  We proposed a theoretical framework to correlate the topological diagram at
quark level and rescattering dynamics at hadron level. In the framework, both
the hadronic triangle diagram, and the topological-scattering diagram, which is
the intermediate structure between topological diagram and triangle diagram,
are expressed in the tensor form. The completeness of topological-scattering
diagram is confirmed by the quark substructure of meson-meson scattering. The
coefficient of each triangle diagram can be derived from the
topological-scattering diagram and the total rescattering amplitudes are
consistent with the ones derived from the chiral Lagrangian. If only the
short-distance $T$ diagram is considered as the weak vertex in triangle
diagram, the rescattering contributions in the $C$, $E$ and $P$ diagrams have
definite proportional relation of $L(C):L(E):L(P)=-2:1:1$ under the $SU(3)_F$
symmetry, and the rescattering contributions in the $T$ and $A$ diagrams only
arise from the $SU(3)_F$ breaking effects. Taking $D\to K\pi$ and $D\to \pi\pi$
modes as examples, we present our framework in detail. We find the Isospin
relations in these decays are still valid in terms of triangle diagrams.
Besides, the conclusions in the $D$ meson decays under the $SU(3)_F$ symmetry
can be generalized to the $B$ meson decays under the $SU(4)_F$ symmetry.
