The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

中文翻译：

---

Marching Cubes 33 算法的扩展三角剖分

Marching Cubes 算法可以说是最流行的等值面提取算法。自成立以来，存在两个问题，即三角形质量和拓扑正确性。尽管有大量文献可以解决这些问题，但实现拓扑正确会损害三角形质量，反之亦然。在本文中，我们提出了行进立方体 33 算法的扩展版本（保证拓扑正确性的行进立方体算法的变体），称为扩展行进立方体 33。在所提出的算法中，网格顶点用“+”标记， “-,”和“=”根据其标量字段值与等值之间的关系。包含“=”网格顶点标签自然避免了退化三角形。作为我们方法的应用，