Keywords: artificial intelligence, geometry reconstruction, reverse engineering, geometry parameterization.

Surface and curve reconstruction, being a very challenging problem, is a key element of reverse engineering methodologies and finds a variety of interesting applications in different disciplines. Shape reconstruction is defined as the construction of a compact mathematical representation of the shape under consideration, using partial information about it, usually in the form of discrete points in the three-dimensional geometric space. Different methodologies have been reported in the open literature, attempting the development of effective, efficient, and robust algorithms that can be used for solving the shape reconstruction problem. Among them, a special category of methodologies utilize techniques categorized in the artificial intelligence (AI) scientific field, such as evolutionary algorithms (EAs), artificial neural networks (ANNs), particle swarm optimization (PSO) techniques, artificial immune systems (AIS), etc. Such methodologies, have proven their effectiveness and usefulness in many different technological fields, especially for the solution of demanding and high-dimensional optimization problems. The application of such methodologies to the shape reconstruction problem is neither a trivial nor a straightforward task, as it will be clarified later in this work. Moreover, population based methodologies (such as EAs, PSO, AIS, etc.) ask for considerable computational resources, and, therefore, cannot be used for real-time applications, in general. Nevertheless, such methodologies can provide alternative and very effective solutions to the shape reconstruction problem. In this work, different aspects of the shape reconstruction problem will be presented and analysed, including a brief presentation of various AI-based methodologies used for this task. The focus of this work will be mainly on surface reconstruction, as the curve reconstruction problem is an easier one, and can be handled with similar procedures.

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