Vec3f Sphere3D::GetFarthestVert( const Vec3f& normalized_dir, const Vec3f& origin, const float radius ) {
    Vec3f add( normalized_dir * radius );
    add += origin;
    return add;
}

Vec3f Capsule3D::GetFarthestVert( const Vec3f& normalized_dir ) const {
    const Vec3f a( Sphere3D::GetFarthestVert( normalized_dir, origin, radius ) );
    const Vec3f b( Sphere3D::GetFarthestVert( normalized_dir, GetEnd(), radius ) );

    if ( a.Dot( normalized_dir ) > b.Dot( normalized_dir ) )
        return a;
    return b;
}

Vec3f Cylinder3D::GetFarthestVert( const Vec3f& normalized_dir ) const {
    const Vec3f spherePoint( Sphere3D::GetFarthestVert( normalized_dir, GetEnd(), radius ) );

    if ( origin.Dot( normalized_dir ) > spherePoint.Dot( normalized_dir ) )
        return origin;

    // ** if the distance of the point is farther than the end of the cylinder, it exists on the sphere and we need to move it
    const float dist = Plane3f::DistanceToPoint( spherePoint, normal, origin );
    if ( dist > length )
        return spherePoint - normal * (dist - length);

    return spherePoint;
}