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use crate::{
DualQuaternion, Isometry3, Quaternion, Scalar, SimdRealField, Translation3, UnitDualQuaternion,
UnitQuaternion,
};
use num::{One, Zero};
#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use simba::scalar::SupersetOf;
impl<T: Scalar> DualQuaternion<T> {
/// Creates a dual quaternion from its rotation and translation components.
///
/// # Example
/// ```
/// # use nalgebra::{DualQuaternion, Quaternion};
/// let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);
/// let trans = Quaternion::new(5.0, 6.0, 7.0, 8.0);
///
/// let dq = DualQuaternion::from_real_and_dual(rot, trans);
/// assert_eq!(dq.real.w, 1.0);
/// ```
#[inline]
pub fn from_real_and_dual(real: Quaternion<T>, dual: Quaternion<T>) -> Self {
Self { real, dual }
}
/// The dual quaternion multiplicative identity.
///
/// # Example
/// ```
/// # use nalgebra::{DualQuaternion, Quaternion};
///
/// let dq1 = DualQuaternion::identity();
/// let dq2 = DualQuaternion::from_real_and_dual(
/// Quaternion::new(1.,2.,3.,4.),
/// Quaternion::new(5.,6.,7.,8.)
/// );
///
/// assert_eq!(dq1 * dq2, dq2);
/// assert_eq!(dq2 * dq1, dq2);
/// ```
#[inline]
pub fn identity() -> Self
where
T: SimdRealField,
{
Self::from_real_and_dual(
Quaternion::from_real(T::one()),
Quaternion::from_real(T::zero()),
)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::{Quaternion, DualQuaternion};
/// let q = DualQuaternion::from_real(Quaternion::new(1.0f64, 2.0, 3.0, 4.0));
/// let q2 = q.cast::<f32>();
/// assert_eq!(q2, DualQuaternion::from_real(Quaternion::new(1.0f32, 2.0, 3.0, 4.0)));
/// ```
pub fn cast<To: Scalar>(self) -> DualQuaternion<To>
where
DualQuaternion<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
impl<T: SimdRealField> DualQuaternion<T>
where
T::Element: SimdRealField,
{
/// Creates a dual quaternion from only its real part, with no translation
/// component.
///
/// # Example
/// ```
/// # use nalgebra::{DualQuaternion, Quaternion};
/// let rot = Quaternion::new(1.0, 2.0, 3.0, 4.0);
///
/// let dq = DualQuaternion::from_real(rot);
/// assert_eq!(dq.real.w, 1.0);
/// assert_eq!(dq.dual.w, 0.0);
/// ```
#[inline]
pub fn from_real(real: Quaternion<T>) -> Self {
Self {
real,
dual: Quaternion::zero(),
}
}
}
impl<T: SimdRealField> One for DualQuaternion<T>
where
T::Element: SimdRealField,
{
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<T: SimdRealField> Zero for DualQuaternion<T>
where
T::Element: SimdRealField,
{
#[inline]
fn zero() -> Self {
DualQuaternion::from_real_and_dual(Quaternion::zero(), Quaternion::zero())
}
#[inline]
fn is_zero(&self) -> bool {
self.real.is_zero() && self.dual.is_zero()
}
}
#[cfg(feature = "arbitrary")]
impl<T> Arbitrary for DualQuaternion<T>
where
T: SimdRealField + Arbitrary + Send,
T::Element: SimdRealField,
{
#[inline]
fn arbitrary(rng: &mut Gen) -> Self {
Self::from_real_and_dual(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
}
}
impl<T: SimdRealField> UnitDualQuaternion<T> {
/// The unit dual quaternion multiplicative identity, which also represents
/// the identity transformation as an isometry.
///
/// # Example
/// ```
/// # use nalgebra::{UnitDualQuaternion, UnitQuaternion, Vector3, Point3};
/// let ident = UnitDualQuaternion::identity();
/// let point = Point3::new(1.0, -4.3, 3.33);
///
/// assert_eq!(ident * point, point);
/// assert_eq!(ident, ident.inverse());
/// ```
#[inline]
pub fn identity() -> Self {
Self::new_unchecked(DualQuaternion::identity())
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::UnitDualQuaternion;
/// let q = UnitDualQuaternion::<f64>::identity();
/// let q2 = q.cast::<f32>();
/// assert_eq!(q2, UnitDualQuaternion::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> UnitDualQuaternion<To>
where
UnitDualQuaternion<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
impl<T: SimdRealField> UnitDualQuaternion<T>
where
T::Element: SimdRealField,
{
/// Return a dual quaternion representing the translation and orientation
/// given by the provided rotation quaternion and translation vector.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{UnitDualQuaternion, UnitQuaternion, Vector3, Point3};
/// let dq = UnitDualQuaternion::from_parts(
/// Vector3::new(0.0, 3.0, 0.0).into(),
/// UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
/// );
/// let point = Point3::new(1.0, 2.0, 3.0);
///
/// assert_relative_eq!(dq * point, Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn from_parts(translation: Translation3<T>, rotation: UnitQuaternion<T>) -> Self {
let half: T = crate::convert(0.5f64);
UnitDualQuaternion::new_unchecked(DualQuaternion {
real: rotation.clone().into_inner(),
dual: Quaternion::from_parts(T::zero(), translation.vector)
* rotation.into_inner()
* half,
})
}
/// Return a unit dual quaternion representing the translation and orientation
/// given by the provided isometry.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Isometry3, UnitDualQuaternion, UnitQuaternion, Vector3, Point3};
/// let iso = Isometry3::from_parts(
/// Vector3::new(0.0, 3.0, 0.0).into(),
/// UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
/// );
/// let dq = UnitDualQuaternion::from_isometry(&iso);
/// let point = Point3::new(1.0, 2.0, 3.0);
///
/// assert_relative_eq!(dq * point, iso * point, epsilon = 1.0e-6);
/// ```
#[inline]
pub fn from_isometry(isometry: &Isometry3<T>) -> Self {
// TODO: take the isometry by-move instead of cloning it.
let isometry = isometry.clone();
UnitDualQuaternion::from_parts(isometry.translation, isometry.rotation)
}
/// Creates a dual quaternion from a unit quaternion rotation.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{UnitQuaternion, UnitDualQuaternion, Quaternion};
/// let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
/// let rot = UnitQuaternion::new_normalize(q);
///
/// let dq = UnitDualQuaternion::from_rotation(rot);
/// assert_relative_eq!(dq.as_ref().real.norm(), 1.0, epsilon = 1.0e-6);
/// assert_eq!(dq.as_ref().dual.norm(), 0.0);
/// ```
#[inline]
pub fn from_rotation(rotation: UnitQuaternion<T>) -> Self {
Self::new_unchecked(DualQuaternion::from_real(rotation.into_inner()))
}
}
impl<T: SimdRealField> One for UnitDualQuaternion<T>
where
T::Element: SimdRealField,
{
#[inline]
fn one() -> Self {
Self::identity()
}
}
#[cfg(feature = "arbitrary")]
impl<T> Arbitrary for UnitDualQuaternion<T>
where
T: SimdRealField + Arbitrary + Send,
T::Element: SimdRealField,
{
#[inline]
fn arbitrary(rng: &mut Gen) -> Self {
Self::new_normalize(Arbitrary::arbitrary(rng))
}
}