This paper presents a novel simplification method for removing vertices from an intrinsic triangulation corresponding to extrinsic vertices lying on near-developable (i.e., with limited Gaussian curvature) and general surfaces. We greedily process all intrinsic vertices with an absolute Gaussian curvature below a user selected threshold. For each vertex, we repeatedly perform local intrinsic edge flips until the vertex reaches the desired valence (three for internal vertices or two for boundary vertices) such that removal of the vertex and incident edges can be locally performed in the intrinsic triangulation. Each removed vertex's intrinsic location is tracked via (intrinsic) barycentric coordinates that are updated to reflect changes in the intrinsic triangulation. We demonstrate the robustness and effectiveness of our method on the Thingi10k dataset and analyze the effect of the curvature threshold on the solutions of PDEs.

翻译：本文提出了一种新颖的简化方法，用于移除对应位于近可展曲面（即高斯曲率有限）及一般曲面上的外在顶点的内在三角剖分中的顶点。我们基于用户设定的阈值，贪婪地处理所有绝对高斯曲率低于该阈值的内在顶点。对于每个顶点，我们重复执行局部内在边翻转，直到该顶点达到所需的度数（内部顶点为三度，边界顶点为两度），从而在内在三角剖分中局部移除该顶点及其关联边。每个被移除顶点的内在位置通过（内在）重心坐标进行追踪，并实时更新以反映内在三角剖分的变化。我们在Thingi10k数据集上验证了该方法的鲁棒性和有效性，并分析了曲率阈值对偏微分方程解的影响。