In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.

翻译：在网格简化中，常见的需求如精度、三角面质量和特征对齐通常被视为需要权衡的因素。现有算法仅专注于这些需求中的一个或几个特定方面。例如，著名的二次误差度量（QEM）方法优先考虑精度，也能保留强特征线/点，但在确保高三角面质量方面存在不足，并可能削弱那些不如强特征显著的弱特征。本文提出一种同时考虑所有这些需求的光滑泛函。该泛函包含一个法向各向异性项和一个质心泰森多边形分割（CVT）能量项，变量为位于曲面上的可移动点集。前者继承了QEM的思想，但在连续设置下运行，而后者鼓励点的均匀分布，并允许使用各种曲面度量。我们进一步引入一个衰减权重来自动平衡这两项。从ABC数据集中选取100个CAD模型和21个有机模型，将现有网格简化算法与我们的算法进行对比。实验结果表明一个重要的观察现象：衰减权重的引入有效减少了两个项之间的冲突，并使得弱特征能够对齐。这一独特特性使我们的方法与大多数现有网格简化方法截然不同，并在形状理解方面展现出显著潜力。