanket Implementations
sourceimpl<T> BorrowMut<T> for T where
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
const: unstable · sourcefn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
Mutably borrows from an owned value. Read more