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Merge pull request #1235 from Masterzach32/feature/euler_angles_ordered

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Add euler_angles_ordered function on Rotation
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Sébastien Crozet 2023-07-08 14:48:35 +02:00 committed by GitHub
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src/geometry/rotation_specialization.rs
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@ -979,6 +979,176 @@ impl<T: SimdRealField> Rotation3<T> {
)
}
}
/// Represent this rotation as Euler angles.
///
/// Returns the angles produced in the order provided by seq parameter, along with the
/// observability flag. The Euler axes passed to seq must form an orthonormal basis. If the
/// rotation is gimbal locked, then the observability flag is false.
///
/// # Panics
///
/// Panics if the Euler axes in `seq` are not orthonormal.
///
/// # Example 1:
/// ```
/// use std::f64::consts::PI;
/// use approx::assert_relative_eq;
/// use nalgebra::{Matrix3, Rotation3, Unit, Vector3};
///
/// // 3-1-2
/// let n = [
/// Unit::new_unchecked(Vector3::new(0.0, 0.0, 1.0)),
/// Unit::new_unchecked(Vector3::new(1.0, 0.0, 0.0)),
/// Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0)),
/// ];
///
/// let r1 = Rotation3::from_axis_angle(&n[2], 20.0 * PI / 180.0);
/// let r2 = Rotation3::from_axis_angle(&n[1], 30.0 * PI / 180.0);
/// let r3 = Rotation3::from_axis_angle(&n[0], 45.0 * PI / 180.0);
///
/// let d = r3 * r2 * r1;
///
/// let (angles, observable) = d.euler_angles_ordered(n, false);
/// assert!(observable);
/// assert_relative_eq!(angles[0] * 180.0 / PI, 45.0, epsilon = 1e-12);
/// assert_relative_eq!(angles[1] * 180.0 / PI, 30.0, epsilon = 1e-12);
/// assert_relative_eq!(angles[2] * 180.0 / PI, 20.0, epsilon = 1e-12);
/// ```
///
/// # Example 2:
/// ```
/// use std::f64::consts::PI;
/// use approx::assert_relative_eq;
/// use nalgebra::{Matrix3, Rotation3, Unit, Vector3};
///
/// let sqrt_2 = 2.0_f64.sqrt();
/// let n = [
/// Unit::new_unchecked(Vector3::new(1.0 / sqrt_2, 1.0 / sqrt_2, 0.0)),
/// Unit::new_unchecked(Vector3::new(1.0 / sqrt_2, -1.0 / sqrt_2, 0.0)),
/// Unit::new_unchecked(Vector3::new(0.0, 0.0, 1.0)),
/// ];
///
/// let r1 = Rotation3::from_axis_angle(&n[2], 20.0 * PI / 180.0);
/// let r2 = Rotation3::from_axis_angle(&n[1], 30.0 * PI / 180.0);
/// let r3 = Rotation3::from_axis_angle(&n[0], 45.0 * PI / 180.0);
///
/// let d = r3 * r2 * r1;
///
/// let (angles, observable) = d.euler_angles_ordered(n, false);
/// assert!(observable);
/// assert_relative_eq!(angles[0] * 180.0 / PI, 45.0, epsilon = 1e-12);
/// assert_relative_eq!(angles[1] * 180.0 / PI, 30.0, epsilon = 1e-12);
/// assert_relative_eq!(angles[2] * 180.0 / PI, 20.0, epsilon = 1e-12);
/// ```
///
/// Algorithm based on:
/// Malcolm D. Shuster, F. Landis Markley, “General formula for extraction the Euler
/// angles”, Journal of guidance, control, and dynamics, vol. 29.1, pp. 215-221. 2006,
/// and modified to be able to produce extrinsic rotations.
#[must_use]
pub fn euler_angles_ordered(
&self,
mut seq: [Unit<Vector3<T>>; 3],
extrinsic: bool,
) -> ([T; 3], bool)
where
T: RealField + Copy,
{
let mut angles = [T::zero(); 3];
let eps = T::from_subset(&1e-7);
let _2 = T::from_subset(&2.0);
if extrinsic {
seq.reverse();
}
let [n1, n2, n3] = &seq;
assert_relative_eq!(n1.dot(n2), T::zero(), epsilon = eps);
assert_relative_eq!(n3.dot(n1), T::zero(), epsilon = eps);
let n1_c_n2 = n1.cross(n2);
let s1 = n1_c_n2.dot(n3);
let c1 = n1.dot(n3);
let lambda = s1.atan2(c1);
let mut c = Matrix3::zeros();
c.column_mut(0).copy_from(n2);
c.column_mut(1).copy_from(&n1_c_n2);
c.column_mut(2).copy_from(n1);
c.transpose_mut();
let r1l = Matrix3::new(
T::one(),
T::zero(),
T::zero(),
T::zero(),
c1,
s1,
T::zero(),
-s1,
c1,
);
let o_t = &c * self.matrix() * (c.transpose() * r1l);
angles[1] = o_t.m33.acos();
let safe1 = angles[1].abs() >= eps;
let safe2 = (angles[1] - T::pi()).abs() >= eps;
let observable = safe1 && safe2;
angles[1] += lambda;
if observable {
angles[0] = o_t.m13.atan2(-o_t.m23);
angles[2] = o_t.m31.atan2(o_t.m32);
} else {
// gimbal lock detected
if extrinsic {
// angle1 is initialized to zero
if !safe1 {
angles[2] = (o_t.m12 - o_t.m21).atan2(o_t.m11 + o_t.m22);
} else {
angles[2] = -(o_t.m12 + o_t.m21).atan2(o_t.m11 - o_t.m22);
};
} else {
// angle3 is initialized to zero
if !safe1 {
angles[0] = (o_t.m12 - o_t.m21).atan2(o_t.m11 + o_t.m22);
} else {
angles[0] = (o_t.m12 + o_t.m21).atan2(o_t.m11 - o_t.m22);
};
};
};
let adjust = if seq[0] == seq[2] {
// lambda = 0, so ensure angle2 -> [0, pi]
angles[1] < T::zero() || angles[1] > T::pi()
} else {
// lamda = + or - pi/2, so ensure angle2 -> [-pi/2, pi/2]
angles[1] < -T::frac_pi_2() || angles[1] > T::frac_pi_2()
};
// dont adjust gimbal locked rotation
if adjust && observable {
angles[0] += T::pi();
angles[1] = _2 * lambda - angles[1];
angles[2] -= T::pi();
}
// ensure all angles are within [-pi, pi]
for angle in angles.as_mut_slice().iter_mut() {
if *angle < -T::pi() {
*angle += T::two_pi();
} else if *angle > T::pi() {
*angle -= T::two_pi();
}
}
if extrinsic {
angles.reverse();
}
(angles, observable)
}
}
#[cfg(feature = "rand-no-std")]