266 lines
9.3 KiB
Rust
266 lines
9.3 KiB
Rust
#![allow(non_snake_case)]
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use alga::linear::{Transformation, ProjectiveTransformation};
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use na::{Vector3, Point3, Similarity3, Translation3, Isometry3, UnitQuaternion};
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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(t: Translation3<f64>, r: UnitQuaternion<f64>, scaling: f64) -> bool {
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if relative_eq!(scaling, 0.0) {
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true
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}
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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(s: Similarity3<f64>, v: Vector3<f64>, p: Point3<f64>) -> 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!(s.inverse() * v, s.inverse_transform_vector(&v), epsilon = 1.0e-7) &&
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relative_eq!(s.inverse() * p, s.inverse_transform_point(&p), epsilon = 1.0e-7)
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}
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fn composition(i: Isometry3<f64>, uq: UnitQuaternion<f64>,
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t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>, scaling: f64) -> 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(s: Similarity3<f64>, i: Isometry3<f64>, uq: UnitQuaternion<f64>,
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t: Translation3<f64>, v: Vector3<f64>, p: Point3<f64>) -> 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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