We present a robust method to generate atlases with low isometric distortion and high packing efficiency. Given a surface that has been cut to disk topology, the algorithm contains four steps: (1) computing a bijective parameterization with low isometric distortion; (2) partitioning the input parameterized charts into a set of rectangle-like patches; (3) mapping rectangle-like patches onto rectangles that are packed into a rectangular domain; and (4) reducing parameterization distortion while maintaining high packing efficiency and bijection. Since there have been elegant and robust solutions for the first, third, and fourth steps, we focus on the second step. Central to the second step is a novel and robust segmentation technique. To improve the robustness of the segmentation, we first deform the parameterized charts to straighten their boundaries while aligning with the axes as much as possible, bounding the deformation distortion, and not introducing intersecting boundaries. Since rectangle-like patches are preferred for the third and fourth steps, we segment the deformed charts by decomposing concave interior angles into several interior angles close to $\frac{\pi }{2}$ or π. To this end, we develop four types of operations: (i) bridging operation, (ii) extension operation, (iii) vertical line operation, and (iv) bisector operation. The pre-deformation process makes our heuristic segmentation very simple and effective. We demonstrate the efficacy of our method on various complex models. Compared to other state-of-the-art methods, our method achieves higher robustness.

我们提出了一种可靠的方法来生成具有低等轴测失真和高包装效率的地图集。给定已切割为磁盘拓扑的表面，该算法包含四个步骤：（1）计算具有低等轴测失真的双射参数化；（2）将输入的参数化图表划分为一组矩形的补丁；（3）将类似矩形的补丁映射到打包成矩形域的矩形上；（4）在保持高打包效率和双射的同时减少参数化失真。由于第一步，第三步和第四步都有精巧而强大的解决方案，因此我们专注于第二步。第二步的中心是一种新颖而强大的分割技术。为了提高细分的鲁棒性，我们首先将参数化图表变形以使其边界变直，同时尽可能与轴对齐，以限制变形失真，并且不引入相交边界。由于在第三和第四步中最好使用矩形补丁，因此我们通过将凹面内角分解为接近$\frac{\pi }{2}$或π。为此，我们开发了四种类型的操作：（i）桥接操作，（ii）扩展操作，（iii）垂直线操作和（iv）等分线操作。变形前的过程使我们的启发式分割非常简单有效。我们证明了我们的方法在各种复杂模型上的有效性。与其他最新方法相比，我们的方法具有更高的鲁棒性。