nalgebra/src/geometry/transform.rs

use std::any::Any;
use std::fmt::Debug;
use std::marker::PhantomData;

#[cfg(feature = "serde-serialize")]
use serde;

use alga::general::Real;

use core::{DefaultAllocator, MatrixN};
use core::dimension::{DimName, DimNameAdd, DimNameSum, U1};
use core::storage::Owned;
use core::allocator::Allocator;

/// Trait implemented by phantom types identifying the projective transformation type.
///
/// NOTE: this trait is not intended to be implementable outside of the `nalgebra` crate.
pub trait TCategory: Any + Debug + Copy + PartialEq + Send {
    /// Indicates whether a `Transform` with the category `Self` has a bottom-row different from
    /// `0 0 .. 1`.
    #[inline]
    fn has_normalizer() -> bool {
        true
    }

    /// Checks that the given matrix is a valid homogeneous representation of an element of the
    /// category `Self`.
    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
    where
        N::Epsilon: Copy,
        DefaultAllocator: Allocator<N, D, D>;
}

/// Traits that gives the `Transform` category that is compatible with the result of the
/// multiplication of transformations with categories `Self` and `Other`.
pub trait TCategoryMul<Other: TCategory>: TCategory {
    /// The transform category that results from the multiplication of a `Transform<Self>` to a
    /// `Transform<Other>`. This is usually equal to `Self` or `Other`, whichever is the most
    /// general category.
    type Representative: TCategory;
}

/// Indicates that `Self` is a more general `Transform` category than `Other`.
pub trait SuperTCategoryOf<Other: TCategory>: TCategory {}

/// Indicates that `Self` is a more specific `Transform` category than `Other`.
///
/// Automatically implemented based on `SuperTCategoryOf`.
pub trait SubTCategoryOf<Other: TCategory>: TCategory {}
impl<T1, T2> SubTCategoryOf<T2> for T1
where
    T1: TCategory,
    T2: SuperTCategoryOf<T1>,
{
}

/// Tag representing the most general (not necessarily inversible) `Transform` type.
#[derive(Debug, Copy, Clone, Hash, PartialEq, Eq)]
pub enum TGeneral {
}

/// Tag representing the most general inversible `Transform` type.
#[derive(Debug, Copy, Clone, Hash, PartialEq, Eq)]
pub enum TProjective {
}

/// Tag representing an affine `Transform`. Its bottom-row is equal to `(0, 0 ... 0, 1)`.
#[derive(Debug, Copy, Clone, Hash, PartialEq, Eq)]
pub enum TAffine {
}

impl TCategory for TGeneral {
    #[inline]
    fn check_homogeneous_invariants<N: Real, D: DimName>(_: &MatrixN<N, D>) -> bool
    where
        N::Epsilon: Copy,
        DefaultAllocator: Allocator<N, D, D>,
    {
        true
    }
}

impl TCategory for TProjective {
    #[inline]
    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
    where
        N::Epsilon: Copy,
        DefaultAllocator: Allocator<N, D, D>,
    {
        mat.is_invertible()
    }
}

impl TCategory for TAffine {
    #[inline]
    fn has_normalizer() -> bool {
        false
    }

    #[inline]
    fn check_homogeneous_invariants<N: Real, D: DimName>(mat: &MatrixN<N, D>) -> bool
    where
        N::Epsilon: Copy,
        DefaultAllocator: Allocator<N, D, D>,
    {
        let last = D::dim() - 1;
        mat.is_invertible() && mat[(last, last)] == N::one()
            && (0..last).all(|i| mat[(last, i)].is_zero())
    }
}

macro_rules! category_mul_impl(
    ($($a: ident * $b: ident => $c: ty);* $(;)*) => {$(
        impl TCategoryMul<$a> for $b {
            type Representative = $c;
        }
    )*}
);

// We require stability uppon multiplication.
impl<T: TCategory> TCategoryMul<T> for T {
    type Representative = T;
}

category_mul_impl!(
//  TGeneral * TGeneral    => TGeneral;
    TGeneral * TProjective => TGeneral;
    TGeneral * TAffine     => TGeneral;

    TProjective * TGeneral    => TGeneral;
//  TProjective * TProjective => TProjective;
    TProjective * TAffine     => TProjective;

    TAffine * TGeneral    => TGeneral;
    TAffine * TProjective => TProjective;
//  TAffine * TAffine     => TAffine;
);

macro_rules! super_tcategory_impl(
    ($($a: ident >= $b: ident);* $(;)*) => {$(
        impl SuperTCategoryOf<$b> for $a { }
    )*}
);

impl<T: TCategory> SuperTCategoryOf<T> for T {}

super_tcategory_impl!(
    TGeneral    >= TProjective;
    TGeneral    >= TAffine;
    TProjective >= TAffine;
);

/// A transformation matrix in homogeneous coordinates.
///
/// It is stored as a matrix with dimensions `(D + 1, D + 1)`, e.g., it stores a 4x4 matrix for a
/// 3D transformation.
#[repr(C)]
#[derive(Debug)]
pub struct Transform<N: Real, D: DimNameAdd<U1>, C: TCategory>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
    matrix: MatrixN<N, DimNameSum<D, U1>>,
    _phantom: PhantomData<C>,
}

// FIXME
// impl<N: Real + hash::Hash, D: DimNameAdd<U1> + hash::Hash, C: TCategory> hash::Hash for Transform<N, D, C>
//     where DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
//           Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: hash::Hash {
//     fn hash<H: hash::Hasher>(&self, state: &mut H) {
//         self.matrix.hash(state);
//     }
// }

impl<N: Real, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Copy,
{
}

impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
    #[inline]
    fn clone(&self) -> Self {
        Transform::from_matrix_unchecked(self.matrix.clone())
    }
}

#[cfg(feature = "serde-serialize")]
impl<N: Real, D: DimNameAdd<U1>, C: TCategory> serde::Serialize for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: serde::Serialize,
{
    fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
    where
        S: serde::Serializer,
    {
        self.matrix.serialize(serializer)
    }
}

#[cfg(feature = "serde-serialize")]
impl<'a, N: Real, D: DimNameAdd<U1>, C: TCategory> serde::Deserialize<'a> for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: serde::Deserialize<'a>,
{
    fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
    where
        Des: serde::Deserializer<'a>,
    {
        let matrix = MatrixN::<N, DimNameSum<D, U1>>::deserialize(deserializer)?;

        Ok(Transform::from_matrix_unchecked(matrix))
    }
}

impl<N: Real + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
}

impl<N: Real, D: DimNameAdd<U1>, C: TCategory> PartialEq for Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
    #[inline]
    fn eq(&self, right: &Self) -> bool {
        self.matrix == right.matrix
    }
}

impl<N: Real, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
    /// Creates a new transformation from the given homogeneous matrix. The transformation category
    /// of `Self` is not checked to be verified by the given matrix.
    #[inline]
    pub fn from_matrix_unchecked(matrix: MatrixN<N, DimNameSum<D, U1>>) -> Self {
        Transform {
            matrix: matrix,
            _phantom: PhantomData,
        }
    }

    /// The underlying matrix.
    #[inline]
    pub fn unwrap(self) -> MatrixN<N, DimNameSum<D, U1>> {
        self.matrix
    }

    /// A reference to the underlynig matrix.
    #[inline]
    pub fn matrix(&self) -> &MatrixN<N, DimNameSum<D, U1>> {
        &self.matrix
    }

    /// A mutable reference to the underlying matrix.
    ///
    /// It is `_unchecked` because direct modifications of this matrix may break invariants
    /// identified by this transformation category.
    #[inline]
    pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
        &mut self.matrix
    }

    /// Sets the category of this transform.
    ///
    /// This can be done only if the new category is more general than the current one, e.g., a
    /// transform with category `TProjective` cannot be converted to a transform with category
    /// `TAffine` because not all projective transformations are affine (the other way-round is
    /// valid though).
    #[inline]
    pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> Transform<N, D, CNew> {
        Transform::from_matrix_unchecked(self.matrix)
    }

    /// Clones this transform into one that owns its data.
    #[inline]
    #[deprecated(note = "This method is a no-op and will be removed in a future release.")]
    pub fn clone_owned(&self) -> Transform<N, D, C> {
        Transform::from_matrix_unchecked(self.matrix.clone_owned())
    }

    /// Converts this transform into its equivalent homogeneous transformation matrix.
    #[inline]
    pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> {
        self.matrix().clone_owned()
    }

    /// Attempts to invert this transformation. You may use `.inverse` instead of this
    /// transformation has a subcategory of `TProjective`.
    #[inline]
    pub fn try_inverse(self) -> Option<Transform<N, D, C>> {
        if let Some(m) = self.matrix.try_inverse() {
            Some(Transform::from_matrix_unchecked(m))
        } else {
            None
        }
    }

    /// Inverts this transformation. Use `.try_inverse` if this transform has the `TGeneral`
    /// category (it may not be invertible).
    #[inline]
    pub fn inverse(self) -> Transform<N, D, C>
    where
        C: SubTCategoryOf<TProjective>,
    {
        // FIXME: specialize for TAffine?
        Transform::from_matrix_unchecked(self.matrix.try_inverse().unwrap())
    }

    /// Attempts to invert this transformation in-place. You may use `.inverse_mut` instead of this
    /// transformation has a subcategory of `TProjective`.
    #[inline]
    pub fn try_inverse_mut(&mut self) -> bool {
        self.matrix.try_inverse_mut()
    }

    /// Inverts this transformation in-place. Use `.try_inverse_mut` if this transform has the
    /// `TGeneral` category (it may not be invertible).
    #[inline]
    pub fn inverse_mut(&mut self)
    where
        C: SubTCategoryOf<TProjective>,
    {
        let _ = self.matrix.try_inverse_mut();
    }
}

impl<N: Real, D: DimNameAdd<U1>> Transform<N, D, TGeneral>
where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
    /// A mutable reference to underlying matrix. Use `.matrix_mut_unchecked` instead if this
    /// transformation category is not `TGeneral`.
    #[inline]
    pub fn matrix_mut(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>> {
        self.matrix_mut_unchecked()
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use core::Matrix4;

    #[test]
    fn checks_homogeneous_invariants_of_square_identity_matrix() {
        assert!(TAffine::check_homogeneous_invariants(
            &Matrix4::<f32>::identity()
        ));
    }
}