hyper spheres

# Hyper spheres are used to bound points in space.
# For a node all it's children are bounded by the
# node's hyper sphere.
immutable HyperSphere{T <: FloatingPoint}
    center::Vector{T}
    r::T
end

# Checks if two spheres overlap.
# They do if the distance between their centers
# is smaller than the sum of the radiuses
function intersects{T <: FloatingPoint}(s1::HyperSphere{T},
                                      s2::HyperSphere{T},
                                      m::MinkowskiMetric)
    d_12 = distance(m, s1.center, s2.center)
    d_12 <= s1.r + s2.r
end

# Checks if one shpere completely encloses the other
# It does if the distance between the centers plus the inner
# spheres r is less than the r of the outer sphere
function encloses{T <: FloatingPoint}(s1::HyperSphere{T},
                                      s2::HyperSphere{T},
                                      m::MinkowskiMetric)
    d_12 = distance(m, s1.center, s2.center)
    d_12 + s1.r <= s2.r
end


# Creates a bounding sphere from two other spheres
function create_bsphere{T <: FloatingPoint}(s1::HyperSphere{T},
                                            s2::HyperSphere{T},
                                            l::Vector{T},
                                            r::Vector{T},
                                            v_12::Vector{T},
                                            m::MinkowskiMetric)
    # Unitvector from s1 to s2
    @devec v_12[:] = s2.center - s1.center
    norm_v_12 = norm(v_12)
    @devec v_12[:] = v_12 ./ norm_v_12

    # The two points furthest away from the center
    @devec l[:] = s1.center - v_12 .* s1.r
    @devec r[:] = s2.center + v_12 .* s2.r

    # r is half distance between edges
    r = distance(m, l, r) / 2.0

    center = Array(T, length(v_12))
    @devec center[:] = (l + r) ./ 2.0

    HyperSphere(center, r)

end