Abstract Direct triangular surface remeshing algorithms work directly on the surface meshes without involving any complex parameterization techniques. The typical goal of surface remeshing is to find a mesh that is a faithful approximation of the input mesh that maintains the geometric fidelity between input and output meshes, achieve a lower bound on the minimal angles to enhance high element quality while maintaining vertex regularity and sharp feature preservation of the input mesh. The goal of each surface remeshing algorithm varies as per the requirement of the end application and thus achieving a balance between all common goals is a challenging task in remeshing. In this paper, a survey of numerous direct surface remeshing algorithms that have been developed over the past decade is presented. A framework of direct surface remeshing is defined and various phases of the framework are discussed in detail to give new insights into both existing methods and issues. A detailed analysis of how significant challenges have already been overcome and promising perspectives of various methods are presented.

中文翻译：

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直接三角面重新划分网格的计算范式

摘要 直接三角曲面网格划分算法直接作用于曲面网格，不涉及任何复杂的参数化技术。表面重新网格划分的典型目标是找到一个忠实近似于输入网格的网格，该网格保持输入和输出网格之间的几何保真度，实现最小角度的下限以提高高元素质量，同时保持顶点规则性和锐度输入网格的特征保留。每个表面重新网格划分算法的目标根据最终应用的要求而变化，因此在所有共同目标之间实现平衡是重新网格划分中的一项具有挑战性的任务。在本文中，对过去十年中开发的众多直接表面重新网格划分算法进行了调查。定义了直接表面重新网格化的框架，并详细讨论了框架的各个阶段，以对现有方法和问题提供新的见解。详细分析了如何克服重大挑战，并提出了各种方法的前景。