  We give a geometric model for any length heart in the derived category of a
gentle algebra, which is equivalent to the module category of some gentle
algebra. To do this, we deform the geometric model for the module category of a
gentle algebra given in [BC21], and then embed it into the geometric model of
the derived category given in [OPS18], in the sense that each so-called zigzag
curve on the surface represents an indecomposable module as well as the minimal
projective resolution of this module. A key point of this embedding is to give
a geometric explanation of the dual between the simple modules and the
projective modules.
  Such a blend of two geometric models provides us with a handy way to describe
the homological properties of a module within the framework of the derived
category. In particular, we realize any higher Yoneda-extension as a polygon on
the surface, and realize the Yoneda-product as gluing of these polygons. As an
application, we realize any length heart in the derived category of a gentle
algebra on the marked surface.
