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use crate::{Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, RealField, SimdRealField};
/// # Interpolation
impl<T: SimdRealField> Isometry3<T> {
/// Interpolates between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
///
/// let t1 = Translation3::new(1.0, 2.0, 3.0);
/// let t2 = Translation3::new(4.0, 8.0, 12.0);
/// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
/// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
/// let iso1 = Isometry3::from_parts(t1, q1);
/// let iso2 = Isometry3::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
/// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
/// ```
#[inline]
#[must_use]
pub fn lerp_slerp(&self, other: &Self, t: T) -> Self
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.slerp(&other.rotation, t);
Self::from_parts(tr.into(), rot)
}
/// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined).
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Vector3, Translation3, Isometry3, UnitQuaternion};
///
/// let t1 = Translation3::new(1.0, 2.0, 3.0);
/// let t2 = Translation3::new(4.0, 8.0, 12.0);
/// let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
/// let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
/// let iso1 = Isometry3::from_parts(t1, q1);
/// let iso2 = Isometry3::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
/// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
/// ```
#[inline]
#[must_use]
pub fn try_lerp_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
Some(Self::from_parts(tr.into(), rot))
}
}
impl<T: SimdRealField> IsometryMatrix3<T> {
/// Interpolates between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
///
/// let t1 = Translation3::new(1.0, 2.0, 3.0);
/// let t2 = Translation3::new(4.0, 8.0, 12.0);
/// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
/// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
/// let iso1 = IsometryMatrix3::from_parts(t1, q1);
/// let iso2 = IsometryMatrix3::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
/// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
/// ```
#[inline]
#[must_use]
pub fn lerp_slerp(&self, other: &Self, t: T) -> Self
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.slerp(&other.rotation, t);
Self::from_parts(tr.into(), rot)
}
/// Attempts to interpolate between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Retuns `None` if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined).
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Vector3, Translation3, Rotation3, IsometryMatrix3};
///
/// let t1 = Translation3::new(1.0, 2.0, 3.0);
/// let t2 = Translation3::new(4.0, 8.0, 12.0);
/// let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
/// let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
/// let iso1 = IsometryMatrix3::from_parts(t1, q1);
/// let iso2 = IsometryMatrix3::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
/// assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));
/// ```
#[inline]
#[must_use]
pub fn try_lerp_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.try_slerp(&other.rotation, t, epsilon)?;
Some(Self::from_parts(tr.into(), rot))
}
}
impl<T: SimdRealField> Isometry2<T> {
/// Interpolates between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Vector2, Translation2, UnitComplex, Isometry2};
///
/// let t1 = Translation2::new(1.0, 2.0);
/// let t2 = Translation2::new(4.0, 8.0);
/// let q1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
/// let q2 = UnitComplex::new(-std::f32::consts::PI);
/// let iso1 = Isometry2::from_parts(t1, q1);
/// let iso2 = Isometry2::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
/// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
/// ```
#[inline]
#[must_use]
pub fn lerp_slerp(&self, other: &Self, t: T) -> Self
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.slerp(&other.rotation, t);
Self::from_parts(tr.into(), rot)
}
}
impl<T: SimdRealField> IsometryMatrix2<T> {
/// Interpolates between two isometries using a linear interpolation for the translation part,
/// and a spherical interpolation for the rotation part.
///
/// Panics if the angle between both rotations is 180 degrees (in which case the interpolation
/// is not well-defined). Use `.try_lerp_slerp` instead to avoid the panic.
///
/// # Examples:
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::{Vector2, Translation2, Rotation2, IsometryMatrix2};
///
/// let t1 = Translation2::new(1.0, 2.0);
/// let t2 = Translation2::new(4.0, 8.0);
/// let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
/// let q2 = Rotation2::new(-std::f32::consts::PI);
/// let iso1 = IsometryMatrix2::from_parts(t1, q1);
/// let iso2 = IsometryMatrix2::from_parts(t2, q2);
///
/// let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);
///
/// assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
/// assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);
/// ```
#[inline]
#[must_use]
pub fn lerp_slerp(&self, other: &Self, t: T) -> Self
where
T: RealField,
{
let tr = self
.translation
.vector
.lerp(&other.translation.vector, t.clone());
let rot = self.rotation.slerp(&other.rotation, t);
Self::from_parts(tr.into(), rot)
}
}