Large-scale 3D models consume large computing and storage resources. To address this challenging problem, this paper proposes a new method to obtain the optimal simplified 3D mesh models with the minimum approximation error. First, we propose a feature-preservation edge collapse operation to maintain the feature edges, in which the collapsing cost is calculated in a novel way by combining Gauss curvature and Quadratic Error Metrics (QEM). Second, we introduce the edge splitting operation into the mesh simplification process and propose a hybrid ‘undo/redo’ mechanism that combines the edge splitting and edge collapse operation to reduce the number of long and narrow triangles. Third, the proposed ‘undo/redo’ mechanism can also reduce the approximation error; however, it is impossible to manually choose the best operation sequence combination that can result in the minimum approximation error. To solve this problem, we formulate the proposed mesh simplification process as an optimization model, in which the solution space is composed of the possible combinations of operation sequences, and the optimization objective is the minimum of the approximation error. Finally, we propose a novel optimization algorithm, WOA-DE, by replacing the exploration phase of the original Whale Optimization Algorithm (WOA) with the mutate and crossover operations of Differential Evolution (DE) to compute the optimal simplified mesh model more efficiently. We conduct numerous experiments to test the capabilities of the proposed method, and the experimental results show that our method outperforms the previous methods in terms of the geometric feature preservation, triangle quality, and approximation error.

中文翻译：

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基于鲸鱼优化算法和差分进化的具有特征保留的3D网格简化

大型3D模型会消耗大量的计算和存储资源。为了解决这个具有挑战性的问题，本文提出了一种新的方法来获得具有最小逼近误差的最优简化3D网格模型。首先，我们提出了一种保留特征的边缘折叠操作以维护特征边缘，其中通过结合高斯曲率和二次误差度量（QEM）以新颖的方式计算折叠成本。其次，我们将边缘分裂操作引入到网格简化过程中，并提出了一种混合的“撤消/重做”机制，该机制结合了边缘分裂和边缘折叠操作以减少长三角形和窄三角形的数量。第三，提出的“撤消/重做”机制还可以减少近似误差。然而，不可能手动选择可以导致最小逼近误差的最佳操作序列组合。为了解决该问题，我们将提出的网格简化过程公式化为优化模型，其中求解空间由操作序列的可能组合组成，并且优化目标是逼近误差的最小值。最后，我们提出了一种新颖的优化算法WOA-DE，该方法通过用差分进化（DE）的变异和交叉操作代替原始的鲸鱼优化算法（WOA）的探索阶段，从而更有效地计算最佳简化网格模型。我们进行了大量实验，以测试所提出方法的功能，