The reconstruction of 3D objects based on point clouds is a difficult and poorly posed problem. This problem is fundamental for many applications such as recognition and identification of objects, robotic navigation, medical diagnostics, etc. In this paper, we propose to reconstruct a 3D object from its 3D point cloud using swarm intelligence algorithms. In our approach, the 3D object is modeled by recent primitives called supershapes; representing the extension of superquadrics with a more prominent limit of demonstrating complex objects. The fundamental idea of our work is to consider the issue of three-dimensional reconstruction as an optimization problem, and then model a 3D object using new primitives. Thus, our approach benefits from the efficiency and robustness of metaheuristics, and the diversity of supershapes. We adjusted and adapted the following swarm intelligence algorithms: artificial bee algorithm, chicken swarm algorithm; for the purpose of tridimensional reconstruction. The employed error function is based in its definition on the Euclidean radial distance. The choice of this function is very important since it will subsequently assume the role of dissimilarities indicator between the initial and reconstructed object. Our approach has demonstrated to be extremely compelling, and has prevailing with regards to giving excellent outcomes, in comparison with other existing methodologies in the literature.