Abstract
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.
Abstract (translated)
在网格简化中，常见的精度、三角形质量以及特征对齐等要求通常被视为一个权衡。现有的算法集中于仅仅关注这些要求的一个或几个特定方面。例如，著名的四元误差度量（QEM）方法优先考虑精度，可以保留强烈的特征线/点，但高三角形质量的保证程度不高，甚至可能削弱那些与强特征不同的弱特征。在本文中，我们提出了一个平滑的函数，同时考虑所有这些要求。该函数包括一个正则化离散度项和一个中心势能项，变量是一个在表面上的可移动点集。前一个项继承了QEM的精神，但在连续设置中操作，而后者鼓励甚至点分布，允许各种表面度量。我们进一步引入了一个衰减权重，以自动平衡这两个项。我们选择了ABC数据集中的100个CAD模型和21个有机模型，与我们的网格简化算法进行比较。实验结果表明，引入衰减权重有效地减少了两个项之间的冲突，并使弱特征对齐。这一独特的特征使我们的方法与大多数现有的网格简化方法区别开来，并展示了在形状理解方面的显著潜力。
URL
https://arxiv.org/abs/2404.15661
