Firefly Algorithm for Shape Reconstruction of 3D Point Clouds with Normal and Gamma Univariate Functions

The conventional reverse engineering approach for quality assessment in manufacturing involves recovering the shape of the manufactured workpieces through surface reconstruction techniques. This process generates a digital representation of the physical object, which is used for shape quality evaluation. Typically, this process begins with a cloud of data points obtained from the workpiece using 3D scanning. Then, surface reconstruction is performed on the point cloud to obtain a mathematical representation of the approximating surface. In this paper, we assume that the data points can be well approximated by using Normal and Gamma univariate distribution functions. As a result, the approximation function combines exponential, polynomial and logarithmic functions, leading to a non-convex nonlinear constrained continuous minimization problem. To address this challenging problem, our method relies on the firefly algorithm, a well-known metaheuristic technique. Our method is applied to three illustrative examples of point clouds following different distribution functions. The graphical and numerical results demonstrate that our approach performs favorably, accurately recovering the underlying shape of the data.