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use std::ops::Mul;
use alga::general::Real;
use na;
use na::{Point2, Point3, Vector1, Vector3, Isometry2, Isometry3, Matrix1, Matrix3};
pub trait InertiaTensor<N, P, AV, M> {
fn apply(&self, a: &AV) -> AV;
fn to_world_space(&self, &M) -> Self;
fn to_relative_wrt_point(&self, N, &P) -> Self;
}
pub trait Volumetric<N: Real, P, I: Mul<N, Output = I>> {
fn area(&self) -> N;
fn volume(&self) -> N;
fn center_of_mass(&self) -> P;
fn unit_angular_inertia(&self) -> I;
fn mass(&self, density: N) -> N {
self.volume() * density
}
fn angular_inertia(&self, mass: N) -> I {
self.unit_angular_inertia() * mass
}
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
}
}