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.

中文翻译：

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一种改进的循环细分，通过多目标优化来协调平滑度和面数

3D 网格细分对于复杂曲面的几何建模至关重要，这有利于多媒体领域的许多重要应用，例如计算机动画。但是，在普通的自适应细分中，随着细分层次的加深，平滑度提升带来的收益跟不上面数增加带来的成本。为了缩小平滑度和面数之间的差距，本文设计了一种新颖的改进网格细分方法来协调平滑度和面数。首先，本文引入了可变阈值，而不是现有自适应细分方法中使用的恒定阈值，以减少冗余面的数量，同时保持每次细分迭代的平滑度。第二，为实现上述目标，开发了一种新的裂纹求解方法，通过细化细分区域的相邻面来消除裂纹。第三，因此，协调平滑度和面数的问题可以表述为多目标优化问题，其中可能的阈值序列构成解空间。最后，对非支配排序遗传算法 II (NSGA-II) 进行了改进，以有效地搜索帕累托边界。大量实验表明，所提出的方法在不同设置下始终优于现有的网格细分方法。协调平滑度和面数的问题可以表述为一个多目标优化问题，其中可能的阈值序列构成解空间。最后，对非支配排序遗传算法 II (NSGA-II) 进行了改进，以有效地搜索帕累托边界。大量实验表明，所提出的方法在不同设置下始终优于现有的网格细分方法。协调平滑度和面数的问题可以表述为一个多目标优化问题，其中可能的阈值序列构成解空间。最后，对非支配排序遗传算法 II (NSGA-II) 进行了改进，以有效地搜索帕累托边界。大量实验表明，所提出的方法在不同设置下始终优于现有的网格细分方法。