nalgebra/tests/geometry/quaternion.rs

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#![cfg(feature = "arbitrary")]
#![allow(non_snake_case)]
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use na::{Point3, Quaternion, Rotation3, Unit, UnitQuaternion, Vector3};
quickcheck!(
/*
*
* Euler angles.
*
*/
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);
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);
let rpy = UnitQuaternion::from_euler_angles(r, p, y);
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let rroll = roll.to_rotation_matrix();
let rpitch = pitch.to_rotation_matrix();
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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)
}
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fn euler_angles(r: f64, p: f64, y: f64) -> bool {
let rpy = UnitQuaternion::from_euler_angles(r, p, y);
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let (roll, pitch, yaw) = rpy.euler_angles();
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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 {
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let r = q.to_rotation_matrix();
let qq = UnitQuaternion::from_rotation_matrix(&r);
let rr = qq.to_rotation_matrix();
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relative_eq!(q, qq, epsilon = 1.0e-7) && relative_eq!(r, rr, epsilon = 1.0e-7)
}
/*
*
* Point/Vector transformation.
*
*/
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#[cfg_attr(rustfmt, rustfmt_skip)]
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fn unit_quaternion_transformation(
q: UnitQuaternion<f64>,
v: Vector3<f64>,
p: Point3<f64>
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) -> bool {
let r = q.to_rotation_matrix();
let rv = r * v;
let rp = r * p;
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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();
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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)
}
/*
*
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* 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
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relative_eq!(UnitQuaternion::new_unchecked(-q.into_inner()) * v, r * v, epsilon = 1.0e-7) &&
relative_eq!(UnitQuaternion::new_unchecked(-q.into_inner()) * p, r * p, epsilon = 1.0e-7)
}
/*
*
* Unit quaternion double-covering.
*
*/
fn unit_quaternion_double_covering(q: UnitQuaternion<f64>) -> bool {
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let mq = UnitQuaternion::new_unchecked(-q.into_inner());
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.
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#[cfg_attr(rustfmt, rustfmt_skip)]
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fn all_op_exist(
q: Quaternion<f64>,
uq: UnitQuaternion<f64>,
v: Vector3<f64>,
p: Point3<f64>,
r: Rotation3<f64>,
s: f64
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) -> bool {
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let uv = Unit::new_normalize(v);
let qpq = q + q;
let qmq = q - q;
let qMq = q * q;
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let mq = -q;
let qMs = q * s;
let qDs = q / s;
let sMq = s * q;
let uqMuq = uq * uq;
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let uqMr = uq * r;
let rMuq = r * uq;
let uqDuq = uq / uq;
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let uqDr = uq / r;
let rDuq = r / uq;
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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;
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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
}
);