use alga::general::{Field, Real, MeetSemilattice, JoinSemilattice, Lattice};
use alga::linear::{AffineSpace, EuclideanSpace};

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

use geometry::Point;


impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
    where N: Scalar + Field,
          DefaultAllocator: Allocator<N, D> {
    type Translation = VectorN<N, D>;
}

impl<N: Real, D: DimName> EuclideanSpace for Point<N, D>
    where DefaultAllocator: Allocator<N, D> {
    type Coordinates = VectorN<N, D>;
    type Real        = N;

    #[inline]
    fn origin() -> Self {
        Self::origin()
    }

    #[inline]
    fn coordinates(&self) -> Self::Coordinates {
        self.coords.clone()
    }

    #[inline]
    fn from_coordinates(coords: Self::Coordinates) -> Self {
        Self::from_coordinates(coords)
    }

    #[inline]
    fn scale_by(&self, n: N) -> Self {
        self * n
    }
}

/*
 *
 * Ordering
 *
 */
impl<N, D: DimName> MeetSemilattice for Point<N, D>
    where N: Scalar + MeetSemilattice,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn meet(&self, other: &Self) -> Self {
        Point::from_coordinates(self.coords.meet(&other.coords))
    }
}

impl<N, D: DimName> JoinSemilattice for Point<N, D>
    where N: Scalar + JoinSemilattice,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn join(&self, other: &Self) -> Self {
        Point::from_coordinates(self.coords.join(&other.coords))
    }
}


impl<N, D: DimName> Lattice for Point<N, D>
    where N: Scalar + Lattice,
          DefaultAllocator: Allocator<N, D> {
    #[inline]
    fn meet_join(&self, other: &Self) -> (Self, Self) {
        let (meet, join) = self.coords.meet_join(&other.coords);

        (Point::from_coordinates(meet), Point::from_coordinates(join))
    }
}