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