use crate::{CoordinateFrameType, EastNorthUp, NorthEastDown};

/// A coordinate frame.
pub trait CoordinateFrame {
    /// The type of each coordinate value.
    type Type;

    /// The coordinate frame type.
    const COORDINATE_FRAME: CoordinateFrameType;

    /// Returns the coordinate frame of this instance.
    fn coordinate_frame(&self) -> CoordinateFrameType;

    /// Converts this type to a [`NorthEastDown`] instance.
    fn to_ned(&self) -> NorthEastDown<Self::Type>
    where
        Self::Type: Copy + SaturatingNeg<Output = Self::Type>;

    /// Converts this type to an [`EastNorthUp`] instance.
    fn to_enu(&self) -> EastNorthUp<Self::Type>
    where
        Self::Type: Copy + SaturatingNeg<Output = Self::Type>;

    /// Gets the value of the first dimension.
    fn x(&self) -> Self::Type
    where
        Self::Type: Clone;

    /// Gets the value of the second dimension.
    fn y(&self) -> Self::Type
    where
        Self::Type: Clone;

    /// Gets the value of the third dimension.
    fn z(&self) -> Self::Type
    where
        Self::Type: Clone;

    /// Gets a reference to the value of the first dimension.
    fn x_ref(&self) -> &Self::Type;

    /// Gets a reference to the value of the second dimension.
    fn y_ref(&self) -> &Self::Type;

    /// Gets a reference to the value of the third dimension.
    fn z_ref(&self) -> &Self::Type;

    /// Gets a mutable reference to the value of the first dimension.
    fn x_mut(&mut self) -> &mut Self::Type;

    /// Gets a mutable reference to the value of the second dimension.
    fn y_mut(&mut self) -> &mut Self::Type;

    /// Gets a mutable reference to the value of the third dimension.
    fn z_mut(&mut self) -> &mut Self::Type;

    /// Indicates whether this coordinate system is right-handed or left-handed.
    fn right_handed(&self) -> bool;

    /// Returns the base vector for the `x` axis in the global frame.
    fn x_axis() -> [Self::Type; 3]
    where
        Self::Type: ZeroOne<Output = Self::Type> + core::ops::Neg<Output = Self::Type>;

    /// Returns the base vector for the `y` axis in the global frame.
    fn y_axis() -> [Self::Type; 3]
    where
        Self::Type: ZeroOne<Output = Self::Type> + core::ops::Neg<Output = Self::Type>;

    /// Returns the base vector for the `z` axis in the global frame.
    fn z_axis() -> [Self::Type; 3]
    where
        Self::Type: ZeroOne<Output = Self::Type> + core::ops::Neg<Output = Self::Type>;
}

/// Marks a right-handed coordinate system.
pub trait RightHanded {}

/// Marks a left-handed coordinate system.
pub trait LeftHanded {}

/// Provides the values zero and one.
pub trait ZeroOne {
    type Output;

    /// Provides the value zero (`0`).
    fn zero() -> Self::Output;

    /// Provides the value one (`1`).
    fn one() -> Self::Output;
}

/// Performs a saturating negation.
pub trait SaturatingNeg {
    type Output;

    /// Like [`Neg`](core::ops::Neg), but returns the maximum value on negation of
    /// a minimum value instead of overflowing.
    fn saturating_neg(self) -> Self::Output;
}

impl SaturatingNeg for i8 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        self.saturating_neg()
    }
}

impl SaturatingNeg for i16 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        self.saturating_neg()
    }
}
impl SaturatingNeg for i32 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        self.saturating_neg()
    }
}

impl SaturatingNeg for i64 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        self.saturating_neg()
    }
}

impl SaturatingNeg for i128 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        self.saturating_neg()
    }
}

impl SaturatingNeg for f32 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        -self
    }
}

impl SaturatingNeg for f64 {
    type Output = Self;

    fn saturating_neg(self) -> Self {
        -self
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for u8 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for i8 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for u16 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for i16 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for u32 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for i32 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for u64 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for i64 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for u128 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for i128 {
    type Output = Self;

    fn zero() -> Self::Output {
        0
    }

    fn one() -> Self::Output {
        1
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for f32 {
    type Output = Self;

    fn zero() -> Self::Output {
        0.0
    }

    fn one() -> Self::Output {
        1.0
    }
}

#[cfg(not(feature = "num-traits"))]
impl ZeroOne for f64 {
    type Output = Self;

    fn zero() -> Self::Output {
        0.0
    }

    fn one() -> Self::Output {
        1.0
    }
}

#[cfg(feature = "num-traits")]
impl<T> ZeroOne for T
where
    T: num_traits::Zero + num_traits::One,
{
    type Output = T;

    fn zero() -> Self::Output {
        <T as num_traits::Zero>::zero()
    }

    fn one() -> Self::Output {
        <T as num_traits::One>::one()
    }
}