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```
```use na::{RealField, Rotation3, Unit, UnitQuaternion, U3};

use crate::aliases::{Qua, TMat3, TMat4, TVec3, TVec4};

/// Rotate the vector `v` by the quaternion `q` assumed to be normalized.
pub fn quat_cross_vec<N: RealField>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
UnitQuaternion::new_unchecked(*q) * v
}

/// Rotate the vector `v` by the inverse of the quaternion `q` assumed to be normalized.
pub fn quat_inv_cross_vec<N: RealField>(v: &TVec3<N>, q: &Qua<N>) -> TVec3<N> {
UnitQuaternion::new_unchecked(*q).inverse() * v
}

/// The quaternion `w` component.
pub fn quat_extract_real_component<N: RealField>(q: &Qua<N>) -> N {
q.w
}

/// Normalized linear interpolation between two quaternions.
pub fn quat_fast_mix<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
Unit::new_unchecked(*x)
.nlerp(&Unit::new_unchecked(*y), a)
.into_inner()
}

//pub fn quat_intermediate<N: RealField>(prev: &Qua<N>, curr: &Qua<N>, next: &Qua<N>) -> Qua<N> {
//    unimplemented!()
//}

/// The squared magnitude of a quaternion `q`.
pub fn quat_length2<N: RealField>(q: &Qua<N>) -> N {
q.norm_squared()
}

/// The squared magnitude of a quaternion `q`.
pub fn quat_magnitude2<N: RealField>(q: &Qua<N>) -> N {
q.norm_squared()
}

/// The quaternion representing the identity rotation.
pub fn quat_identity<N: RealField>() -> Qua<N> {
UnitQuaternion::identity().into_inner()
}

/// Rotates a vector by a quaternion assumed to be normalized.
pub fn quat_rotate_vec3<N: RealField>(q: &Qua<N>, v: &TVec3<N>) -> TVec3<N> {
UnitQuaternion::new_unchecked(*q) * v
}

/// Rotates a vector in homogeneous coordinates by a quaternion assumed to be normalized.
pub fn quat_rotate_vec<N: RealField>(q: &Qua<N>, v: &TVec4<N>) -> TVec4<N> {
let rotated = Unit::new_unchecked(*q) * v.fixed_rows::<U3>(0);
TVec4::new(rotated.x, rotated.y, rotated.z, v.w)
}

/// The rotation required to align `orig` to `dest`.
pub fn quat_rotation<N: RealField>(orig: &TVec3<N>, dest: &TVec3<N>) -> Qua<N> {
UnitQuaternion::rotation_between(orig, dest)
.unwrap_or_else(UnitQuaternion::identity)
.into_inner()
}

/// The spherical linear interpolation between two quaternions.
pub fn quat_short_mix<N: RealField>(x: &Qua<N>, y: &Qua<N>, a: N) -> Qua<N> {
Unit::new_normalize(*x)
.slerp(&Unit::new_normalize(*y), a)
.into_inner()
}

//pub fn quat_squad<N: RealField>(q1: &Qua<N>, q2: &Qua<N>, s1: &Qua<N>, s2: &Qua<N>, h: N) -> Qua<N> {
//    unimplemented!()
//}

/// Converts a quaternion to a rotation matrix.
pub fn quat_to_mat3<N: RealField>(x: &Qua<N>) -> TMat3<N> {
UnitQuaternion::new_unchecked(*x)
.to_rotation_matrix()
.into_inner()
}

/// Converts a quaternion to a rotation matrix in homogenous coordinates.
pub fn quat_to_mat4<N: RealField>(x: &Qua<N>) -> TMat4<N> {
UnitQuaternion::new_unchecked(*x).to_homogeneous()
}

/// Converts a rotation matrix to a quaternion.
pub fn mat3_to_quat<N: RealField>(x: &TMat3<N>) -> Qua<N> {
let r = Rotation3::from_matrix_unchecked(*x);
UnitQuaternion::from_rotation_matrix(&r).into_inner()
}

/// Converts a rotation matrix in homogeneous coordinates to a quaternion.
pub fn to_quat<N: RealField>(x: &TMat4<N>) -> Qua<N> {
let rot = x.fixed_slice::<U3, U3>(0, 0).into_owned();
mat3_to_quat(&rot)
}
```