A comparative study of geometric primitives fitting to 3D point clouds

Abstract

The rapid development of scanning technologies has led to new challenges in Computer Aided Design (CAD) such as the reconstruction of the geometric model from a set of 3D points cloud. In fact, this model is the geometric support in various activities such as the analysis activity and the computer aided manufacturing activity. The CAD model is used in order to visualize scanned 3D objects by the approximation of the adequate shape using different mathematical equations. Thus, the most difficult stage in reconstructing a CAD model is 3D surface fitting. There are two sorts of 3D surfaces: simple geometric primitives (sphere, cylinder, cone, torus, etc.) and complex 3D surfaces (Bezier, B-Spline, NURBS, etc.). In this paper, we focus on the reconstruction of simple geometric primitives. These primitives can be found in a variety of settings, from home to industrial. The aim of this work is to select the appropriate algorithm that facilitates the approximation of geometric primitives given 3D point clouds. The following three strategies are proposed for a comparative study: the Levenberg Marquardt algorithm, the Spherical Harmonic method and the Trust-Region Reflective method. Based on the results of these algorithms, designers, manufacturers, and inspectors can choose the best method to reconstruct their final CAD model based on their specific needs.