Since correct critical points are crucial for most shape decomposition algorithms, a variety of part-related measures have been presented to detect these critical points. Among this, the electrical charge distribution on the shape (ECDS) and its variants have some distinguishing characteristics and advantages, such as invariance and smoothness. However, we find it is still challenging to obtain satisfactory critical points, especially in the flat area such as the tails and legs of shapes. In this paper, we propose a novel way to make ECDS exhibit low values at given critical points. That is to say, critical points from other part-related measures can be introduced in ECDS, which will highly improve its descriptive ability. To achieve it, we propose to add constraints to linear equations, meanwhile relax these constraints in an anisotropy heat diffusion manner. Furthermore, we put forward a novel approach to find the stable extreme points of the improved ECDS (IECDS), which usually corresponding to critical points. Finally, we conduct experiments on the shapes in the MPEG-7 dataset, demonstrating that our method can obtain more meaningful critical points than existing methods.