nalgebra/tests/quaternion.rs

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#![allow(non_snake_case)]
#[cfg(feature = "arbitrary")]
#[macro_use]
extern crate quickcheck;
#[macro_use]
extern crate approx;
extern crate num_traits as num;
extern crate alga;
extern crate nalgebra as na;
use na::{Unit, UnitQuaternion, Quaternion, Vector3, Point3, Rotation3};
quickcheck!(
/*
*
* From/to rotation matrix.
*
*/
fn unit_quaternion_rotation_conversion(q: UnitQuaternion<f64>) -> bool {
let r = q.to_rotation_matrix();
let qq = UnitQuaternion::from_rotation_matrix(&r);
let rr = qq.to_rotation_matrix();
relative_eq!(q, qq, epsilon = 1.0e-7) &&
relative_eq!(r, rr, epsilon = 1.0e-7)
}
/*
*
* PointBase/Vector transformation.
*
*/
fn unit_quaternion_transformation(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
let r = q.to_rotation_matrix();
let rv = r * v;
let rp = r * p;
relative_eq!( q * v, rv, epsilon = 1.0e-7) &&
relative_eq!( q * &v, rv, epsilon = 1.0e-7) &&
relative_eq!(&q * v, rv, epsilon = 1.0e-7) &&
relative_eq!(&q * &v, rv, epsilon = 1.0e-7) &&
relative_eq!( q * p, rp, epsilon = 1.0e-7) &&
relative_eq!( q * &p, rp, epsilon = 1.0e-7) &&
relative_eq!(&q * p, rp, epsilon = 1.0e-7) &&
relative_eq!(&q * &p, rp, epsilon = 1.0e-7)
}
/*
*
* Inversion.
*
*/
fn unit_quaternion_inv(q: UnitQuaternion<f64>) -> bool {
let iq = q.inverse();
relative_eq!(&iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!( iq * &q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!(&iq * q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!( iq * q, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!(&q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!( q * &iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!(&q * iq, UnitQuaternion::identity(), epsilon = 1.0e-7) &&
relative_eq!( q * iq, UnitQuaternion::identity(), epsilon = 1.0e-7)
}
/*
*
* Quaterion * Vector == RotationBase * Vector
*
*/
fn unit_quaternion_mul_vector(q: UnitQuaternion<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
let r = q.to_rotation_matrix();
relative_eq!(q * v, r * v, epsilon = 1.0e-7) &&
relative_eq!(q * p, r * p, epsilon = 1.0e-7) &&
// Equivalence q = -q
relative_eq!((-q) * v, r * v, epsilon = 1.0e-7) &&
relative_eq!((-q) * p, r * p, epsilon = 1.0e-7)
}
/*
*
* Unit quaternion double-covering.
*
*/
fn unit_quaternion_double_covering(q: UnitQuaternion<f64>) -> bool {
let mq = -q;
mq == q && mq.angle() == q.angle() && mq.axis() == q.axis()
}
// Test that all operators (incl. all combinations of references) work.
// See the top comment on `geometry/quaternion_ops.rs` for details on which operations are
// supported.
fn all_op_exist(q: Quaternion<f64>, uq: UnitQuaternion<f64>,
v: Vector3<f64>, p: Point3<f64>, r: Rotation3<f64>,
s: f64) -> bool {
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let uv = Unit::new_normalize(v);
let qpq = q + q;
let qmq = q - q;
let qMq = q * q;
let mq = -q;
let qMs = q * s;
let qDs = q / s;
let sMq = s * q;
let uqMuq = uq * uq;
let uqMr = uq * r;
let rMuq = r * uq;
let uqDuq = uq / uq;
let uqDr = uq / r;
let rDuq = r / uq;
let uqMp = uq * p;
let uqMv = uq * v;
let uqMuv = uq * uv;
let mut qMs1 = q;
let mut qMq1 = q;
let mut qMq2 = q;
let mut qpq1 = q;
let mut qpq2 = q;
let mut qmq1 = q;
let mut qmq2 = q;
let mut uqMuq1 = uq;
let mut uqMuq2 = uq;
let mut uqMr1 = uq;
let mut uqMr2 = uq;
let mut uqDuq1 = uq;
let mut uqDuq2 = uq;
let mut uqDr1 = uq;
let mut uqDr2 = uq;
qMs1 *= s;
qMq1 *= q;
qMq2 *= &q;
qpq1 += q;
qpq2 += &q;
qmq1 -= q;
qmq2 -= &q;
uqMuq1 *= uq;
uqMuq2 *= &uq;
uqMr1 *= r;
uqMr2 *= &r;
uqDuq1 /= uq;
uqDuq2 /= &uq;
uqDr1 /= r;
uqDr2 /= &r;
qMs1 == qMs &&
qMq1 == qMq &&
qMq1 == qMq2 &&
qpq1 == qpq &&
qpq1 == qpq2 &&
qmq1 == qmq &&
qmq1 == qmq2 &&
uqMuq1 == uqMuq &&
uqMuq1 == uqMuq2 &&
uqMr1 == uqMr &&
uqMr1 == uqMr2 &&
uqDuq1 == uqDuq &&
uqDuq1 == uqDuq2 &&
uqDr1 == uqDr &&
uqDr1 == uqDr2 &&
qpq == &q + &q &&
qpq == q + &q &&
qpq == &q + q &&
qmq == &q - &q &&
qmq == q - &q &&
qmq == &q - q &&
qMq == &q * &q &&
qMq == q * &q &&
qMq == &q * q &&
mq == -&q &&
qMs == &q * s &&
qDs == &q / s &&
sMq == s * &q &&
uqMuq == &uq * &uq &&
uqMuq == uq * &uq &&
uqMuq == &uq * uq &&
uqMr == &uq * &r &&
uqMr == uq * &r &&
uqMr == &uq * r &&
rMuq == &r * &uq &&
rMuq == r * &uq &&
rMuq == &r * uq &&
uqDuq == &uq / &uq &&
uqDuq == uq / &uq &&
uqDuq == &uq / uq &&
uqDr == &uq / &r &&
uqDr == uq / &r &&
uqDr == &uq / r &&
rDuq == &r / &uq &&
rDuq == r / &uq &&
rDuq == &r / uq &&
uqMp == &uq * &p &&
uqMp == uq * &p &&
uqMp == &uq * p &&
uqMv == &uq * &v &&
uqMv == uq * &v &&
uqMv == &uq * v &&
uqMuv == &uq * &uv &&
uqMuv == uq * &uv &&
uqMuv == &uq * uv
}
);