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    #[cfg(feature = "arbitrary")]
    use crate::base::storage::Owned;
    #[cfg(feature = "arbitrary")]
    use quickcheck::{Arbitrary, Gen};

    use num::One;
    use rand::distributions::{Distribution, Standard};
    use rand::Rng;

    use alga::general::RealField;
    use alga::linear::Rotation as AlgaRotation;

    use crate::base::allocator::Allocator;
    use crate::base::dimension::{DimName, U2, U3};
    use crate::base::{DefaultAllocator, Vector2, Vector3};

    use crate::geometry::{
        Isometry, Point, Point3, Rotation2, Rotation3, Similarity, Translation, UnitComplex,
        UnitQuaternion,
    };

    impl<N: RealField, D: DimName, R> Similarity<N, D, R>
    where
        R: AlgaRotation<Point<N, D>>,
        DefaultAllocator: Allocator<N, D>,
    {
        /// Creates a new identity similarity.
        ///
        /// # Example
        ///
        /// ```
        /// # use nalgebra::{Similarity2, Point2, Similarity3, Point3};
        ///
        /// let sim = Similarity2::identity();
        /// let pt = Point2::new(1.0, 2.0);
        /// assert_eq!(sim * pt, pt);
        ///
        /// let sim = Similarity3::identity();
        /// let pt = Point3::new(1.0, 2.0, 3.0);
        /// assert_eq!(sim * pt, pt);
        /// ```
        #[inline]
        pub fn identity() -> Self {
            Self::from_isometry(Isometry::identity(), N::one())
        }
    }

    impl<N: RealField, D: DimName, R> One for Similarity<N, D, R>
    where
        R: AlgaRotation<Point<N, D>>,
        DefaultAllocator: Allocator<N, D>,
    {
        /// Creates a new identity similarity.
        #[inline]
        fn one() -> Self {
            Self::identity()
        }
    }

    impl<N: RealField, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
    where
        R: AlgaRotation<Point<N, D>>,
        DefaultAllocator: Allocator<N, D>,
        Standard: Distribution<N> + Distribution<R>,
    {
        #[inline]
        fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, D, R> {
            let mut s = rng.gen();
            while relative_eq!(s, N::zero()) {
                s = rng.gen()
            }

            Similarity::from_isometry(rng.gen(), s)
        }
    }

    impl<N: RealField, D: DimName, R> Similarity<N, D, R>
    where
        R: AlgaRotation<Point<N, D>>,
        DefaultAllocator: Allocator<N, D>,
    {
        /// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
        /// its axis passing through the point `p`.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Similarity2, Point2, UnitComplex};
        /// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
        /// let pt = Point2::new(3.0, 2.0);
        /// let sim = Similarity2::rotation_wrt_point(rot, pt, 4.0);
        ///
        /// assert_relative_eq!(sim * Point2::new(1.0, 2.0), Point2::new(-3.0, 3.0), epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn rotation_wrt_point(r: R, p: Point<N, D>, scaling: N) -> Self {
            let shift = r.transform_vector(&-&p.coords);
            Self::from_parts(Translation::from(shift + p.coords), r, scaling)
        }
    }

    #[cfg(feature = "arbitrary")]
    impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
    where
        N: RealField + Arbitrary + Send,
        R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
        DefaultAllocator: Allocator<N, D>,
        Owned<N, D>: Send,
    {
        #[inline]
        fn arbitrary<G: Gen>(rng: &mut G) -> Self {
            let mut s = Arbitrary::arbitrary(rng);
            while relative_eq!(s, N::zero()) {
                s = Arbitrary::arbitrary(rng)
            }

            Self::from_isometry(Arbitrary::arbitrary(rng), s)
        }
    }

    /*
     *
     * Constructors for various static dimensions.
     *
     */

    // 2D rotation.
    impl<N: RealField> Similarity<N, U2, Rotation2<N>> {
        /// Creates a new similarity from a translation, a rotation, and an uniform scaling factor.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{SimilarityMatrix2, Vector2, Point2};
        /// let sim = SimilarityMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
        ///
        /// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self {
            Self::from_parts(
                Translation::from(translation),
                Rotation2::new(angle),
                scaling,
            )
        }
    }

    impl<N: RealField> Similarity<N, U2, UnitComplex<N>> {
        /// Creates a new similarity from a translation and a rotation angle.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{Similarity2, Vector2, Point2};
        /// let sim = Similarity2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
        ///
        /// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self {
            Self::from_parts(
                Translation::from(translation),
                UnitComplex::new(angle),
                scaling,
            )
        }
    }

    // 3D rotation.
    macro_rules! similarity_construction_impl(
        ($Rot: ty) => {
            impl<N: RealField> Similarity<N, U3, $Rot> {
                /// Creates a new similarity from a translation, rotation axis-angle, and scaling
                /// factor.
                ///
                /// # Example
                ///
                /// ```
                /// # #[macro_use] extern crate approx;
                /// # use std::f32;
                /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
                /// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
                /// let translation = Vector3::new(1.0, 2.0, 3.0);
                /// // Point and vector being transformed in the tests.
                /// let pt = Point3::new(4.0, 5.0, 6.0);
                /// let vec = Vector3::new(4.0, 5.0, 6.0);
                ///
                /// // Similarity with its rotation part represented as a UnitQuaternion
                /// let sim = Similarity3::new(translation, axisangle, 3.0);
                /// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
                /// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
                ///
                /// // Similarity with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
                /// let sim = SimilarityMatrix3::new(translation, axisangle, 3.0);
                /// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
                /// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
                /// ```
                #[inline]
                pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self {
                    Self::from_isometry(Isometry::<_, U3, $Rot>::new(translation, axisangle), scaling)
                }

                /// Creates an similarity that corresponds to a scaling factor and a local frame of
                /// an observer standing at the point `eye` and looking toward `target`.
                ///
                /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
                /// `eye`.
                ///
                /// # Arguments
                ///   * eye - The observer position.
                ///   * target - The target position.
                ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
                ///   to `eye - at`. Non-collinearity is not checked.
                ///
                /// # Example
                ///
                /// ```
                /// # #[macro_use] extern crate approx;
                /// # use std::f32;
                /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
                /// let eye = Point3::new(1.0, 2.0, 3.0);
                /// let target = Point3::new(2.0, 2.0, 3.0);
                /// let up = Vector3::y();
                ///
                /// // Similarity with its rotation part represented as a UnitQuaternion
                /// let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
                /// assert_eq!(sim * Point3::origin(), eye);
                /// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
                ///
                /// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
                /// let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
                /// assert_eq!(sim * Point3::origin(), eye);
                /// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
                /// ```
                #[inline]
                pub fn face_towards(eye:    &Point3<N>,
                                          target: &Point3<N>,
                                          up:     &Vector3<N>,
                                          scaling: N)
                                          -> Self {
                    Self::from_isometry(Isometry::<_, U3, $Rot>::face_towards(eye, target, up), scaling)
                }

                /// Deprecated: Use [SimilarityMatrix3::face_towards] instead.
                #[deprecated(note="renamed to `face_towards`")]
                pub fn new_observer_frames(eye:    &Point3<N>,
                                          target: &Point3<N>,
                                          up:     &Vector3<N>,
                                          scaling: N)
                                          -> Self {
                    Self::face_towards(eye, target, up, scaling)
                }

                /// Builds a right-handed look-at view matrix including scaling factor.
                ///
                /// This conforms to the common notion of right handed look-at matrix from the computer
                /// graphics community.
                ///
                /// # Arguments
                ///   * eye - The eye position.
                ///   * target - The target position.
                ///   * up - A vector approximately aligned with required the vertical axis. The only
                ///   requirement of this parameter is to not be collinear to `target - eye`.
                ///
                /// # Example
                ///
                /// ```
                /// # #[macro_use] extern crate approx;
                /// # use std::f32;
                /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
                /// let eye = Point3::new(1.0, 2.0, 3.0);
                /// let target = Point3::new(2.0, 2.0, 3.0);
                /// let up = Vector3::y();
                ///
                /// // Similarity with its rotation part represented as a UnitQuaternion
                /// let iso = Similarity3::look_at_rh(&eye, &target, &up, 3.0);
                /// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
                ///
                /// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
                /// let iso = SimilarityMatrix3::look_at_rh(&eye, &target, &up, 3.0);
                /// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
                /// ```
                #[inline]
                pub fn look_at_rh(eye:     &Point3<N>,
                                  target:  &Point3<N>,
                                  up:      &Vector3<N>,
                                  scaling: N)
                                  -> Self {
                    Self::from_isometry(Isometry::<_, U3, $Rot>::look_at_rh(eye, target, up), scaling)
                }

                /// Builds a left-handed look-at view matrix including a scaling factor.
                ///
                /// This conforms to the common notion of left handed look-at matrix from the computer
                /// graphics community.
                ///
                /// # Arguments
                ///   * eye - The eye position.
                ///   * target - The target position.
                ///   * up - A vector approximately aligned with required the vertical axis. The only
                ///   requirement of this parameter is to not be collinear to `target - eye`.
                ///
                /// # Example
                ///
                /// ```
                /// # #[macro_use] extern crate approx;
                /// # use std::f32;
                /// # use nalgebra::{Similarity3, SimilarityMatrix3, Point3, Vector3};
                /// let eye = Point3::new(1.0, 2.0, 3.0);
                /// let target = Point3::new(2.0, 2.0, 3.0);
                /// let up = Vector3::y();
                ///
                /// // Similarity with its rotation part represented as a UnitQuaternion
                /// let sim = Similarity3::look_at_lh(&eye, &target, &up, 3.0);
                /// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
                ///
                /// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
                /// let sim = SimilarityMatrix3::look_at_lh(&eye, &target, &up, 3.0);
                /// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
                /// ```
                #[inline]
                pub fn look_at_lh(eye:     &Point3<N>,
                                  target:  &Point3<N>,
                                  up:      &Vector3<N>,
                                  scaling: N)
                                  -> Self {
                    Self::from_isometry(Isometry::<_, _, $Rot>::look_at_lh(eye, target, up), scaling)
                }
            }
        }
    );

    similarity_construction_impl!(Rotation3<N>);
    similarity_construction_impl!(UnitQuaternion<N>);

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