use std::f64::consts::PI; use na::{Matrix3, Quaternion, RealField, Rotation3, UnitQuaternion, UnitVector3, Vector2, Vector3}; #[test] fn angle_2() { let a = Vector2::new(4.0, 0.0); let b = Vector2::new(9.0, 0.0); assert_eq!(a.angle(&b), 0.0); } #[test] fn angle_3() { let a = Vector3::new(4.0, 0.0, 0.5); let b = Vector3::new(8.0, 0.0, 1.0); assert_eq!(a.angle(&b), 0.0); } #[test] fn from_rotation_matrix() { // Test degenerate case when from_matrix gets stuck in Identity rotation let identity = Rotation3::from_matrix(&Matrix3::new( 1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 1.0, )); assert_relative_eq!(identity, &Rotation3::identity(), epsilon = 0.001); let rotated_z = Rotation3::from_matrix(&Matrix3::new( 1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, -1.0, )); assert_relative_eq!(rotated_z, &Rotation3::from_axis_angle(&UnitVector3::new_unchecked(Vector3::new(1.0, 0.0, 0.0)), PI), epsilon = 0.001); // Test that issue 628 is fixed let m_628 = nalgebra::Matrix3::::new(-1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0); assert_relative_ne!(identity, nalgebra::Rotation3::from_matrix(&m_628), epsilon = 0.01); assert_relative_eq!(nalgebra::Rotation3::from_matrix_unchecked(m_628.clone()), nalgebra::Rotation3::from_matrix(&m_628), epsilon = 0.001); // Test that issue 1078 is fixed let m_1078 = nalgebra::Matrix3::::new(0.0, 0.0, 1.0, 0.0, -1.0, 0.0, 1.0, 0.0, 0.0); assert_relative_ne!(identity, nalgebra::Rotation3::from_matrix(&m_1078), epsilon = 0.01); assert_relative_eq!(nalgebra::Rotation3::from_matrix_unchecked(m_1078.clone()), nalgebra::Rotation3::from_matrix(&m_1078), epsilon = 0.001); } #[test] fn quaternion_euler_angles_issue_494() { let quat = UnitQuaternion::from_quaternion(Quaternion::new( -0.10405792, -0.6993922f32, -0.10406871, 0.69942284, )); let angs = quat.euler_angles(); assert_eq!(angs.0, 2.8461843); assert_eq!(angs.1, f32::frac_pi_2()); assert_eq!(angs.2, 0.0); } #[cfg(feature = "proptest-support")] mod proptest_tests { use approx::AbsDiffEq; use na::{self, Rotation2, Rotation3, Unit}; use na::{UnitComplex, UnitQuaternion}; use simba::scalar::RealField; use std::f64; use crate::proptest::*; use proptest::{prop_assert, prop_assert_eq, proptest}; proptest! { /* * * Euler angles. * */ #[test] fn from_euler_angles(r in PROPTEST_F64, p in PROPTEST_F64, y in PROPTEST_F64) { let roll = Rotation3::from_euler_angles(r, 0.0, 0.0); let pitch = Rotation3::from_euler_angles(0.0, p, 0.0); let yaw = Rotation3::from_euler_angles(0.0, 0.0, y); let rpy = Rotation3::from_euler_angles(r, p, y); prop_assert_eq!(roll[(0, 0)], 1.0); // rotation wrt. x axis. prop_assert_eq!(pitch[(1, 1)], 1.0); // rotation wrt. y axis. prop_assert_eq!(yaw[(2, 2)], 1.0); // rotation wrt. z axis. prop_assert_eq!(yaw * pitch * roll, rpy); } #[test] fn euler_angles(r in PROPTEST_F64, p in PROPTEST_F64, y in PROPTEST_F64) { let rpy = Rotation3::from_euler_angles(r, p, y); let (roll, pitch, yaw) = rpy.euler_angles(); prop_assert!(relative_eq!(Rotation3::from_euler_angles(roll, pitch, yaw), rpy, epsilon = 1.0e-7)); } #[test] fn euler_angles_gimble_lock(r in PROPTEST_F64, y in PROPTEST_F64) { let pos = Rotation3::from_euler_angles(r, f64::frac_pi_2(), y); let neg = Rotation3::from_euler_angles(r, -f64::frac_pi_2(), y); let (pos_r, pos_p, pos_y) = pos.euler_angles(); let (neg_r, neg_p, neg_y) = neg.euler_angles(); prop_assert!(relative_eq!(Rotation3::from_euler_angles(pos_r, pos_p, pos_y), pos, epsilon = 1.0e-7)); prop_assert!(relative_eq!(Rotation3::from_euler_angles(neg_r, neg_p, neg_y), neg, epsilon = 1.0e-7)); } /* * * Inversion is transposition. * */ #[test] fn rotation_inv_3(a in rotation3()) { let ta = a.transpose(); let ia = a.inverse(); prop_assert_eq!(ta, ia); prop_assert!(relative_eq!(&ta * &a, Rotation3::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!(&ia * a, Rotation3::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!( a * &ta, Rotation3::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!( a * ia, Rotation3::identity(), epsilon = 1.0e-7)); } #[test] fn rotation_inv_2(a in rotation2()) { let ta = a.transpose(); let ia = a.inverse(); prop_assert_eq!(ta, ia); prop_assert!(relative_eq!(&ta * &a, Rotation2::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!(&ia * a, Rotation2::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!( a * &ta, Rotation2::identity(), epsilon = 1.0e-7)); prop_assert!(relative_eq!( a * ia, Rotation2::identity(), epsilon = 1.0e-7)); } /* * * Angle between vectors. * */ #[test] fn angle_is_commutative_2(a in vector2(), b in vector2()) { prop_assert_eq!(a.angle(&b), b.angle(&a)) } #[test] fn angle_is_commutative_3(a in vector3(), b in vector3()) { prop_assert_eq!(a.angle(&b), b.angle(&a)) } /* * * Rotation matrix between vectors. * */ #[test] fn rotation_between_is_anticommutative_2(a in vector2(), b in vector2()) { let rab = Rotation2::rotation_between(&a, &b); let rba = Rotation2::rotation_between(&b, &a); prop_assert!(relative_eq!(rab * rba, Rotation2::identity())); } #[test] fn rotation_between_is_anticommutative_3(a in vector3(), b in vector3()) { let rots = (Rotation3::rotation_between(&a, &b), Rotation3::rotation_between(&b, &a)); if let (Some(rab), Some(rba)) = rots { prop_assert!(relative_eq!(rab * rba, Rotation3::identity(), epsilon = 1.0e-7)); } } #[test] fn rotation_between_is_identity(v2 in vector2(), v3 in vector3()) { let vv2 = 3.42 * v2; let vv3 = 4.23 * v3; prop_assert!(relative_eq!(v2.angle(&vv2), 0.0, epsilon = 1.0e-7)); prop_assert!(relative_eq!(v3.angle(&vv3), 0.0, epsilon = 1.0e-7)); prop_assert!(relative_eq!(Rotation2::rotation_between(&v2, &vv2), Rotation2::identity())); prop_assert_eq!(Rotation3::rotation_between(&v3, &vv3).unwrap(), Rotation3::identity()); } #[test] fn rotation_between_2(a in vector2(), b in vector2()) { if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) { let r = Rotation2::rotation_between(&a, &b); prop_assert!(relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7)) } } #[test] fn rotation_between_3(a in vector3(), b in vector3()) { if !relative_eq!(a.angle(&b), 0.0, epsilon = 1.0e-7) { let r = Rotation3::rotation_between(&a, &b).unwrap(); prop_assert!(relative_eq!((r * a).angle(&b), 0.0, epsilon = 1.0e-7)) } } /* * * Rotation construction. * */ #[test] fn new_rotation_2(angle in PROPTEST_F64) { let r = Rotation2::new(angle); let angle = na::wrap(angle, -f64::pi(), f64::pi()); prop_assert!(relative_eq!(r.angle(), angle, epsilon = 1.0e-7)) } #[test] fn new_rotation_3(axisangle in vector3()) { let r = Rotation3::new(axisangle); if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) { let angle = na::wrap(angle, -f64::pi(), f64::pi()); prop_assert!((relative_eq!(r.angle(), angle, epsilon = 1.0e-7) && relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) || (relative_eq!(r.angle(), -angle, epsilon = 1.0e-7) && relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7))) } else { prop_assert_eq!(r, Rotation3::identity()) } } /* * * Rotation pow. * */ #[test] fn powf_rotation_2(angle in PROPTEST_F64, pow in PROPTEST_F64) { let r = Rotation2::new(angle).powf(pow); let angle = na::wrap(angle, -f64::pi(), f64::pi()); let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi()); prop_assert!(relative_eq!(r.angle(), pangle, epsilon = 1.0e-7)); } #[test] fn powf_rotation_3(axisangle in vector3(), pow in PROPTEST_F64) { let r = Rotation3::new(axisangle).powf(pow); if let Some((axis, angle)) = Unit::try_new_and_get(axisangle, 0.0) { let angle = na::wrap(angle, -f64::pi(), f64::pi()); let pangle = na::wrap(angle * pow, -f64::pi(), f64::pi()); prop_assert!((relative_eq!(r.angle(), pangle, epsilon = 1.0e-7) && relative_eq!(r.axis().unwrap(), axis, epsilon = 1.0e-7)) || (relative_eq!(r.angle(), -pangle, epsilon = 1.0e-7) && relative_eq!(r.axis().unwrap(), -axis, epsilon = 1.0e-7))); } else { prop_assert_eq!(r, Rotation3::identity()) } } // //In general, `slerp(a,b,t)` should equal `(b/a)^t * a` even though in practice, //we may not use that formula directly for complex numbers or quaternions // #[test] fn slerp_powf_agree_2(a in unit_complex(), b in unit_complex(), t in PROPTEST_F64) { let z1 = a.slerp(&b, t); let z2 = (b/a).powf(t) * a; prop_assert!(relative_eq!(z1,z2,epsilon=1e-10)); } #[test] fn slerp_powf_agree_3(a in unit_quaternion(), b in unit_quaternion(), t in PROPTEST_F64) { if let Some(z1) = a.try_slerp(&b, t, f64::default_epsilon()) { let z2 = (b/a).powf(t) * a; prop_assert!(relative_eq!(z1,z2,epsilon=1e-10)); } } // //when not antipodal, slerp should always take the shortest path between two orientations // #[test] fn slerp_takes_shortest_path_2( z in unit_complex(), dtheta in -f64::pi()..f64::pi(), t in 0.0..1.0f64 ) { //ambiguous when at ends of angle range, so we don't really care here if dtheta.abs() != f64::pi() { //make two complex numbers separated by an angle between -pi and pi let (z1, z2) = (z, z * UnitComplex::new(dtheta)); let z3 = z1.slerp(&z2, t); //since the angle is no larger than a half-turn, and t is between 0 and 1, //the shortest path just corresponds to adding the scaled angle let a1 = z3.angle(); let a2 = na::wrap(z1.angle() + dtheta*t, -f64::pi(), f64::pi()); prop_assert!(relative_eq!(a1, a2, epsilon=1e-10)); } } #[test] fn slerp_takes_shortest_path_3( q in unit_quaternion(), dtheta in -f64::pi()..f64::pi(), t in 0.0..1.0f64 ) { //ambiguous when at ends of angle range, so we don't really care here if let Some(axis) = q.axis() { //make two quaternions separated by an angle between -pi and pi let (q1, q2) = (q, q * UnitQuaternion::from_axis_angle(&axis, dtheta)); let q3 = q1.slerp(&q2, t); //since the angle is no larger than a half-turn, and t is between 0 and 1, //the shortest path just corresponds to adding the scaled angle let q4 = q1 * UnitQuaternion::from_axis_angle(&axis, dtheta*t); prop_assert!(relative_eq!(q3, q4, epsilon=1e-10)); } } } }