use num;

use na::{self, Matrix3, RealField};

use crate::math::Point;
use crate::utils;

/// Computes the volume of a tetrahedron.
#[inline]
pub fn tetrahedron_volume<N: RealField>(
    p1: &Point<N>,
    p2: &Point<N>,
    p3: &Point<N>,
    p4: &Point<N>,
) -> N {
    num::abs(tetrahedron_signed_volume(p1, p2, p3, p4))
}

/// Computes the signed volume of a tetrahedron.
///
/// If it is positive, `p4` is on the half-space pointed by the normal of the oriented triangle
/// `(p1, p2, p3)`.
#[inline]
pub fn tetrahedron_signed_volume<N: RealField>(
    p1: &Point<N>,
    p2: &Point<N>,
    p3: &Point<N>,
    p4: &Point<N>,
) -> N {
    let p1p2 = *p2 - *p1;
    let p1p3 = *p3 - *p1;
    let p1p4 = *p4 - *p1;

    let mat = Matrix3::new(
        p1p2[0], p1p3[0], p1p4[0], p1p2[1], p1p3[1], p1p4[1], p1p2[2], p1p3[2], p1p4[2],
    );

    mat.determinant() / na::convert(6.0f64)
}

/// Computes the center of a tetrahedron.
#[inline]
pub fn tetrahedron_center<N: RealField>(
    p1: &Point<N>,
    p2: &Point<N>,
    p3: &Point<N>,
    p4: &Point<N>,
) -> Point<N> {
    utils::center(&[*p1, *p2, *p3, *p4])
}