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