IEEE Trans Vis Comput Graph. 2017 Dec;23(12):2560-2573. doi: 10.1109/TVCG.2016.2632720. Epub 2016 Nov 24.
Surface remeshing is a key component in many geometry processing applications. The typical goal consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application (e.g., the minimum interior angle is above an application-dependent threshold). Our algorithm is designed to address all three optimization goals simultaneously by targeting prescribed bounds on approximation error , minimal interior angle and maximum mesh complexity (number of vertices). The approximation error bound is a hard constraint, while the other two criteria are modeled as optimization goals to guarantee feasibility. Our optimization framework applies carefully prioritized local operators in order to greedily search for the coarsest mesh with minimal interior angle above and approximation error bounded by . Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that for reasonable angle bounds ( ) our approach delivers high-quality meshes with implicitly preserved features (no tagging required) and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.
曲面重网格化是许多几何处理应用中的关键组成部分。典型的目标是找到一个网格，该网格 (1) 在几何上忠实于原始几何，(2) 尽可能粗糙，以获得低复杂度的表示，(3) 没有会阻碍所需应用的不良元素（例如，最小内角高于应用相关的阈值）。我们的算法旨在通过针对规定的逼近误差、最小内角和最大网格复杂度（顶点数）的界限同时解决所有三个优化目标。逼近误差界限是一个硬性约束，而其他两个标准则被建模为优化目标，以保证可行性。我们的优化框架应用精心优先的局部操作符，以便贪婪地搜索具有最小内角和逼近误差的最粗糙网格界限为 。通过局部逼近误差估计实现快速运行时，通过专门设计的顶点重定位操作符实现隐式特征保留。实验表明，对于合理的角度界限（），我们的方法提供了具有隐式保留特征的高质量网格（无需标记），并且在几何保真度、网格复杂度和元素质量之间的平衡优于最新技术。
