pub struct Quat(/* private fields */);
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.
SIMD vector types are used for storage on supported platforms.
This type is 16 byte aligned.
Implementations§
source§impl Quat
impl Quat
sourcepub const fn from_xyzw(x: f32, y: f32, z: f32, w: f32) -> Self
pub const fn from_xyzw(x: f32, y: f32, z: f32, w: f32) -> Self
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.
§Preconditions
This function does not check if the input is normalized, it is up to the user to provide normalized input or to normalized the resulting quaternion.
sourcepub const fn from_array(a: [f32; 4]) -> Self
pub const fn from_array(a: [f32; 4]) -> Self
Creates a rotation quaternion from an array.
§Preconditions
This function does not check if the input is normalized, it is up to the user to provide normalized input or to normalized the resulting quaternion.
sourcepub const fn from_vec4(v: Vec4) -> Self
pub const fn from_vec4(v: Vec4) -> Self
Creates a new rotation quaternion from a 4D vector.
§Preconditions
This function does not check if the input is normalized, it is up to the user to provide normalized input or to normalized the resulting quaternion.
sourcepub fn from_slice(slice: &[f32]) -> Self
pub fn from_slice(slice: &[f32]) -> Self
sourcepub fn write_to_slice(self, slice: &mut [f32])
pub fn write_to_slice(self, slice: &mut [f32])
sourcepub fn from_axis_angle(axis: Vec3, angle: f32) -> Self
pub fn from_axis_angle(axis: Vec3, angle: f32) -> Self
Create a quaternion for a normalized rotation axis
and angle
(in radians).
The axis must be a unit vector.
§Panics
Will panic if axis
is not normalized when glam_assert
is enabled.
sourcepub fn from_scaled_axis(v: Vec3) -> Self
pub fn from_scaled_axis(v: Vec3) -> Self
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) -> Self
pub fn from_rotation_x(angle: f32) -> Self
Creates a quaternion from the angle
(in radians) around the x axis.
sourcepub fn from_rotation_y(angle: f32) -> Self
pub fn from_rotation_y(angle: f32) -> Self
Creates a quaternion from the angle
(in radians) around the y axis.
sourcepub fn from_rotation_z(angle: f32) -> Self
pub fn from_rotation_z(angle: f32) -> Self
Creates a quaternion from the angle
(in radians) around the z axis.
sourcepub fn from_euler(euler: EulerRot, a: f32, b: f32, c: f32) -> Self
pub fn from_euler(euler: EulerRot, a: f32, b: f32, c: f32) -> Self
Creates a quaternion from the given Euler rotation sequence and the angles (in radians).
sourcepub fn from_mat3a(mat: &Mat3A) -> Self
pub fn from_mat3a(mat: &Mat3A) -> Self
Creates a quaternion from a 3x3 SIMD aligned rotation matrix.
sourcepub fn from_mat4(mat: &Mat4) -> Self
pub fn from_mat4(mat: &Mat4) -> Self
Creates a quaternion from a 3x3 rotation matrix inside a homogeneous 4x4 matrix.
sourcepub fn from_rotation_arc(from: Vec3, to: Vec3) -> Self
pub fn from_rotation_arc(from: Vec3, to: Vec3) -> Self
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 inputs must be unit vectors.
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
).
§Panics
Will panic if from
or to
are not normalized when glam_assert
is enabled.
sourcepub fn from_rotation_arc_colinear(from: Vec3, to: Vec3) -> Self
pub fn from_rotation_arc_colinear(from: Vec3, to: Vec3) -> Self
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 inputs must be unit vectors.
to.dot(from_rotation_arc_colinear(from, to) * from).abs() ≈ 1
.
§Panics
Will panic if from
or to
are not normalized when glam_assert
is enabled.
sourcepub fn from_rotation_arc_2d(from: Vec2, to: Vec2) -> Self
pub fn from_rotation_arc_2d(from: Vec2, to: Vec2) -> Self
Gets the minimal rotation for transforming from
to to
. The resulting rotation is
around the z axis. Will rotate at most 180 degrees.
The inputs must be unit vectors.
from_rotation_arc_2d(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
).
§Panics
Will panic if from
or to
are not normalized when glam_assert
is enabled.
sourcepub fn to_axis_angle(self) -> (Vec3, f32)
pub fn to_axis_angle(self) -> (Vec3, f32)
Returns the rotation axis (normalized) 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 to_euler(self, euler: EulerRot) -> (f32, f32, f32)
pub fn to_euler(self, euler: EulerRot) -> (f32, f32, f32)
Returns the rotation angles for the given euler rotation sequence.
sourcepub fn conjugate(self) -> Self
pub fn conjugate(self) -> Self
Returns the quaternion conjugate of self
. For a unit quaternion the
conjugate is also the inverse.
sourcepub fn inverse(self) -> Self
pub fn inverse(self) -> Self
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.
§Panics
Will panic if self
is not normalized when glam_assert
is enabled.
sourcepub fn dot(self, rhs: Self) -> f32
pub fn dot(self, rhs: Self) -> f32
Computes the dot product of self
and rhs
. The dot product is
equal to 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) -> Self
pub fn normalize(self) -> Self
Returns self
normalized to length 1.0.
For valid results, self
must not be of length zero.
Panics
Will panic if self
is zero length when glam_assert
is enabled.
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, rhs: Self) -> f32
pub fn angle_between(self, rhs: Self) -> f32
Returns the angle (in radians) for the minimal rotation for transforming this quaternion into another.
Both quaternions must be normalized.
§Panics
Will panic if self
or rhs
are not normalized when glam_assert
is enabled.
sourcepub fn abs_diff_eq(self, rhs: Self, max_abs_diff: f32) -> bool
pub fn abs_diff_eq(self, rhs: Self, max_abs_diff: f32) -> bool
Returns true if the absolute difference of all elements between self
and rhs
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: Self, s: f32) -> Self
pub fn lerp(self, end: Self, s: f32) -> Self
Performs a linear interpolation between self
and rhs
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 rhs
.
§Panics
Will panic if self
or end
are not normalized when glam_assert
is enabled.
sourcepub fn slerp(self, end: Self, s: f32) -> Self
pub fn slerp(self, end: Self, s: f32) -> Self
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
.
§Panics
Will panic if self
or end
are not normalized when glam_assert
is enabled.
sourcepub fn mul_vec3(self, rhs: Vec3) -> Vec3
pub fn mul_vec3(self, rhs: Vec3) -> Vec3
Multiplies a quaternion and a 3D vector, returning the rotated vector.
§Panics
Will panic if self
is not normalized when glam_assert
is enabled.
sourcepub fn mul_quat(self, rhs: Self) -> Self
pub fn mul_quat(self, rhs: Self) -> Self
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.
§Panics
Will panic if self
or rhs
are not normalized when glam_assert
is enabled.
sourcepub fn from_affine3(a: &Affine3A) -> Self
pub fn from_affine3(a: &Affine3A) -> Self
Creates a quaternion from a 3x3 rotation matrix inside a 3D affine transform.
sourcepub fn mul_vec3a(self, rhs: Vec3A) -> Vec3A
pub fn mul_vec3a(self, rhs: Vec3A) -> Vec3A
Multiplies a quaternion and a 3D vector, returning the rotated vector.
pub fn as_dquat(self) -> DQuat
pub fn as_f64(self) -> DQuat
Trait Implementations§
source§impl Add for Quat
impl Add for Quat
source§impl<'de> Deserialize<'de> for Quat
impl<'de> Deserialize<'de> for Quat
source§fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
source§impl Distribution<Quat> for Standard
impl Distribution<Quat> for Standard
source§impl Mul for Quat
impl Mul for Quat
source§fn mul(self, rhs: Self) -> Self
fn mul(self, rhs: Self) -> Self
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.
§Panics
Will panic if self
or rhs
are not normalized when glam_assert
is enabled.
source§impl MulAssign for Quat
impl MulAssign for Quat
source§fn mul_assign(&mut self, rhs: Self)
fn mul_assign(&mut self, rhs: Self)
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.
§Panics
Will panic if self
or rhs
are not normalized when glam_assert
is enabled.
impl Copy for Quat
impl Pod for Quat
Auto Trait Implementations§
impl Freeze for Quat
impl RefUnwindSafe for Quat
impl Send for Quat
impl Sync for Quat
impl Unpin for Quat
impl UnwindSafe for Quat
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> CheckedBitPattern for Twhere
T: AnyBitPattern,
impl<T> CheckedBitPattern for Twhere
T: AnyBitPattern,
§type Bits = T
type Bits = T
Self
must have the same layout as the specified Bits
except for
the possible invalid bit patterns being checked during
is_valid_bit_pattern
.source§fn is_valid_bit_pattern(_bits: &T) -> bool
fn is_valid_bit_pattern(_bits: &T) -> bool
bits
as &Self
.