Blended CoordinatesBased on Point Polygons

In order to construct nonnegative and smooth generalized barycentric coordinates, a blended coordinates construction method based on point polygons was proposed. Firstly, triangulated the original polygon, calculated the barycentric coordinates of all mesh vertices, and determined the point polygons of each mesh vertex; Furthermore, the barycentric coordinates and blended coefficients of the point inside the original polygon with respect to the point polygons of the triangle in which they were located were calculated respectively, then the blended coordinates were obtained according to the above calculation results. Finally, the barycentric coordinates of the mesh vertices were calculated using iterative coordinates or harmonic coordinates, and the barycentric coordinates of the points inside the original polygon with respect to the point polygons were calculated using mean value coordinates and iterative coordinates. Numerical examples and derivation results show that the proposed method has good smoothness and is nonnegative inside any polygon.