360 lines
13 KiB
Rust
360 lines
13 KiB
Rust
use na::{
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Matrix3, Quaternion, RealField, Rotation3, UnitQuaternion, UnitVector3, Vector2, Vector3,
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};
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use std::f64::consts::PI;
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#[test]
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fn angle_2() {
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let a = Vector2::new(4.0, 0.0);
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let b = Vector2::new(9.0, 0.0);
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assert_eq!(a.angle(&b), 0.0);
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}
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#[test]
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fn angle_3() {
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let a = Vector3::new(4.0, 0.0, 0.5);
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let b = Vector3::new(8.0, 0.0, 1.0);
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assert_eq!(a.angle(&b), 0.0);
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}
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#[test]
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fn from_rotation_matrix() {
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// Test degenerate case when from_matrix gets stuck in Identity rotation
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let identity =
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Rotation3::from_matrix(&Matrix3::new(1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0));
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assert_relative_eq!(identity, &Rotation3::identity(), epsilon = 0.001);
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let rotated_z =
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Rotation3::from_matrix(&Matrix3::new(1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, -1.0));
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assert_relative_eq!(
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rotated_z,
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&Rotation3::from_axis_angle(&UnitVector3::new_unchecked(Vector3::new(1.0, 0.0, 0.0)), PI),
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epsilon = 0.001
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);
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// Test that issue 627 is fixed
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let m_627 = Matrix3::<f64>::new(-1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0);
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assert_relative_ne!(identity, Rotation3::from_matrix(&m_627), epsilon = 0.01);
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assert_relative_eq!(
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Rotation3::from_matrix_unchecked(m_627.clone()),
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Rotation3::from_matrix(&m_627),
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epsilon = 0.001
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);
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// Test that issue 1078 is fixed
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let m_1078 = Matrix3::<f64>::new(0.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.0);
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assert_relative_ne!(identity, Rotation3::from_matrix(&m_1078), epsilon = 0.01);
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assert_relative_eq!(
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Rotation3::from_matrix_unchecked(m_1078.clone()),
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Rotation3::from_matrix(&m_1078),
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epsilon = 0.001
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);
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// Additional test cases for eps >= 1.0
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assert_relative_ne!(
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identity,
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Rotation3::from_matrix_eps(&m_627, 1.2, 0, Rotation3::identity()),
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epsilon = 0.6
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);
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assert_relative_eq!(
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Rotation3::from_matrix_unchecked(m_627.clone()),
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Rotation3::from_matrix_eps(&m_627, 1.2, 0, Rotation3::identity()),
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epsilon = 0.6
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);
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assert_relative_ne!(
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identity,
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Rotation3::from_matrix_eps(&m_1078, 1.0, 0, Rotation3::identity()),
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epsilon = 0.1
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);
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assert_relative_eq!(
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Rotation3::from_matrix_unchecked(m_1078.clone()),
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Rotation3::from_matrix_eps(&m_1078, 1.0, 0, Rotation3::identity()),
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epsilon = 0.1
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);
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}
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#[test]
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fn quaternion_euler_angles_issue_494() {
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let quat = UnitQuaternion::from_quaternion(Quaternion::new(
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-0.10405792,
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-0.6993922f32,
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-0.10406871,
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0.69942284,
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));
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let angs = quat.euler_angles();
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assert_eq!(angs.0, 2.8461843);
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assert_eq!(angs.1, f32::frac_pi_2());
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assert_eq!(angs.2, 0.0);
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}
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#[cfg(feature = "proptest-support")]
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mod proptest_tests {
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use approx::AbsDiffEq;
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use na::{self, Rotation2, Rotation3, Unit};
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use na::{UnitComplex, UnitQuaternion};
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use simba::scalar::RealField;
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use std::f64;
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use crate::proptest::*;
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use proptest::{prop_assert, prop_assert_eq, proptest};
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proptest! {
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/*
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*
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* Euler angles.
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*
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*/
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#[test]
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fn from_euler_angles(r in PROPTEST_F64, p in PROPTEST_F64, y in PROPTEST_F64) {
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let roll = Rotation3::from_euler_angles(r, 0.0, 0.0);
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let pitch = Rotation3::from_euler_angles(0.0, p, 0.0);
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let yaw = Rotation3::from_euler_angles(0.0, 0.0, y);
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let rpy = Rotation3::from_euler_angles(r, p, y);
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prop_assert_eq!(roll[(0, 0)], 1.0); // rotation wrt. x axis.
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prop_assert_eq!(pitch[(1, 1)], 1.0); // rotation wrt. y axis.
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prop_assert_eq!(yaw[(2, 2)], 1.0); // rotation wrt. z axis.
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prop_assert_eq!(yaw * pitch * roll, rpy);
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}
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#[test]
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fn euler_angles(r in PROPTEST_F64, p in PROPTEST_F64, y in PROPTEST_F64) {
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let rpy = Rotation3::from_euler_angles(r, p, y);
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let (roll, pitch, yaw) = rpy.euler_angles();
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prop_assert!(relative_eq!(Rotation3::from_euler_angles(roll, pitch, yaw), rpy, epsilon = 1.0e-7));
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}
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#[test]
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fn euler_angles_gimble_lock(r in PROPTEST_F64, y in PROPTEST_F64) {
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let pos = Rotation3::from_euler_angles(r, f64::frac_pi_2(), y);
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let neg = Rotation3::from_euler_angles(r, -f64::frac_pi_2(), y);
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let (pos_r, pos_p, pos_y) = pos.euler_angles();
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let (neg_r, neg_p, neg_y) = neg.euler_angles();
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prop_assert!(relative_eq!(Rotation3::from_euler_angles(pos_r, pos_p, pos_y), pos, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(Rotation3::from_euler_angles(neg_r, neg_p, neg_y), neg, epsilon = 1.0e-7));
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}
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/*
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*
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* Inversion is transposition.
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*
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*/
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#[test]
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fn rotation_inv_3(a in rotation3()) {
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let ta = a.transpose();
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let ia = a.inverse();
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prop_assert_eq!(ta, ia);
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prop_assert!(relative_eq!(&ta * &a, Rotation3::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!(&ia * a, Rotation3::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!( a * &ta, Rotation3::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!( a * ia, Rotation3::identity(), epsilon = 1.0e-7));
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}
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#[test]
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fn rotation_inv_2(a in rotation2()) {
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let ta = a.transpose();
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let ia = a.inverse();
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prop_assert_eq!(ta, ia);
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prop_assert!(relative_eq!(&ta * &a, Rotation2::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!(&ia * a, Rotation2::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!( a * &ta, Rotation2::identity(), epsilon = 1.0e-7));
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prop_assert!(relative_eq!( a * ia, Rotation2::identity(), epsilon = 1.0e-7));
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}
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/*
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*
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* Angle between vectors.
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*
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*/
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#[test]
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fn angle_is_commutative_2(a in vector2(), b in vector2()) {
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prop_assert_eq!(a.angle(&b), b.angle(&a))
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}
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#[test]
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fn angle_is_commutative_3(a in vector3(), b in vector3()) {
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prop_assert_eq!(a.angle(&b), b.angle(&a))
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}
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/*
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*
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* Rotation matrix between vectors.
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*
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*/
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#[test]
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fn rotation_between_is_anticommutative_2(a in vector2(), b in vector2()) {
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let rab = Rotation2::rotation_between(&a, &b);
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let rba = Rotation2::rotation_between(&b, &a);
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prop_assert!(relative_eq!(rab * rba, Rotation2::identity()));
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}
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#[test]
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fn rotation_between_is_anticommutative_3(a in vector3(), b in vector3()) {
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let rots = (Rotation3::rotation_between(&a, &b), Rotation3::rotation_between(&b, &a));
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if let (Some(rab), Some(rba)) = rots {
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prop_assert!(relative_eq!(rab * rba, Rotation3::identity(), epsilon = 1.0e-7));
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}
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}
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#[test]
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fn rotation_between_is_identity(v2 in vector2(), v3 in vector3()) {
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let vv2 = 3.42 * v2;
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let vv3 = 4.23 * v3;
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prop_assert!(relative_eq!(v2.angle(&vv2), 0.0, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(v3.angle(&vv3), 0.0, epsilon = 1.0e-7));
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prop_assert!(relative_eq!(Rotation2::rotation_between(&v2, &vv2), Rotation2::identity()));
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prop_assert_eq!(Rotation3::rotation_between(&v3, &vv3).unwrap(), Rotation3::identity());
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}
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#[test]
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fn rotation_between_2(a in vector2(), b in vector2()) {
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if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) {
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let r = Rotation2::rotation_between(&a, &b);
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prop_assert!(relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7))
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}
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}
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#[test]
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fn rotation_between_3(a in vector3(), b in vector3()) {
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if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) {
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let r = Rotation3::rotation_between(&a, &b).unwrap();
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prop_assert!(relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7))
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}
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}
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/*
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*
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* Rotation construction.
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*
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*/
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#[test]
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fn new_rotation_2(angle in PROPTEST_F64) {
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let r = Rotation2::new(angle);
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let angle = na::wrap(angle, -f64::pi(), f64::pi());
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prop_assert!(relative_eq!(r.angle(), angle, epsilon = 1.0e-7))
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}
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#[test]
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fn new_rotation_3(axisangle in vector3()) {
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let r = Rotation3::new(axisangle);
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if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) {
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let angle = na::wrap(angle, -f64::pi(), f64::pi());
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prop_assert!((relative_eq!(r.angle(), angle, epsilon = 1.0e-7) &&
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relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) ||
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(relative_eq!(r.angle(), -angle, epsilon = 1.0e-7) &&
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relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7)))
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}
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else {
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prop_assert_eq!(r, Rotation3::identity())
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}
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}
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/*
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*
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* Rotation pow.
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*
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*/
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#[test]
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fn powf_rotation_2(angle in PROPTEST_F64, pow in PROPTEST_F64) {
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let r = Rotation2::new(angle).powf(pow);
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let angle = na::wrap(angle, -f64::pi(), f64::pi());
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let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi());
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prop_assert!(relative_eq!(r.angle(), pangle, epsilon = 1.0e-7));
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}
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#[test]
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fn powf_rotation_3(axisangle in vector3(), pow in PROPTEST_F64) {
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let r = Rotation3::new(axisangle).powf(pow);
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if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) {
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let angle = na::wrap(angle, -f64::pi(), f64::pi());
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let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi());
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prop_assert!((relative_eq!(r.angle(), pangle, epsilon = 1.0e-7) &&
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relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) ||
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(relative_eq!(r.angle(), -pangle, epsilon = 1.0e-7) &&
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relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7)));
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}
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else {
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prop_assert_eq!(r, Rotation3::identity())
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}
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}
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//
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//In general, `slerp(a,b,t)` should equal `(b/a)^t * a` even though in practice,
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//we may not use that formula directly for complex numbers or quaternions
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//
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#[test]
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fn slerp_powf_agree_2(a in unit_complex(), b in unit_complex(), t in PROPTEST_F64) {
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let z1 = a.slerp(&b, t);
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let z2 = (b/a).powf(t) * a;
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prop_assert!(relative_eq!(z1,z2,epsilon=1e-10));
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}
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#[test]
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fn slerp_powf_agree_3(a in unit_quaternion(), b in unit_quaternion(), t in PROPTEST_F64) {
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if let Some(z1) = a.try_slerp(&b, t, f64::default_epsilon()) {
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let z2 = (b/a).powf(t) * a;
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prop_assert!(relative_eq!(z1,z2,epsilon=1e-10));
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}
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}
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//
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//when not antipodal, slerp should always take the shortest path between two orientations
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//
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#[test]
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fn slerp_takes_shortest_path_2(
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z in unit_complex(), dtheta in -f64::pi()..f64::pi(), t in 0.0..1.0f64
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) {
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//ambiguous when at ends of angle range, so we don't really care here
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if dtheta.abs() != f64::pi() {
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//make two complex numbers separated by an angle between -pi and pi
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let (z1, z2) = (z, z * UnitComplex::new(dtheta));
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let z3 = z1.slerp(&z2, t);
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//since the angle is no larger than a half-turn, and t is between 0 and 1,
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//the shortest path just corresponds to adding the scaled angle
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let a1 = z3.angle();
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let a2 = na::wrap(z1.angle() + dtheta*t, -f64::pi(), f64::pi());
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prop_assert!(relative_eq!(a1, a2, epsilon=1e-10));
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}
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}
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#[test]
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fn slerp_takes_shortest_path_3(
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q in unit_quaternion(), dtheta in -f64::pi()..f64::pi(), t in 0.0..1.0f64
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) {
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//ambiguous when at ends of angle range, so we don't really care here
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if let Some(axis) = q.axis() {
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//make two quaternions separated by an angle between -pi and pi
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let (q1, q2) = (q, q * UnitQuaternion::from_axis_angle(&axis, dtheta));
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let q3 = q1.slerp(&q2, t);
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//since the angle is no larger than a half-turn, and t is between 0 and 1,
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//the shortest path just corresponds to adding the scaled angle
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let q4 = q1 * UnitQuaternion::from_axis_angle(&axis, dtheta*t);
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prop_assert!(relative_eq!(q3, q4, epsilon=1e-10));
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}
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}
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}
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}
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