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use crate::mass_properties::MassProperties;
use crate::math::{Point, PrincipalAngularInertia, Real, Rotation, Vector};
use na::RealField;

impl MassProperties {
    pub(crate) fn cone_y_volume_unit_inertia(
        half_height: Real,
        radius: Real,
    ) -> (Real, PrincipalAngularInertia<Real>) {
        let volume = radius * radius * Real::pi() * half_height * 2.0 / 3.0;
        let sq_radius = radius * radius;
        let sq_height = half_height * half_height * 4.0;
        let off_principal = sq_radius * 3.0 / 20.0 + sq_height * 3.0 / 80.0;
        let principal = sq_radius * 3.0 / 10.0;

        (volume, Vector::new(off_principal, principal, off_principal))
    }

    /// Computes the mass properties of a cone.
    pub fn from_cone(density: Real, half_height: Real, radius: Real) -> Self {
        let (cyl_vol, cyl_unit_i) = Self::cone_y_volume_unit_inertia(half_height, radius);
        let cyl_mass = cyl_vol * density;

        Self::with_principal_inertia_frame(
            Point::new(0.0, -half_height / 2.0, 0.0),
            cyl_mass,
            cyl_unit_i * cyl_mass,
            Rotation::identity(),
        )
    }
}