use alga::general::{AbstractMagma, AbstractGroup, AbstractLoop, AbstractMonoid, AbstractQuasigroup,
                    AbstractSemigroup, Real, Inverse, Multiplicative, Identity};
use alga::linear::{Transformation, AffineTransformation, Rotation, ProjectiveTransformation};
use alga::linear::Similarity as AlgaSimilarity;

use core::{DefaultAllocator, VectorN};
use core::dimension::DimName;
use core::allocator::Allocator;

use geometry::{Similarity, Translation, Point};


/*
 *
 * Algebraic structures.
 *
 */
impl<N: Real, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn identity() -> Self {
        Self::identity()
    }
}

impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn inverse(&self) -> Self {
        self.inverse()
    }

    #[inline]
    fn inverse_mut(&mut self) {
        self.inverse_mut()
    }
}

impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn operate(&self, rhs: &Self) -> Self {
        self * rhs
    }
}

macro_rules! impl_multiplicative_structures(
    ($($marker: ident<$operator: ident>),* $(,)*) => {$(
        impl<N: Real, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
            where R: Rotation<Point<N, D>>,
                  DefaultAllocator: Allocator<N, D> { }
    )*}
);

impl_multiplicative_structures!(
    AbstractSemigroup<Multiplicative>,
    AbstractMonoid<Multiplicative>,
    AbstractQuasigroup<Multiplicative>,
    AbstractLoop<Multiplicative>,
    AbstractGroup<Multiplicative>
);

/*
 *
 * Transformation groups.
 *
 */
impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
        self * pt
    }

    #[inline]
    fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
        self * v
    }
}

impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
        self.isometry.inverse_transform_point(pt) / self.scaling()
    }

    #[inline]
    fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
        self.isometry.inverse_transform_vector(v) / self.scaling()
    }
}

impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    type NonUniformScaling = N;
    type Rotation          = R;
    type Translation       = Translation<N, D>;

    #[inline]
    fn decompose(&self) -> (Translation<N, D>, R, N, R) {
        (self.isometry.translation.clone(), self.isometry.rotation.clone(), self.scaling(), R::identity())
    }

    #[inline]
    fn append_translation(&self, t: &Self::Translation) -> Self {
        t * self
    }

    #[inline]
    fn prepend_translation(&self, t: &Self::Translation) -> Self {
        self * t
    }

    #[inline]
    fn append_rotation(&self, r: &Self::Rotation) -> Self {
        Similarity::from_isometry(self.isometry.append_rotation(r), self.scaling())
    }

    #[inline]
    fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
        self * r
    }

    #[inline]
    fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self {
        self.append_scaling(*s)
    }

    #[inline]
    fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self {
        self.prepend_scaling(*s)
    }

    #[inline]
    fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
        let mut res = self.clone();
        res.append_rotation_wrt_point_mut(r, p);
        Some(res)
    }
}

impl<N: Real, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R>
    where R: Rotation<Point<N, D>>,
          DefaultAllocator: Allocator<N, D> {
    type Scaling = N;

    #[inline]
    fn translation(&self) -> Translation<N, D> {
        self.isometry.translation()
    }

    #[inline]
    fn rotation(&self) -> R {
        self.isometry.rotation()
    }

    #[inline]
    fn scaling(&self) -> N {
        self.scaling()
    }
}