Struct valence_math::DQuat
source · #[repr(C)]pub struct DQuat {
pub x: f64,
pub y: f64,
pub z: f64,
pub w: f64,
}
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.
Fields§
§x: f64
§y: f64
§z: f64
§w: f64
Implementations§
source§impl DQuat
impl DQuat
sourcepub const fn from_xyzw(x: f64, y: f64, z: f64, w: f64) -> DQuat
pub const fn from_xyzw(x: f64, y: f64, z: f64, w: f64) -> DQuat
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: [f64; 4]) -> DQuat
pub const fn from_array(a: [f64; 4]) -> DQuat
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: DVec4) -> DQuat
pub const fn from_vec4(v: DVec4) -> DQuat
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: &[f64]) -> DQuat
pub fn from_slice(slice: &[f64]) -> DQuat
sourcepub fn write_to_slice(self, slice: &mut [f64])
pub fn write_to_slice(self, slice: &mut [f64])
sourcepub fn from_axis_angle(axis: DVec3, angle: f64) -> DQuat
pub fn from_axis_angle(axis: DVec3, angle: f64) -> DQuat
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: DVec3) -> DQuat
pub fn from_scaled_axis(v: DVec3) -> DQuat
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: f64) -> DQuat
pub fn from_rotation_x(angle: f64) -> DQuat
Creates a quaternion from the angle
(in radians) around the x axis.
sourcepub fn from_rotation_y(angle: f64) -> DQuat
pub fn from_rotation_y(angle: f64) -> DQuat
Creates a quaternion from the angle
(in radians) around the y axis.
sourcepub fn from_rotation_z(angle: f64) -> DQuat
pub fn from_rotation_z(angle: f64) -> DQuat
Creates a quaternion from the angle
(in radians) around the z axis.
sourcepub fn from_euler(euler: EulerRot, a: f64, b: f64, c: f64) -> DQuat
pub fn from_euler(euler: EulerRot, a: f64, b: f64, c: f64) -> DQuat
Creates a quaternion from the given Euler rotation sequence and the angles (in radians).
sourcepub fn from_mat3(mat: &DMat3) -> DQuat
pub fn from_mat3(mat: &DMat3) -> DQuat
Creates a quaternion from a 3x3 rotation matrix.
Note if the input matrix contain scales, shears, or other non-rotation transformations then the resulting quaternion will be ill-defined.
§Panics
Will panic if any input matrix column is not normalized when glam_assert
is enabled.
sourcepub fn from_mat4(mat: &DMat4) -> DQuat
pub fn from_mat4(mat: &DMat4) -> DQuat
Creates a quaternion from the upper 3x3 rotation matrix inside a homogeneous 4x4 matrix.
Note if the upper 3x3 matrix contain scales, shears, or other non-rotation transformations then the resulting quaternion will be ill-defined.
§Panics
Will panic if any column of the upper 3x3 rotation matrix is not normalized when
glam_assert
is enabled.
sourcepub fn from_rotation_arc(from: DVec3, to: DVec3) -> DQuat
pub fn from_rotation_arc(from: DVec3, to: DVec3) -> DQuat
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: DVec3, to: DVec3) -> DQuat
pub fn from_rotation_arc_colinear(from: DVec3, to: DVec3) -> DQuat
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: DVec2, to: DVec2) -> DQuat
pub fn from_rotation_arc_2d(from: DVec2, to: DVec2) -> DQuat
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) -> (DVec3, f64)
pub fn to_axis_angle(self) -> (DVec3, f64)
Returns the rotation axis (normalized) and angle (in radians) of self
.
sourcepub fn to_scaled_axis(self) -> DVec3
pub fn to_scaled_axis(self) -> DVec3
Returns the rotation axis scaled by the rotation in radians.
sourcepub fn to_euler(self, order: EulerRot) -> (f64, f64, f64)
pub fn to_euler(self, order: EulerRot) -> (f64, f64, f64)
Returns the rotation angles for the given euler rotation sequence.
sourcepub fn conjugate(self) -> DQuat
pub fn conjugate(self) -> DQuat
Returns the quaternion conjugate of self
. For a unit quaternion the
conjugate is also the inverse.
sourcepub fn inverse(self) -> DQuat
pub fn inverse(self) -> DQuat
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: DQuat) -> f64
pub fn dot(self, rhs: DQuat) -> f64
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) -> f64
pub fn length_squared(self) -> f64
Computes the squared length of self
.
This is generally faster than length()
as it avoids a square
root operation.
sourcepub fn length_recip(self) -> f64
pub fn length_recip(self) -> f64
Computes 1.0 / length()
.
For valid results, self
must not be of length zero.
sourcepub fn normalize(self) -> DQuat
pub fn normalize(self) -> DQuat
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: DQuat) -> f64
pub fn angle_between(self, rhs: DQuat) -> f64
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 rotate_towards(&self, rhs: DQuat, max_angle: f64) -> DQuat
pub fn rotate_towards(&self, rhs: DQuat, max_angle: f64) -> DQuat
Rotates towards rhs
up to max_angle
(in radians).
When max_angle
is 0.0
, the result will be equal to self
. When max_angle
is equal to
self.angle_between(rhs)
, the result will be equal to rhs
. If max_angle
is negative,
rotates towards the exact opposite of rhs
. Will not go past the target.
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: DQuat, max_abs_diff: f64) -> bool
pub fn abs_diff_eq(self, rhs: DQuat, max_abs_diff: f64) -> 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: DQuat, s: f64) -> DQuat
pub fn lerp(self, end: DQuat, s: f64) -> DQuat
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: DQuat, s: f64) -> DQuat
pub fn slerp(self, end: DQuat, s: f64) -> DQuat
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: DVec3) -> DVec3
pub fn mul_vec3(self, rhs: DVec3) -> DVec3
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: DQuat) -> DQuat
pub fn mul_quat(self, rhs: DQuat) -> DQuat
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: &DAffine3) -> DQuat
pub fn from_affine3(a: &DAffine3) -> DQuat
Creates a quaternion from a 3x3 rotation matrix inside a 3D affine transform.
Note if the input affine matrix contain scales, shears, or other non-rotation transformations then the resulting quaternion will be ill-defined.
§Panics
Will panic if any input affine matrix column is not normalized when glam_assert
is
enabled.
pub fn as_quat(self) -> Quat
Trait Implementations§
source§impl Add for DQuat
impl Add for DQuat
source§impl Mul for DQuat
impl Mul for DQuat
source§fn mul(self, rhs: DQuat) -> DQuat
fn mul(self, rhs: DQuat) -> DQuat
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 DQuat
impl MulAssign for DQuat
source§fn mul_assign(&mut self, rhs: DQuat)
fn mul_assign(&mut self, rhs: DQuat)
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 DQuat
Auto Trait Implementations§
impl Freeze for DQuat
impl RefUnwindSafe for DQuat
impl Send for DQuat
impl Sync for DQuat
impl Unpin for DQuat
impl UnwindSafe for DQuat
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> CloneToUninit for Twhere
T: Clone,
impl<T> CloneToUninit for Twhere
T: Clone,
source§unsafe fn clone_to_uninit(&self, dst: *mut T)
unsafe fn clone_to_uninit(&self, dst: *mut T)
clone_to_uninit
)