Merge pull request #1235 from Masterzach32/feature/euler_angles_ordered
Add euler_angles_ordered function on Rotation
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Sébastien Crozet
GitHub
commit
bea7f9d1f2
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@ -979,6 +979,176 @@ impl<T: SimdRealField> Rotation3<T> {
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)
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}
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}
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/// Represent this rotation as Euler angles.
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///
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/// Returns the angles produced in the order provided by seq parameter, along with the
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/// observability flag. The Euler axes passed to seq must form an orthonormal basis. If the
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/// rotation is gimbal locked, then the observability flag is false.
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///
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/// # Panics
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///
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/// Panics if the Euler axes in `seq` are not orthonormal.
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///
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/// # Example 1:
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/// ```
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/// use std::f64::consts::PI;
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/// use approx::assert_relative_eq;
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/// use nalgebra::{Matrix3, Rotation3, Unit, Vector3};
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///
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/// // 3-1-2
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/// let n = [
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/// Unit::new_unchecked(Vector3::new(0.0, 0.0, 1.0)),
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/// Unit::new_unchecked(Vector3::new(1.0, 0.0, 0.0)),
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/// Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0)),
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/// ];
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///
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/// let r1 = Rotation3::from_axis_angle(&n[2], 20.0 * PI / 180.0);
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/// let r2 = Rotation3::from_axis_angle(&n[1], 30.0 * PI / 180.0);
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/// let r3 = Rotation3::from_axis_angle(&n[0], 45.0 * PI / 180.0);
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///
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/// let d = r3 * r2 * r1;
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///
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/// let (angles, observable) = d.euler_angles_ordered(n, false);
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/// assert!(observable);
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/// assert_relative_eq!(angles[0] * 180.0 / PI, 45.0, epsilon = 1e-12);
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/// assert_relative_eq!(angles[1] * 180.0 / PI, 30.0, epsilon = 1e-12);
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/// assert_relative_eq!(angles[2] * 180.0 / PI, 20.0, epsilon = 1e-12);
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/// ```
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///
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/// # Example 2:
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/// ```
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/// use std::f64::consts::PI;
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/// use approx::assert_relative_eq;
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/// use nalgebra::{Matrix3, Rotation3, Unit, Vector3};
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///
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/// let sqrt_2 = 2.0_f64.sqrt();
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/// let n = [
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/// Unit::new_unchecked(Vector3::new(1.0 / sqrt_2, 1.0 / sqrt_2, 0.0)),
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/// Unit::new_unchecked(Vector3::new(1.0 / sqrt_2, -1.0 / sqrt_2, 0.0)),
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/// Unit::new_unchecked(Vector3::new(0.0, 0.0, 1.0)),
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/// ];
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///
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/// let r1 = Rotation3::from_axis_angle(&n[2], 20.0 * PI / 180.0);
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/// let r2 = Rotation3::from_axis_angle(&n[1], 30.0 * PI / 180.0);
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/// let r3 = Rotation3::from_axis_angle(&n[0], 45.0 * PI / 180.0);
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///
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/// let d = r3 * r2 * r1;
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///
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/// let (angles, observable) = d.euler_angles_ordered(n, false);
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/// assert!(observable);
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/// assert_relative_eq!(angles[0] * 180.0 / PI, 45.0, epsilon = 1e-12);
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/// assert_relative_eq!(angles[1] * 180.0 / PI, 30.0, epsilon = 1e-12);
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/// assert_relative_eq!(angles[2] * 180.0 / PI, 20.0, epsilon = 1e-12);
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/// ```
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///
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/// Algorithm based on:
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/// Malcolm D. Shuster, F. Landis Markley, “General formula for extraction the Euler
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/// angles”, Journal of guidance, control, and dynamics, vol. 29.1, pp. 215-221. 2006,
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/// and modified to be able to produce extrinsic rotations.
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#[must_use]
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pub fn euler_angles_ordered(
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&self,
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mut seq: [Unit<Vector3<T>>; 3],
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extrinsic: bool,
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) -> ([T; 3], bool)
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where
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T: RealField + Copy,
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{
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let mut angles = [T::zero(); 3];
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let eps = T::from_subset(&1e-7);
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let _2 = T::from_subset(&2.0);
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if extrinsic {
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seq.reverse();
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}
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let [n1, n2, n3] = &seq;
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assert_relative_eq!(n1.dot(n2), T::zero(), epsilon = eps);
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assert_relative_eq!(n3.dot(n1), T::zero(), epsilon = eps);
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let n1_c_n2 = n1.cross(n2);
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let s1 = n1_c_n2.dot(n3);
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let c1 = n1.dot(n3);
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let lambda = s1.atan2(c1);
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let mut c = Matrix3::zeros();
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c.column_mut(0).copy_from(n2);
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c.column_mut(1).copy_from(&n1_c_n2);
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c.column_mut(2).copy_from(n1);
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c.transpose_mut();
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let r1l = Matrix3::new(
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T::one(),
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T::zero(),
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T::zero(),
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T::zero(),
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c1,
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s1,
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T::zero(),
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-s1,
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c1,
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);
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let o_t = &c * self.matrix() * (c.transpose() * r1l);
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angles[1] = o_t.m33.acos();
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let safe1 = angles[1].abs() >= eps;
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let safe2 = (angles[1] - T::pi()).abs() >= eps;
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let observable = safe1 && safe2;
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angles[1] += lambda;
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if observable {
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angles[0] = o_t.m13.atan2(-o_t.m23);
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angles[2] = o_t.m31.atan2(o_t.m32);
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} else {
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// gimbal lock detected
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if extrinsic {
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// angle1 is initialized to zero
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if !safe1 {
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angles[2] = (o_t.m12 - o_t.m21).atan2(o_t.m11 + o_t.m22);
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} else {
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angles[2] = -(o_t.m12 + o_t.m21).atan2(o_t.m11 - o_t.m22);
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};
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} else {
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// angle3 is initialized to zero
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if !safe1 {
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angles[0] = (o_t.m12 - o_t.m21).atan2(o_t.m11 + o_t.m22);
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} else {
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angles[0] = (o_t.m12 + o_t.m21).atan2(o_t.m11 - o_t.m22);
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};
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};
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};
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let adjust = if seq[0] == seq[2] {
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// lambda = 0, so ensure angle2 -> [0, pi]
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angles[1] < T::zero() || angles[1] > T::pi()
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} else {
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// lamda = + or - pi/2, so ensure angle2 -> [-pi/2, pi/2]
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angles[1] < -T::frac_pi_2() || angles[1] > T::frac_pi_2()
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};
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// dont adjust gimbal locked rotation
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if adjust && observable {
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angles[0] += T::pi();
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angles[1] = _2 * lambda - angles[1];
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angles[2] -= T::pi();
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}
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// ensure all angles are within [-pi, pi]
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for angle in angles.as_mut_slice().iter_mut() {
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if *angle < -T::pi() {
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*angle += T::two_pi();
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} else if *angle > T::pi() {
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*angle -= T::two_pi();
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}
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}
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if extrinsic {
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angles.reverse();
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}
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(angles, observable)
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}
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}
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#[cfg(feature = "rand-no-std")]
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