  We present a prescription for choosing orthogonal bases of differential
$n$-forms belonging to quadratic twisted period integrals, with respect to the
intersection number inner product. To evaluate these inner products, we
additionally propose a new closed formula for intersection numbers beyond
$\mathrm{d} \log$ forms. These findings allow us to systematically construct
orthonormal bases between twisted period integrals of this type. In the context
of Feynman integrals, this represents all diagrams at one-loop.
