Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it intersects; (2) filling the so generated hole with two polygons that have the wanted segment as shared edge; (3) triangulate each polygon separately. In this article we prove that these polygons are such that all their convex vertices but two can be used to form triangles in an earcut fashion, without the need to check whether other polygon points are located within each ear. The fact that any simple polygon contains at least three convex vertices guarantees the existence of a valid ear to cut, ensuring convergence. Not only this translates to an optimal deterministic linear time triangulation algorithm, but such algorithm is also trivial to implement. We formally prove the correctness of our approach, also validating it in practical applications and comparing it with prior art.

中文翻译：

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使用简化耳切的确定性线性时间约束三角剖分

符合一组非相交输入段的三角剖分算法通常以增量方式进行，首先插入点，然后插入段。插入一个线段相当于：（1）删除它相交的所有三角形；(2) 用两个多边形填充这样生成的孔，这些多边形具有想要的段作为共享边；(3) 分别对每个多边形进行三角剖分。在本文中，我们证明了这些多边形使得它们的所有凸顶点（除了两个）都可以用于以耳切方式形成三角形，而无需检查其他多边形点是否位于每个耳内。任何简单的多边形都包含至少三个凸顶点这一事实保证了有效耳朵的存在，从而确保了收敛。这不仅转化为最佳确定性线性时间三角剖分算法，但是这样的算法实现起来也很简单。我们正式证明了我们方法的正确性，也在实际应用中对其进行了验证，并将其与现有技术进行了比较。