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use num::Zero;

use alga::general::Real;
use na::{Point3, Matrix3};
use na;
use ncollide::utils;
use ncollide::procedural::{TriMesh, IndexBuffer};
use ncollide::transformation;
use ncollide::shape::ConvexHull3;
use volumetric::Volumetric;
use math::{Point, AngularInertia};



fn tetrahedron_unit_inertia_tensor_wrt_point<N: Real>(point: &Point<N>,
                                                      p1:    &Point<N>,
                                                      p2:    &Point<N>,
                                                      p3:    &Point<N>,
                                                      p4:    &Point<N>)
                                                      -> AngularInertia<N> {
    let p1 = *p1 - *point;
    let p2 = *p2 - *point;
    let p3 = *p3 - *point;
    let p4 = *p4 - *point;

    let _frac_10: N = na::convert(0.1f64);
    let _frac_20: N = na::convert(0.05f64);
    let _2      : N = na::convert(2.0f64);

    // Just for readability.
    let x1 = p1[0]; let y1 = p1[1]; let z1 = p1[2];
    let x2 = p2[0]; let y2 = p2[1]; let z2 = p2[2];
    let x3 = p3[0]; let y3 = p3[1]; let z3 = p3[2];
    let x4 = p4[0]; let y4 = p4[1]; let z4 = p4[2];

    let diag_x = x1 * x1 + x1 * x2 + x2 * x2 + x1 * x3 + x2 * x3 + x3 * x3 + x1 * x4 + x2 * x4 + x3 * x4 + x4 * x4;
    let diag_y = y1 * y1 + y1 * y2 + y2 * y2 + y1 * y3 + y2 * y3 + y3 * y3 + y1 * y4 + y2 * y4 + y3 * y4 + y4 * y4;
    let diag_z = z1 * z1 + z1 * z2 + z2 * z2 + z1 * z3 + z2 * z3 + z3 * z3 + z1 * z4 + z2 * z4 + z3 * z4 + z4 * z4;

    let a0 = (diag_y + diag_z) * _frac_10;
    let b0 = (diag_z + diag_x) * _frac_10;
    let c0 = (diag_x + diag_y) * _frac_10;

    let a1 = (y1 * z1 * _2 + y2 * z1      + y3 * z1      + y4 * z1 +
              y1 * z2      + y2 * z2 * _2 + y3 * z2      + y4 * z2 +
              y1 * z3      + y2 * z3      + y3 * z3 * _2 + y4 * z3 +
              y1 * z4      + y2 * z4      + y3 * z4      + y4 * z4 * _2) * _frac_20;
    let b1 = (x1 * z1 * _2 + x2 * z1      + x3 * z1      + x4 * z1 +
              x1 * z2      + x2 * z2 * _2 + x3 * z2      + x4 * z2 +
              x1 * z3      + x2 * z3      + x3 * z3 * _2 + x4 * z3 +
              x1 * z4      + x2 * z4      + x3 * z4      + x4 * z4 * _2) * _frac_20;
    let c1 = (x1 * y1 * _2 + x2 * y1      + x3 * y1      + x4 * y1 +
              x1 * y2      + x2 * y2 * _2 + x3 * y2      + x4 * y2 +
              x1 * y3      + x2 * y3      + x3 * y3 * _2 + x4 * y3 +
              x1 * y4      + x2 * y4      + x3 * y4      + x4 * y4 * _2) * _frac_20;

    let mut res = AngularInertia::zero();

    res[(0, 0)] =  a0; res[(0, 1)] = -b1; res[(0, 2)] = -c1;
    res[(1, 0)] = -b1; res[(1, 1)] =  b0; res[(1, 2)] = -a1;
    res[(2, 0)] = -c1; res[(2, 1)] = -a1; res[(2, 2)] =  c0;

    res
}

/// The volume and center of mass of a 3D convex mesh.
///
/// The mesh is not checked to be actually convex.
pub fn convex_mesh_volume_and_center_of_mass_unchecked<N: Real>(convex_mesh: &TriMesh<Point<N>>)
                                                                -> (N, Point<N>) {
    let geometric_center = utils::center(&convex_mesh.coords[..]);

    let mut res = Point::origin();
    let mut vol = N::zero();

    match convex_mesh.indices {
        IndexBuffer::Unified(ref idx) => {
            for t in idx.iter() {
                let p2 = &convex_mesh.coords[t.x as usize];
                let p3 = &convex_mesh.coords[t.y as usize];
                let p4 = &convex_mesh.coords[t.z as usize];

                let volume = utils::tetrahedron_volume(&geometric_center, p2, p3, p4);
                let center = utils::tetrahedron_center(&geometric_center, p2, p3, p4);

                res = res + center.coords * volume;
                vol = vol + volume;
            }
        },
        IndexBuffer::Split(_) => unreachable!()
    }

    if vol.is_zero() {
        (vol, geometric_center)
    }
    else {
        (vol, res / vol)
    }
}

/// The mass properties of a convex mesh.
///
/// The mesh is not checked to be actually convex.
pub fn convex_mesh_mass_properties_unchecked<N: Real>(convex_mesh: &TriMesh<Point<N>>,
                                                      density:     N)
                                                      -> (N, Point<N>, AngularInertia<N>) {
    let (volume, com) = convex_mesh_volume_and_center_of_mass_unchecked(convex_mesh);

    if volume.is_zero() {
        return (na::zero(), com, na::zero());
    }

    let mut itot = AngularInertia::zero();

    match convex_mesh.indices {
        IndexBuffer::Unified(ref idx) => {
            for t in idx.iter() {
                let p2 = &convex_mesh.coords[t.x as usize];
                let p3 = &convex_mesh.coords[t.y as usize];
                let p4 = &convex_mesh.coords[t.z as usize];

                let vol   = utils::tetrahedron_volume(&com, p2, p3, p4);
                let ipart = tetrahedron_unit_inertia_tensor_wrt_point(&com, &com, p2, p3, p4);

                itot = itot + ipart * vol;
            }
        },
        IndexBuffer::Split(_) => unreachable!()
    }

    (volume * density, com, itot * density)
}

/// The area of a convex mesh.
///
/// The mesh is not checked to be actually convex.
pub fn convex_mesh_area_unchecked<N: Real>(convex_mesh: &TriMesh<Point<N>>) -> N {
    let mut area = N::zero();

    match convex_mesh.indices {
        IndexBuffer::Unified(ref idx) => {
            for t in idx.iter() {
                let p1 = &convex_mesh.coords[t.x as usize];
                let p2 = &convex_mesh.coords[t.y as usize];
                let p3 = &convex_mesh.coords[t.z as usize];

                area = area + utils::triangle_area(p1, p2, p3);
            }
        },
        IndexBuffer::Split(_) => unreachable!()
    }

    area
}

/// The area of a convex hull.
pub fn convex_hull_area<N: Real>(points: &[Point<N>]) -> N {
    let convex_mesh = transformation::convex_hull3(points);
    convex_mesh_area_unchecked(&convex_mesh)
}

/// The volume of the convex hull of a set of points.
pub fn convex_hull_volume<N: Real>(points: &[Point<N>]) -> N {
    let convex_mesh = transformation::convex_hull3(points);
    convex_mesh_volume_and_center_of_mass_unchecked(&convex_mesh).0
}

/// The center of mass of the convex hull of a set of points.
pub fn convex_hull_center_of_mass<N: Real>(points: &[Point<N>]) -> Point<N> {
    let convex_mesh = transformation::convex_hull3(points);
    convex_mesh_volume_and_center_of_mass_unchecked(&convex_mesh).1
}

/// The angular inertia of the convex hull of a set of points.
pub fn convex_hull_unit_angular_inertia<N: Real>(points: &[Point<N>]) -> AngularInertia<N> {
    let convex_mesh = transformation::convex_hull3(points);
    let (vol, _, i) = convex_mesh_mass_properties_unchecked(&convex_mesh, na::one());

    i * (N::one() / vol)
}

impl<N: Real> Volumetric<N, Point3<N>, Matrix3<N>> for ConvexHull3<N> {
    fn area(&self) -> N {
        convex_hull_area(self.points())
    }

    fn volume(&self) -> N {
        convex_hull_volume(self.points())
    }

    fn center_of_mass(&self) -> Point3<N> {
        convex_hull_center_of_mass(self.points())
    }

    fn unit_angular_inertia(&self) -> Matrix3<N> {
        convex_hull_unit_angular_inertia(self.points())
    }

    fn mass_properties(&self, density: N) -> (N, Point3<N>, Matrix3<N>) {
        let convex_mesh = transformation::convex_hull3(self.points());
        convex_mesh_mass_properties_unchecked(&convex_mesh, density)
    }
}