An improved Loop subdivision to coordinate the smoothness and the number of faces via multi-objective optimization

3D mesh subdivision is essential for geometry modeling of complex surfaces, which benefits many important applications in the fields of multimedia such as computer animation. However, in the ordinary adaptive subdivision, with the deepening of the subdivision level, the benefits gained from the improvement of smoothness cannot keep pace with the cost caused by the incremental number of faces. To mitigate the gap between the smoothness and the number of faces, this paper devises a novel improved mesh subdivision method to coordinate the smoothness and the number of faces in a harmonious way. First, this paper introduces a variable threshold, rather than a constant threshold used in existing adaptive subdivision methods, to reduce the number of redundant faces while keeping the smoothness in each subdivision iteration. Second, to achieve the above goal, a new crack-solving method is developed to remove the cracks by refining the adjacent faces of the subdivided area. Third, as a result, the problem of coordinating the smoothness and the number of faces can be formulated as a multi-objective optimization problem, in which the possible threshold sequences constitute the solution space. Finally, the Non-dominated sorting genetic algorithm II (NSGA-II) is improved to efficiently search the Pareto frontier. Extensive experiments demonstrate that the proposed method consistently outperforms existing mesh subdivision methods in different settings.