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//! Traits to compute inertial properties.

use std::ops::Mul;
use alga::general::Real;
use na;
use na::{Point2, Point3, Vector1, Vector3, Isometry2, Isometry3, Matrix1, Matrix3};

/// Trait implemented by inertia tensors.
pub trait InertiaTensor<N, P, AV, M> {
    /// Applies this inertia tensor to a vector.
    ///
    /// This is usually done by a matrix-vector multiplication.
    fn apply(&self, a: &AV) -> AV;

    /// Transforms this inertia tensor from local space to world space.
    fn to_world_space(&self, &M) -> Self;

    /// Computes this inertia tensor relative to a given point.
    fn to_relative_wrt_point(&self, N, &P) -> Self;
}

/// Trait implemented by objects which have a mass, a center of mass, and an inertia tensor.
pub trait Volumetric<N: Real, P, I: Mul<N, Output = I>> {
    /// Computes the area of this object.
    fn area(&self) -> N;

    /// Computes the volume of this object.
    fn volume(&self) -> N;

    /// Computes the center of mass of this object.
    fn center_of_mass(&self) -> P;

    /// Computes the angular inertia tensor of this object.
    fn unit_angular_inertia(&self) -> I;

    /// Given its density, this computes the mass of this object.
    fn mass(&self, density: N) -> N {
        self.volume() * density
    }

    /// Given its mass, this computes the angular inertia of this object.
    fn angular_inertia(&self, mass: N) -> I {
        self.unit_angular_inertia() * mass
    }

    /// Given its density, this computes the mass, center of mass, and inertia tensor of this object.
    fn mass_properties(&self, density: N) -> (N, P, I) {
        let mass = self.mass(density);
        let com  = self.center_of_mass();
        let ai   = self.angular_inertia(mass);

        (mass, com, ai)
    }

}

impl<N: Real> InertiaTensor<N, Point2<N>, Vector1<N>, Isometry2<N>> for Matrix1<N> {
    #[inline]
    fn apply(&self, av: &Vector1<N>) -> Vector1<N> {
        *self * *av
    }

    #[inline]
    fn to_world_space(&self, _: &Isometry2<N>) -> Matrix1<N> {
        self.clone()
    }

    #[inline]
    fn to_relative_wrt_point(&self, mass: N, pt: &Point2<N>) -> Matrix1<N> {
        *self + Matrix1::new(mass * na::norm_squared(&pt.coords))
    }
}

impl<N: Real> InertiaTensor<N, Point3<N>, Vector3<N>, Isometry3<N>> for Matrix3<N> {
    #[inline]
    fn apply(&self, av: &Vector3<N>) -> Vector3<N> {
        *self * *av
    }

    #[inline]
    fn to_world_space(&self, t: &Isometry3<N>) -> Matrix3<N> {
        let rot  = t.rotation.to_rotation_matrix();
        let irot = rot.inverse();
        rot * *self * irot
    }

    #[inline]
    fn to_relative_wrt_point(&self, mass: N, pt: &Point3<N>) -> Matrix3<N> {
        let diag  = na::norm_squared(&pt.coords);
        let diagm = Matrix3::new(
            diag.clone(), na::zero(),   na::zero(),
            na::zero(),   diag.clone(), na::zero(),
            na::zero(),   na::zero(),   diag
        );

        *self + (diagm - pt.coords * pt.coords.transpose()) * mass
    }
}