Optimization of non-uniform relational B-Spline surface reconstruction using growing grid-differential evolution

Abstract

Computer graphics is a fast growing field as it contributes significantly to the advancement of modern technology aimed at empowering human and nation wealth creation. Computer-Aided Design (CAD), Computer-Aided Manufacturing (CAM) and Computer-Aided Geometric Design (CAGD) are commonly used to reconstruct surfaces in order to obtain a set of limited and disorganized geometric sample values. The process of surface reconstruction consists of two main steps: parameterization and surface fitting. Various solutions have been used in previous studies to reconstruct surfaces such as Non Uniform Rational B-Spline (NURBS) and B-Spline. However, in recent years, Artificial Intelligence (AI) methods such as Advanced Neural Network and Evolutionary Algorithm (EA) have emerged and are extensively used to reconstruct and optimize complex surfaces. This study aims to optimize NURBS surfaces from unstructured 3D data points with feasible control points while preserving the shape of the objects by using Differential Evolution Algorithm (DEA). The Growing Grid Network (GGN) is implemented on a map structure, while DEA is optimally fit on to the NURBS surfaces. In this study, undefined or unstructured data points from several 2D and 3D datasets were used to validate the performance of the proposed method. An error analysis was also conducted to reconfirm the efficacy of the proposed algorithm. This is done by comparing the generated surface with the original surface using other EAs such as: Genetic Algorithm and Particle Swarm Optimization. Experimental results indicate that the proposed Growing Grid Network Differential Evolution (GGNDE) has successfully generated smoother surfaces with lesser number of control points and produced minimum feasible errors while preserving the shape of the objects.