267 lines
6.8 KiB
Rust
267 lines
6.8 KiB
Rust
#![allow(non_snake_case)]
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use na::{Unit, UnitQuaternion, Quaternion, Vector3, Point3, Rotation3};
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quickcheck!(
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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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fn from_euler_angles(r: f64, p: f64, y: f64) -> bool {
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let roll = UnitQuaternion::from_euler_angles(r, 0.0, 0.0);
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let pitch = UnitQuaternion::from_euler_angles(0.0, p, 0.0);
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let yaw = UnitQuaternion::from_euler_angles(0.0, 0.0, y);
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let rpy = UnitQuaternion::from_euler_angles(r, p, y);
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let rroll = roll.to_rotation_matrix();
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let rpitch = pitch.to_rotation_matrix();
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let ryaw = yaw.to_rotation_matrix();
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relative_eq!(rroll[(0, 0)], 1.0, epsilon = 1.0e-7) && // rotation wrt. x axis.
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relative_eq!(rpitch[(1, 1)], 1.0, epsilon = 1.0e-7) && // rotation wrt. y axis.
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relative_eq!(ryaw[(2, 2)], 1.0, epsilon = 1.0e-7) && // rotation wrt. z axis.
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relative_eq!(yaw * pitch * roll, rpy, epsilon = 1.0e-7)
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}
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fn to_euler_angles(r: f64, p: f64, y: f64) -> bool {
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let rpy = UnitQuaternion::from_euler_angles(r, p, y);
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let (roll, pitch, yaw) = rpy.to_euler_angles();
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relative_eq!(UnitQuaternion::from_euler_angles(roll, pitch, yaw), rpy, epsilon = 1.0e-7)
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}
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/*
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*
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* From/to rotation matrix.
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*
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*/
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fn unit_quaternion_rotation_conversion(q: UnitQuaternion<f64>) -> bool {
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let r = q.to_rotation_matrix();
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let qq = UnitQuaternion::from_rotation_matrix(&r);
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let rr = qq.to_rotation_matrix();
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relative_eq!(q, qq, epsilon = 1.0e-7) &&
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relative_eq!(r, rr, epsilon = 1.0e-7)
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}
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/*
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*
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* Point/Vector transformation.
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*
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*/
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fn unit_quaternion_transformation(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
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let r = q.to_rotation_matrix();
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let rv = r * v;
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let rp = r * p;
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relative_eq!( q * v, rv, epsilon = 1.0e-7) &&
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relative_eq!( q * &v, rv, epsilon = 1.0e-7) &&
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relative_eq!(&q * v, rv, epsilon = 1.0e-7) &&
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relative_eq!(&q * &v, rv, epsilon = 1.0e-7) &&
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relative_eq!( q * p, rp, epsilon = 1.0e-7) &&
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relative_eq!( q * &p, rp, epsilon = 1.0e-7) &&
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relative_eq!(&q * p, rp, epsilon = 1.0e-7) &&
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relative_eq!(&q * &p, rp, epsilon = 1.0e-7)
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}
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/*
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*
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* Inversion.
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*
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*/
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fn unit_quaternion_inv(q: UnitQuaternion<f64>) -> bool {
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let iq = q.inverse();
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relative_eq!(&iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!( iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!(&iq * q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!( iq * q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!(&q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!( q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!(&q * iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
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relative_eq!( q * iq, UnitQuaternion::identity(), epsilon = 1.0e-7)
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}
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/*
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*
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* Quaterion * Vector == Rotation * Vector
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*
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*/
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fn unit_quaternion_mul_vector(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
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let r = q.to_rotation_matrix();
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relative_eq!(q * v, r * v, epsilon = 1.0e-7) &&
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relative_eq!(q * p, r * p, epsilon = 1.0e-7) &&
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// Equivalence q = -q
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relative_eq!((-q) * v, r * v, epsilon = 1.0e-7) &&
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relative_eq!((-q) * p, r * p, epsilon = 1.0e-7)
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}
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/*
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*
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* Unit quaternion double-covering.
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*
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*/
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fn unit_quaternion_double_covering(q: UnitQuaternion<f64>) -> bool {
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let mq = -q;
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mq == q && mq.angle() == q.angle() && mq.axis() == q.axis()
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}
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// Test that all operators (incl. all combinations of references) work.
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// See the top comment on `geometry/quaternion_ops.rs` for details on which operations are
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// supported.
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fn all_op_exist(q: Quaternion<f64>, uq: UnitQuaternion<f64>,
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v: Vector3<f64>, p: Point3<f64>, r: Rotation3<f64>,
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s: f64) -> bool {
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let uv = Unit::new_normalize(v);
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let qpq = q + q;
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let qmq = q - q;
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let qMq = q * q;
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let mq = -q;
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let qMs = q * s;
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let qDs = q / s;
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let sMq = s * q;
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let uqMuq = uq * uq;
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let uqMr = uq * r;
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let rMuq = r * uq;
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let uqDuq = uq / uq;
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let uqDr = uq / r;
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let rDuq = r / uq;
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let uqMp = uq * p;
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let uqMv = uq * v;
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let uqMuv = uq * uv;
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let mut qMs1 = q;
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let mut qMq1 = q;
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let mut qMq2 = q;
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let mut qpq1 = q;
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let mut qpq2 = q;
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let mut qmq1 = q;
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let mut qmq2 = q;
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let mut uqMuq1 = uq;
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let mut uqMuq2 = uq;
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let mut uqMr1 = uq;
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let mut uqMr2 = uq;
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let mut uqDuq1 = uq;
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let mut uqDuq2 = uq;
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let mut uqDr1 = uq;
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let mut uqDr2 = uq;
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qMs1 *= s;
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qMq1 *= q;
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qMq2 *= &q;
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qpq1 += q;
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qpq2 += &q;
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qmq1 -= q;
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qmq2 -= &q;
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uqMuq1 *= uq;
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uqMuq2 *= &uq;
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uqMr1 *= r;
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uqMr2 *= &r;
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uqDuq1 /= uq;
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uqDuq2 /= &uq;
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uqDr1 /= r;
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uqDr2 /= &r;
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qMs1 == qMs &&
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qMq1 == qMq &&
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qMq1 == qMq2 &&
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qpq1 == qpq &&
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qpq1 == qpq2 &&
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qmq1 == qmq &&
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qmq1 == qmq2 &&
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uqMuq1 == uqMuq &&
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uqMuq1 == uqMuq2 &&
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uqMr1 == uqMr &&
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uqMr1 == uqMr2 &&
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uqDuq1 == uqDuq &&
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uqDuq1 == uqDuq2 &&
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uqDr1 == uqDr &&
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uqDr1 == uqDr2 &&
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qpq == &q + &q &&
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qpq == q + &q &&
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qpq == &q + q &&
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qmq == &q - &q &&
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qmq == q - &q &&
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qmq == &q - q &&
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qMq == &q * &q &&
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qMq == q * &q &&
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qMq == &q * q &&
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mq == -&q &&
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qMs == &q * s &&
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qDs == &q / s &&
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sMq == s * &q &&
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uqMuq == &uq * &uq &&
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uqMuq == uq * &uq &&
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uqMuq == &uq * uq &&
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uqMr == &uq * &r &&
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uqMr == uq * &r &&
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uqMr == &uq * r &&
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rMuq == &r * &uq &&
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rMuq == r * &uq &&
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rMuq == &r * uq &&
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uqDuq == &uq / &uq &&
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uqDuq == uq / &uq &&
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uqDuq == &uq / uq &&
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uqDr == &uq / &r &&
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uqDr == uq / &r &&
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uqDr == &uq / r &&
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rDuq == &r / &uq &&
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rDuq == r / &uq &&
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rDuq == &r / uq &&
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uqMp == &uq * &p &&
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uqMp == uq * &p &&
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uqMp == &uq * p &&
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uqMv == &uq * &v &&
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uqMv == uq * &v &&
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uqMv == &uq * v &&
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uqMuv == &uq * &uv &&
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uqMuv == uq * &uv &&
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uqMuv == &uq * uv
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}
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);
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