nalgebra 0.13.0

#![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
    }
);