nalgebra/tests/geometry/isometry.rs

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#![cfg(feature = "arbitrary")]
#![allow(non_snake_case)]
use na::{
Isometry2, Isometry3, Point2, Point3, Rotation2, Rotation3, Translation2, Translation3,
UnitComplex, UnitQuaternion, Vector2, Vector3,
};
quickcheck!(
fn append_rotation_wrt_point_to_id(r: UnitQuaternion<f64>, p: Point3<f64>) -> bool {
let mut iso = Isometry3::identity();
iso.append_rotation_wrt_point_mut(&r, &p);
iso == Isometry3::rotation_wrt_point(r, p)
}
fn rotation_wrt_point_invariance(r: UnitQuaternion<f64>, p: Point3<f64>) -> bool {
let iso = Isometry3::rotation_wrt_point(r, p);
relative_eq!(iso * p, p, epsilon = 1.0e-7)
}
fn look_at_rh_3(eye: Point3<f64>, target: Point3<f64>, up: Vector3<f64>) -> bool {
let viewmatrix = Isometry3::look_at_rh(&eye, &target, &up);
let origin = Point3::origin();
relative_eq!(viewmatrix * eye, origin, epsilon = 1.0e-7)
&& relative_eq!(
(viewmatrix * (target - eye)).normalize(),
-Vector3::z(),
epsilon = 1.0e-7
)
}
fn observer_frame_3(eye: Point3<f64>, target: Point3<f64>, up: Vector3<f64>) -> bool {
let observer = Isometry3::face_towards(&eye, &target, &up);
let origin = Point3::origin();
relative_eq!(observer * origin, eye, epsilon = 1.0e-7)
&& relative_eq!(
observer * Vector3::z(),
(target - eye).normalize(),
epsilon = 1.0e-7
)
}
fn inverse_is_identity(i: Isometry3<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
let ii = i.inverse();
relative_eq!(i * ii, Isometry3::identity(), epsilon = 1.0e-7)
&& relative_eq!(ii * i, Isometry3::identity(), epsilon = 1.0e-7)
&& relative_eq!((i * ii) * p, p, epsilon = 1.0e-7)
&& relative_eq!((ii * i) * p, p, epsilon = 1.0e-7)
&& relative_eq!((i * ii) * v, v, epsilon = 1.0e-7)
&& relative_eq!((ii * i) * v, v, epsilon = 1.0e-7)
}
fn inverse_is_parts_inversion(t: Translation3<f64>, r: UnitQuaternion<f64>) -> bool {
let i = t * r;
i.inverse() == r.inverse() * t.inverse()
}
fn multiply_equals_alga_transform(i: Isometry3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
i * v == i.transform_vector(&v)
&& i * p == i.transform_point(&p)
&& relative_eq!(
i.inverse() * v,
i.inverse_transform_vector(&v),
epsilon = 1.0e-7
)
&& relative_eq!(
i.inverse() * p,
i.inverse_transform_point(&p),
epsilon = 1.0e-7
)
}
fn composition2(
i: Isometry2<f64>,
uc: UnitComplex<f64>,
r: Rotation2<f64>,
t: Translation2<f64>,
v: Vector2<f64>,
p: Point2<f64>,
) -> bool {
// (rotation × translation) * point = rotation × (translation * point)
relative_eq!((uc * t) * v, uc * v, epsilon = 1.0e-7) &&
relative_eq!((r * t) * v, r * v, epsilon = 1.0e-7) &&
relative_eq!((uc * t) * p, uc * (t * p), epsilon = 1.0e-7) &&
relative_eq!((r * t) * p, r * (t * p), epsilon = 1.0e-7) &&
// (translation × rotation) * point = translation × (rotation * point)
(t * uc) * v == uc * v &&
(t * r) * v == r * v &&
(t * uc) * p == t * (uc * p) &&
(t * r) * p == t * (r * p) &&
// (rotation × isometry) * point = rotation × (isometry * point)
relative_eq!((uc * i) * v, uc * (i * v), epsilon = 1.0e-7) &&
relative_eq!((uc * i) * p, uc * (i * p), epsilon = 1.0e-7) &&
// (isometry × rotation) * point = isometry × (rotation * point)
relative_eq!((i * uc) * v, i * (uc * v), epsilon = 1.0e-7) &&
relative_eq!((i * uc) * p, i * (uc * p), epsilon = 1.0e-7) &&
// (translation × isometry) * point = translation × (isometry * point)
relative_eq!((t * i) * v, (i * v), epsilon = 1.0e-7) &&
relative_eq!((t * i) * p, t * (i * p), epsilon = 1.0e-7) &&
// (isometry × translation) * point = isometry × (translation * point)
relative_eq!((i * t) * v, i * v, epsilon = 1.0e-7) &&
relative_eq!((i * t) * p, i * (t * p), epsilon = 1.0e-7)
}
fn composition3(
i: Isometry3<f64>,
uq: UnitQuaternion<f64>,
r: Rotation3<f64>,
t: Translation3<f64>,
v: Vector3<f64>,
p: Point3<f64>,
) -> bool {
// (rotation × translation) * point = rotation × (translation * point)
relative_eq!((uq * t) * v, uq * v, epsilon = 1.0e-7) &&
relative_eq!((r * t) * v, r * v, epsilon = 1.0e-7) &&
relative_eq!((uq * t) * p, uq * (t * p), epsilon = 1.0e-7) &&
relative_eq!((r * t) * p, r * (t * p), epsilon = 1.0e-7) &&
// (translation × rotation) * point = translation × (rotation * point)
(t * uq) * v == uq * v &&
(t * r) * v == r * v &&
(t * uq) * p == t * (uq * p) &&
(t * r) * p == t * (r * p) &&
// (rotation × isometry) * point = rotation × (isometry * point)
relative_eq!((uq * i) * v, uq * (i * v), epsilon = 1.0e-7) &&
relative_eq!((uq * i) * p, uq * (i * p), epsilon = 1.0e-7) &&
// (isometry × rotation) * point = isometry × (rotation * point)
relative_eq!((i * uq) * v, i * (uq * v), epsilon = 1.0e-7) &&
relative_eq!((i * uq) * p, i * (uq * p), epsilon = 1.0e-7) &&
// (translation × isometry) * point = translation × (isometry * point)
relative_eq!((t * i) * v, (i * v), epsilon = 1.0e-7) &&
relative_eq!((t * i) * p, t * (i * p), epsilon = 1.0e-7) &&
// (isometry × translation) * point = isometry × (translation * point)
relative_eq!((i * t) * v, i * v, epsilon = 1.0e-7) &&
relative_eq!((i * t) * p, i * (t * p), epsilon = 1.0e-7)
}
fn all_op_exist(
i: Isometry3<f64>,
uq: UnitQuaternion<f64>,
t: Translation3<f64>,
v: Vector3<f64>,
p: Point3<f64>,
r: Rotation3<f64>,
) -> bool {
let iMi = i * i;
let iMuq = i * uq;
let iDi = i / i;
let iDuq = i / uq;
let iMp = i * p;
let iMv = i * v;
let iMt = i * t;
let tMi = t * i;
let tMr = t * r;
let tMuq = t * uq;
let uqMi = uq * i;
let uqDi = uq / i;
let rMt = r * t;
let uqMt = uq * t;
let mut iMt1 = i;
let mut iMt2 = i;
let mut iMi1 = i;
let mut iMi2 = i;
let mut iMuq1 = i;
let mut iMuq2 = i;
let mut iDi1 = i;
let mut iDi2 = i;
let mut iDuq1 = i;
let mut iDuq2 = i;
iMt1 *= t;
iMt2 *= &t;
iMi1 *= i;
iMi2 *= &i;
iMuq1 *= uq;
iMuq2 *= &uq;
iDi1 /= i;
iDi2 /= &i;
iDuq1 /= uq;
iDuq2 /= &uq;
iMt == iMt1
&& iMt == iMt2
&& iMi == iMi1
&& iMi == iMi2
&& iMuq == iMuq1
&& iMuq == iMuq2
&& iDi == iDi1
&& iDi == iDi2
&& iDuq == iDuq1
&& iDuq == iDuq2
&& iMi == &i * &i
&& iMi == i * &i
&& iMi == &i * i
&& iMuq == &i * &uq
&& iMuq == i * &uq
&& iMuq == &i * uq
&& iDi == &i / &i
&& iDi == i / &i
&& iDi == &i / i
&& iDuq == &i / &uq
&& iDuq == i / &uq
&& iDuq == &i / uq
&& iMp == &i * &p
&& iMp == i * &p
&& iMp == &i * p
&& iMv == &i * &v
&& iMv == i * &v
&& iMv == &i * v
&& iMt == &i * &t
&& iMt == i * &t
&& iMt == &i * t
&& tMi == &t * &i
&& tMi == t * &i
&& tMi == &t * i
&& tMr == &t * &r
&& tMr == t * &r
&& tMr == &t * r
&& tMuq == &t * &uq
&& tMuq == t * &uq
&& tMuq == &t * uq
&& uqMi == &uq * &i
&& uqMi == uq * &i
&& uqMi == &uq * i
&& uqDi == &uq / &i
&& uqDi == uq / &i
&& uqDi == &uq / i
&& rMt == &r * &t
&& rMt == r * &t
&& rMt == &r * t
&& uqMt == &uq * &t
&& uqMt == uq * &t
&& uqMt == &uq * t
}
);