nalgebra/tests/geometry/similarity.rs

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#![cfg(feature = "arbitrary")]
#![allow(non_snake_case)]
use alga::linear::{Transformation, ProjectiveTransformation};
use na::{Vector3, Point3, Similarity3, Translation3, Isometry3, UnitQuaternion};
quickcheck!(
fn inverse_is_identity(i: Similarity3<f64>, p: Point3<f64>, v: Vector3<f64>) -> bool {
let ii = i.inverse();
relative_eq!(i * ii, Similarity3::identity(), epsilon = 1.0e-7) &&
relative_eq!(ii * i, Similarity3::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>, scaling: f64) -> bool {
if relative_eq!(scaling, 0.0) {
true
}
else {
let s = Similarity3::from_isometry(t * r, scaling);
s.inverse() == Similarity3::from_scaling(1.0 / scaling) * r.inverse() * t.inverse()
}
}
fn multiply_equals_alga_transform(s: Similarity3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
s * v == s.transform_vector(&v) &&
s * p == s.transform_point(&p) &&
relative_eq!(s.inverse() * v, s.inverse_transform_vector(&v), epsilon = 1.0e-7) &&
relative_eq!(s.inverse() * p, s.inverse_transform_point(&p), epsilon = 1.0e-7)
}
fn composition(i: Isometry3<f64>, uq: UnitQuaternion<f64>,
t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>, scaling: f64) -> bool {
if relative_eq!(scaling, 0.0) {
return true;
}
let s = Similarity3::from_scaling(scaling);
// (rotation × translation × scaling) × point = rotation × (translation × (scaling × point))
relative_eq!((uq * t * s) * v, uq * (scaling * v), epsilon = 1.0e-7) &&
relative_eq!((uq * t * s) * p, uq * (t * (scaling * p)), epsilon = 1.0e-7) &&
// (translation × rotation × scaling) × point = translation × (rotation × (scaling × point))
relative_eq!((t * uq * s) * v, uq * (scaling * v), epsilon = 1.0e-7) &&
relative_eq!((t * uq * s) * p, t * (uq * (scaling * p)), epsilon = 1.0e-7) &&
// (rotation × isometry × scaling) × point = rotation × (isometry × (scaling × point))
relative_eq!((uq * i * s) * v, uq * (i * (scaling * v)), epsilon = 1.0e-7) &&
relative_eq!((uq * i * s) * p, uq * (i * (scaling * p)), epsilon = 1.0e-7) &&
// (isometry × rotation × scaling) × point = isometry × (rotation × (scaling × point))
relative_eq!((i * uq * s) * v, i * (uq * (scaling * v)), epsilon = 1.0e-7) &&
relative_eq!((i * uq * s) * p, i * (uq * (scaling * p)), epsilon = 1.0e-7) &&
// (translation × isometry × scaling) × point = translation × (isometry × (scaling × point))
relative_eq!((t * i * s) * v, (i * (scaling * v)), epsilon = 1.0e-7) &&
relative_eq!((t * i * s) * p, t * (i * (scaling * p)), epsilon = 1.0e-7) &&
// (isometry × translation × scaling) × point = isometry × (translation × (scaling × point))
relative_eq!((i * t * s) * v, i * (scaling * v), epsilon = 1.0e-7) &&
relative_eq!((i * t * s) * p, i * (t * (scaling * p)), epsilon = 1.0e-7) &&
/*
* Same as before but with scaling on the middle.
*/
// (rotation × scaling × translation) × point = rotation × (scaling × (translation × point))
relative_eq!((uq * s * t) * v, uq * (scaling * v), epsilon = 1.0e-7) &&
relative_eq!((uq * s * t) * p, uq * (scaling * (t * p)), epsilon = 1.0e-7) &&
// (translation × scaling × rotation) × point = translation × (scaling × (rotation × point))
relative_eq!((t * s * uq) * v, scaling * (uq * v), epsilon = 1.0e-7) &&
relative_eq!((t * s * uq) * p, t * (scaling * (uq * p)), epsilon = 1.0e-7) &&
// (rotation × scaling × isometry) × point = rotation × (scaling × (isometry × point))
relative_eq!((uq * s * i) * v, uq * (scaling * (i * v)), epsilon = 1.0e-7) &&
relative_eq!((uq * s * i) * p, uq * (scaling * (i * p)), epsilon = 1.0e-7) &&
// (isometry × scaling × rotation) × point = isometry × (scaling × (rotation × point))
relative_eq!((i * s * uq) * v, i * (scaling * (uq * v)), epsilon = 1.0e-7) &&
relative_eq!((i * s * uq) * p, i * (scaling * (uq * p)), epsilon = 1.0e-7) &&
// (translation × scaling × isometry) × point = translation × (scaling × (isometry × point))
relative_eq!((t * s * i) * v, (scaling * (i * v)), epsilon = 1.0e-7) &&
relative_eq!((t * s * i) * p, t * (scaling * (i * p)), epsilon = 1.0e-7) &&
// (isometry × scaling × translation) × point = isometry × (scaling × (translation × point))
relative_eq!((i * s * t) * v, i * (scaling * v), epsilon = 1.0e-7) &&
relative_eq!((i * s * t) * p, i * (scaling * (t * p)), epsilon = 1.0e-7) &&
/*
* Same as before but with scaling on the left.
*/
// (scaling × rotation × translation) × point = scaling × (rotation × (translation × point))
relative_eq!((s * uq * t) * v, scaling * (uq * v), epsilon = 1.0e-7) &&
relative_eq!((s * uq * t) * p, scaling * (uq * (t * p)), epsilon = 1.0e-7) &&
// (scaling × translation × rotation) × point = scaling × (translation × (rotation × point))
relative_eq!((s * t * uq) * v, scaling * (uq * v), epsilon = 1.0e-7) &&
relative_eq!((s * t * uq) * p, scaling * (t * (uq * p)), epsilon = 1.0e-7) &&
// (scaling × rotation × isometry) × point = scaling × (rotation × (isometry × point))
relative_eq!((s * uq * i) * v, scaling * (uq * (i * v)), epsilon = 1.0e-7) &&
relative_eq!((s * uq * i) * p, scaling * (uq * (i * p)), epsilon = 1.0e-7) &&
// (scaling × isometry × rotation) × point = scaling × (isometry × (rotation × point))
relative_eq!((s * i * uq) * v, scaling * (i * (uq * v)), epsilon = 1.0e-7) &&
relative_eq!((s * i * uq) * p, scaling * (i * (uq * p)), epsilon = 1.0e-7) &&
// (scaling × translation × isometry) × point = scaling × (translation × (isometry × point))
relative_eq!((s * t * i) * v, (scaling * (i * v)), epsilon = 1.0e-7) &&
relative_eq!((s * t * i) * p, scaling * (t * (i * p)), epsilon = 1.0e-7) &&
// (scaling × isometry × translation) × point = scaling × (isometry × (translation × point))
relative_eq!((s * i * t) * v, scaling * (i * v), epsilon = 1.0e-7) &&
relative_eq!((s * i * t) * p, scaling * (i * (t * p)), epsilon = 1.0e-7)
}
fn all_op_exist(s: Similarity3<f64>, i: Isometry3<f64>, uq: UnitQuaternion<f64>,
t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>) -> bool {
let sMs = s * s;
let sMuq = s * uq;
let sDs = s / s;
let sDuq = s / uq;
let sMp = s * p;
let sMv = s * v;
let sMt = s * t;
let tMs = t * s;
let uqMs = uq * s;
let uqDs = uq / s;
let sMi = s * i;
let sDi = s / i;
let iMs = i * s;
let iDs = i / s;
let mut sMt1 = s;
let mut sMt2 = s;
let mut sMs1 = s;
let mut sMs2 = s;
let mut sMuq1 = s;
let mut sMuq2 = s;
let mut sMi1 = s;
let mut sMi2 = s;
let mut sDs1 = s;
let mut sDs2 = s;
let mut sDuq1 = s;
let mut sDuq2 = s;
let mut sDi1 = s;
let mut sDi2 = s;
sMt1 *= t;
sMt2 *= &t;
sMs1 *= s;
sMs2 *= &s;
sMuq1 *= uq;
sMuq2 *= &uq;
sMi1 *= i;
sMi2 *= &i;
sDs1 /= s;
sDs2 /= &s;
sDuq1 /= uq;
sDuq2 /= &uq;
sDi1 /= i;
sDi2 /= &i;
sMt == sMt1 &&
sMt == sMt2 &&
sMs == sMs1 &&
sMs == sMs2 &&
sMuq == sMuq1 &&
sMuq == sMuq2 &&
sMi == sMi1 &&
sMi == sMi2 &&
sDs == sDs1 &&
sDs == sDs2 &&
sDuq == sDuq1 &&
sDuq == sDuq2 &&
sDi == sDi1 &&
sDi == sDi2 &&
sMs == &s * &s &&
sMs == s * &s &&
sMs == &s * s &&
sMuq == &s * &uq &&
sMuq == s * &uq &&
sMuq == &s * uq &&
sDs == &s / &s &&
sDs == s / &s &&
sDs == &s / s &&
sDuq == &s / &uq &&
sDuq == s / &uq &&
sDuq == &s / uq &&
sMp == &s * &p &&
sMp == s * &p &&
sMp == &s * p &&
sMv == &s * &v &&
sMv == s * &v &&
sMv == &s * v &&
sMt == &s * &t &&
sMt == s * &t &&
sMt == &s * t &&
tMs == &t * &s &&
tMs == t * &s &&
tMs == &t * s &&
uqMs == &uq * &s &&
uqMs == uq * &s &&
uqMs == &uq * s &&
uqDs == &uq / &s &&
uqDs == uq / &s &&
uqDs == &uq / s &&
sMi == &s * &i &&
sMi == s * &i &&
sMi == &s * i &&
sDi == &s / &i &&
sDi == s / &i &&
sDi == &s / i &&
iMs == &i * &s &&
iMs == i * &s &&
iMs == &i * s &&
iDs == &i / &s &&
iDs == i / &s &&
iDs == &i / s
}
);