forked from M-Labs/nalgebra
267 lines
6.8 KiB
Rust
267 lines
6.8 KiB
Rust
#![cfg(feature = "arbitrary")]
|
|
#![allow(non_snake_case)]
|
|
|
|
use na::{Point3, Quaternion, Rotation3, Unit, UnitQuaternion, Vector3};
|
|
|
|
quickcheck!(
|
|
/*
|
|
*
|
|
* Euler angles.
|
|
*
|
|
*/
|
|
fn from_euler_angles(r: f64, p: f64, y: f64) -> bool {
|
|
let roll = UnitQuaternion::from_euler_angles(r, 0.0, 0.0);
|
|
let pitch = UnitQuaternion::from_euler_angles(0.0, p, 0.0);
|
|
let yaw = UnitQuaternion::from_euler_angles(0.0, 0.0, y);
|
|
|
|
let rpy = UnitQuaternion::from_euler_angles(r, p, y);
|
|
|
|
let rroll = roll.to_rotation_matrix();
|
|
let rpitch = pitch.to_rotation_matrix();
|
|
let ryaw = yaw.to_rotation_matrix();
|
|
|
|
relative_eq!(rroll[(0, 0)], 1.0, epsilon = 1.0e-7) && // rotation wrt. x axis.
|
|
relative_eq!(rpitch[(1, 1)], 1.0, epsilon = 1.0e-7) && // rotation wrt. y axis.
|
|
relative_eq!(ryaw[(2, 2)], 1.0, epsilon = 1.0e-7) && // rotation wrt. z axis.
|
|
relative_eq!(yaw * pitch * roll, rpy, epsilon = 1.0e-7)
|
|
}
|
|
|
|
fn to_euler_angles(r: f64, p: f64, y: f64) -> bool {
|
|
let rpy = UnitQuaternion::from_euler_angles(r, p, y);
|
|
let (roll, pitch, yaw) = rpy.to_euler_angles();
|
|
relative_eq!(UnitQuaternion::from_euler_angles(roll, pitch, yaw), rpy, epsilon = 1.0e-7)
|
|
}
|
|
|
|
|
|
/*
|
|
*
|
|
* 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)
|
|
}
|
|
|
|
/*
|
|
*
|
|
* Point/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 == Rotation * 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 {
|
|
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
|
|
}
|
|
);
|