3 维 Delauny 网格三角剖分算法的输出应该是什么？
如果这是输入点：
到 Delaunay Mesh Triangulation 算法，那么 Delaunay Mesh Triangulation 算法 的输出是什么3维？
A. 这一个：
或 B.这个 [所有给定输入点的 ConvexHull]
你的答案是什么？ A 或 B
If this are the input points:
to the Delauny Mesh Triangulation algorithm, then what will be output of Delauny Mesh Triangulation algorithm for 3-Dimension?
A. This one:
or B. This one [ConvexHull of all given input points]
What is your answer? A or B
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你得到的不是一个表面，而是一个由以 B 为表面的四面体组成的“体积”。
必须移除四面体的大部分面才能获得干净的表面，如 A 所示，但为此您必须确定哪些四面体在内部，哪些在外部。
在 2D 中，同样的问题是从三角形网格中获取一条线。当数据来自某个传感器时，可以选择正确的线的是与表面对齐的点的密度。对于随机点，没有“好的”解决方案。
You don't get a surface but a "volume" made of tetrahedrons with B as surface.
Most of the faces of the tetrahedrons have to be removed to get a clean surface as in A, but for this you have to decide which tetrahedrons are inside and which are outside.
In 2D the same problem would be to get a line from the triangle mesh. What may allow to choose the right line is the density of points which aligns with the surface when data comes from some sensor. For random points there is no "good" solution.
A 中的输出是通过从点重建表面获得的。有多种方法可以实现此目的，其中许多方法基于 Delaunay 三角测量。例如，请参见 http://cgal.inria.fr/Reconstruction/ 和 http://www.cse.ohio-state.edu/~tamaldey/surfrecon.htm 。
The output in A is obtained by surface reconstruction from points. There are several methods for this, many of them based on Delaunay triangulation. See for instance http://cgal.inria.fr/Reconstruction/ and http://www.cse.ohio-state.edu/~tamaldey/surfrecon.htm .
严格来说，您的结果 B 是正确的，并且 A 是“修剪”版本，边缘长度不超过特定阈值。
但是：查看alpha 形状。他们概括了这个概念以适合您的结果！它们只是成为具有不同 alpha 值的结果。
然而，阿尔法形状主要是一个理论概念。从点构造曲面的最流行的算法之一是ball-pivoting ，这将生成特定 alpha 形状的表面。
Strictly speaking, your result B is correct, and A is a "trimmed down" version without edges longer than a certain threshold.
But: check out alpha shapes. They generalize the concept to fit both your results! They simply become the results with different alpha values.
However, alpha shapes are mostly a theoretical concept. One of the most popular algorithms that constructs surfaces from points is ball-pivoting, which will generate the surface of a specific alpha-shape.
Delaunay 三角剖分相当于计算点的凸包
来源： http://www.exaflop.org/docs/cgafaq/cga6.html#Subject 6.01：我在哪里可以获得源代码Voronoi/Delaunay 三角剖分？
The Delaunay triangulation is equivalent to computing the convex hull of the points
SOURCE: http://www.exaflop.org/docs/cgafaq/cga6.html#Subject 6.01: Where can I get source for Voronoi/Delaunay triangulation?