The Navier-Stokes momentum equation is applied for demonstrating the motion of viscous fluid substances. In this equation the curvature, as one of the main parameters which occurs in the surface tension, can be determined through classical methods such as volume of fluid (VOF) method where demands to determine the volume of fraction in a Cartesian grid. Alternatively, solving the momentum equation can be done using a front-tracking method which involves a more straightforward computation of surface tension. However, these approaches are in general rather expensive and time consuming. Therefore, it would be worthwhile to develop a numerical algorithmic method which approximates the curvatures of points with reasonable errors . This work is devoted to find a new algorithmic method for computing curvatures of distinct points on a moving particle cloud which is used for investigating topological changing of the moving surfaces e.g. merging and breakup of bubbles. More precisely, in this method, we obtain local fitted curves through computing the polynomials with least square errors for the points located in different parts of the cloud and then we calculate curvatures of the corresponding points placed on these fitted curves. We present a MATLAB function called LSEcurve which manipulates computations of LSE curves and the corresponding curvatures automatically and display graphical results as output. We also test our method for a series of clouds obtained by taking snapshots from a bubble in different times which enable us to study changes of fitted curves to the clouds and their curvatures.