Within the thee-dimensional objects deformation techniques, the ones using control polyhedrons allow fast and intuitive interaction, and therefore gained considerable interest in recent years. Those techiques write the model points as function of the vertices of the control polyhedron, for exemple using barycentric coordinates or its extensions. This way, deforming the control polyhedron induces a corresponding strain on the model, recomputing each point of the object from the new positions of control vertices. To do so, due to the flexibility in its construction, different generalizations of barycentric coordinates has been proposed in recent years for 3D models. In this work, we present a study of recent generalizations of barycentric coordinates and the main characteristics of the resulting deformations of three-dimensional model. We deduce from this study a new extension of barycentric coordinates that retains the simplicity of the original method and fixes some of the its defects.