  We construct on-shell ${\mathcal{N}}=2$ nonlinear sigma models on
$SO(2N)/U(N)$ and $Sp(N)/U(N)$ by holomorphically embedding the models in the
hyper-K\"{a}hler nonlinear sigma model on the cotangent bundle of the Grassmann
manifold $T^\ast G_{2N,N}$ in the ${\mathcal{N}}=1$ superspace formalism. We
apply the moduli matrix formalism to the mass-deformed nonlinear sigma models
on the quadrics to study three-pronged junctions by using a recently proposed
diagram method.
