Struct Quat

pub struct Quat(/* private fields */);

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

impl Quat

pub const IDENTITY: Self = _

The identity quaternion. Corresponds to no rotation.

pub const NAN: Self = _

All NANs.

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.

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.

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.

pub fn from_slice(slice: &[f32]) -> Self

Creates a rotation quaternion from a slice.

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.

Panics

Panics if slice length is less than 4.

pub fn write_to_slice(self, slice: &mut [f32])

Writes the quaternion to an unaligned slice.

Panics

Panics if slice length is less than 4.

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.

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.

pub fn from_rotation_x(angle: f32) -> Self

Creates a quaternion from the angle (in radians) around the x axis.

pub fn from_rotation_y(angle: f32) -> Self

Creates a quaternion from the angle (in radians) around the y axis.

pub fn from_rotation_z(angle: f32) -> Self

Creates a quaternion from the angle (in radians) around the z axis.

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).

pub fn from_mat3(mat: &Mat3) -> Self

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.

pub fn from_mat3a(mat: &Mat3A) -> Self

Creates a quaternion from a 3x3 SIMD aligned 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.

pub fn from_mat4(mat: &Mat4) -> Self

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.

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.

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.

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.

pub fn to_axis_angle(self) -> (Vec3, f32)

Returns the rotation axis (normalized) and angle (in radians) of self.

pub fn to_scaled_axis(self) -> Vec3

Returns the rotation axis scaled by the rotation in radians.

pub fn to_euler(self, order: EulerRot) -> (f32, f32, f32)

Returns the rotation angles for the given euler rotation sequence.

pub fn to_array(&self) -> [f32; 4]

[x, y, z, w]

pub fn xyz(self) -> Vec3

Returns the vector part of the quaternion.

pub fn conjugate(self) -> Self

Returns the quaternion conjugate of self. For a unit quaternion the conjugate is also the inverse.

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.

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.

pub fn length(self) -> f32

Computes the length of self.

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.

pub fn length_recip(self) -> f32

Computes 1.0 / length().

For valid results, self must not be of length zero.

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.

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

Returns true if any elements are NAN.

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

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.

pub fn rotate_towards(&self, rhs: Self, max_angle: f32) -> Self

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.

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.

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.

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.

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.

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.

pub fn from_affine3(a: &Affine3A) -> Self

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 mul_vec3a(self, rhs: Vec3A) -> Vec3A

Multiplies a quaternion and a 3D vector, returning the rotated vector.

pub fn as_dquat(self) -> DQuat

Trait Implementations

impl Add for Quat

fn add(self, rhs: Self) -> Self

Adds two quaternions.

The sum is not guaranteed to be normalized.

Note that addition is not the same as combining the rotations represented by the two quaternions! That corresponds to multiplication.

type Output = Quat

The resulting type after applying the + operator.

impl AsRef<[f32; 4]> for Quat

fn as_ref(&self) -> &[f32; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl Clone for Quat

fn clone(&self) -> Quat

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Quat

fn fmt(&self, fmt: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for Quat

fn default() -> Self

Returns the “default value” for a type.

impl Deref for Quat

type Target = Vec4<f32>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl DerefMut for Quat

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl Display for Quat

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Div<f32> for Quat

fn div(self, rhs: f32) -> Self

Divides a quaternion by a scalar value. The quotient is not guaranteed to be normalized.

type Output = Quat

The resulting type after applying the / operator.

impl From<Quat> for [f32; 4]

fn from(q: Quat) -> Self

Converts to this type from the input type.

impl From<Quat> for (f32, f32, f32, f32)

fn from(q: Quat) -> Self

Converts to this type from the input type.

impl From<Quat> for Vec4

fn from(q: Quat) -> Self

Converts to this type from the input type.

impl From<Quat> for __m128

fn from(q: Quat) -> Self

Converts to this type from the input type.

impl Mul<Vec3> for Quat

fn mul(self, rhs: Vec3) -> Self::Output

Multiplies a quaternion and a 3D vector, returning the rotated vector.

Panics

Will panic if self is not normalized when glam_assert is enabled.

type Output = Vec3

The resulting type after applying the * operator.

impl Mul<Vec3A> for Quat

type Output = Vec3A

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3A) -> Self::Output

Performs the * operation.

impl Mul<f32> for Quat

fn mul(self, rhs: f32) -> Self

Multiplies a quaternion by a scalar value.

The product is not guaranteed to be normalized.

type Output = Quat

The resulting type after applying the * operator.

impl Mul for Quat

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.

type Output = Quat

The resulting type after applying the * operator.

impl MulAssign for Quat

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 Neg for Quat

type Output = Quat

The resulting type after applying the - operator.

fn neg(self) -> Self

Performs the unary - operation.

impl PartialEq for Quat

fn eq(&self, rhs: &Self) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a> Product<&'a Quat> for Quat

fn product<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Product for Quat

fn product<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl Sub for Quat

fn sub(self, rhs: Self) -> Self

Subtracts the rhs quaternion from self.

The difference is not guaranteed to be normalized.

type Output = Quat

The resulting type after applying the - operator.

impl<'a> Sum<&'a Quat> for Quat

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = &'a Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Sum for Quat

fn sum<I>(iter: I) -> Self

where I: Iterator<Item = Self>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl Copy for Quat