Abstract: To address the issue of Blended barycentric coordinates being dependent on the triangulation method, proposes a method for constructing barycentric coordinates——Blended Polygon coordinates. First, we triangulate any input polygon Ω and then construct blended polygons based on the triangulation results, including vertex polygons, edge polygons, and triangulated triangles. Then, we randomly select a calculation point inside Ω and find the blended polygons that correspond to that point. Next, we calculate the barycentric coordinates and blending functions of the point with respect to the blended polygons, the barycentric coordinates of the blended polygon vertices with respect to the triangulation vertices, and the barycentric coordinates of the triangulation vertices with respect to Ω. Finally, we combine all the calculated results to obtain the blended polygon coordinates of the calculation point with respect to Ω. According to theoretical derivation, Blended Polygon coordinates within any polygon satisfy the properties of linear reproduction, partition of unity, the Lagrange, non-negativity and smoothness, and they achieve at least C¹ continuity. Through the functional distribution diagram of barycentric coordinates, the comparison of different triangulation methods, and the application in image deformation, it has been verified that Blended Polygon coordinates not only address the problem of Blended barycentric coordinates, Harmonic coordinates and Local barycentric coordinates but also have obvious advantages over other barycentric coordinates in terms of smoothness, non-negativity, and deformation effects.