This paper introduces the geometric continuity equations of the closed planar polygons and gives the definition of a morphing with geometric continuity between two arbitrary planar polygons, including simple, non-3 and even degenerated polygons. A simple morphing technique based on linear interpolation of the geometric continuity equations is proposed. The closureness of the in-between polygons is precisely achieved. Two global invariants: rotation indexes and winding numbers are introduced to describe the most general polygons. The demo shows that this technique is efficient and natural for morphing between polygons with arbitrary rotation indexes and winding numbers.