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use super::*;

/// Computes the determinant of a matrix.
///
/// This gives the scale factor of a unit square (or cube, or hyper-cube) in the
/// matrix's modified coordinate space:
/// * Positive means that the output orientation is generally similar.
/// * Negative means that the output orientation is flipped.
/// * Zero means that the output loses _at least_ 1 dimension (meaning that
///   hyper-cubes become cubes, squares, lines, or points).
#[inline]
pub fn determinant<M: CanDeterminant>(m: M) -> f32 {
  m.determinant()
}

/// A trait for types that can have a determinant computed.
pub trait CanDeterminant {
  /// See [`determinant`](module@determinant) for info.
  fn determinant(self) -> f32;
}

impl CanDeterminant for Mat2 {
  #[inline]
  fn determinant(self) -> f32 {
    Mat2::determinant(self)
  }
}

impl CanDeterminant for Mat3 {
  #[inline]
  fn determinant(self) -> f32 {
    Mat3::determinant(self)
  }
}

impl CanDeterminant for Mat4 {
  #[inline]
  fn determinant(self) -> f32 {
    Mat4::determinant(self)
  }
}