类似于 Matlab 的 convhulln 的 Javascript 3D 凸包算法

Question

我一直在努力寻找一个用于 Javascript 的凸包库，它提供与 Matlab convhulln 函数相同的输出。

我正在将一些代码从 Matlab 转录到 Javascript，我需要找到构成一组顶点的凸包的三角形。 Matlab 使用 convhulln（利用 qhull 函数）计算一些 3D 点的凸包。在这种情况下，当我将相同的顶点传递给每个顶点时，Matlab convhulln 输出一组与 quickhull3d 不同的三角形面。有些面孔重合，但通常大多数不重合。它们唯一的相似之处是它们都输出相同数量的面（尽管面的实际顶点并不相同）。

http://www.mathworks.com/help/matlab/ref/convhulln.html

在 Javascript 中，我尝试了不同的库，每个库都给出不同的输出..

从 npm 我试过了：

quickhull3d - https://github.com/maurizzzio/quickhull3d

convex-hull

delaunay-triangulate

大多数其他算法都是为 2D 点设计的，所以我排除了它们。

任何想法、提示或反馈将不胜感激！谢谢！

这是我正在使用的顶点以及 MATlab 的 convhulln 和 quickhull3d 的结果。请注意，我使用排序算法从第一个顶点到最后一个顶点对它们进行排序。这不应该影响实际的三角形面，因为我在 MATlab 和 JS 代码中以完全相同的方式对它们进行排序。

这是两个船体的图。

注意孔。我已经与 quickhull3d 算法的开发人员交谈过（感谢您的回复！！），他建议可能是他使用的三角测量过程与 matlab 使用的不同。

vertices = [ 
  [ 0.9510565162951535, -0.3090169943749474, 0 ],
  [ 0.5877852522924731, -0.8090169943749475, 0 ],
  [ 6.123233995736766e-17, -1, 0 ],
  [ -0.5591929034707466, 0.8290375725550418, 0 ],
  [ -0.9510565162951535, -0.3090169943749475, 0 ],
  [ -0.9510565162951536, 0.3090169943749473, 0 ],
  [ -0.5877852522924732, 0.8090169943749473, 0 ],
  [ -1.8369701987210297e-16, 1, 0 ],
  [ 0.5877852522924729, 0.8090169943749476, 0 ],
  [ 0.9510565162951535, 0.3090169943749476, 0 ],
  [ 0.984807753012208, 0, -0.17364817766693033 ],
  [ 0.30432233187297814, -0.9366078308002486, -0.17364817766693033 ],
  [ -0.796726208379082, -0.5788554735638644, -0.17364817766693033 ],
  [ -0.7967262083790821, 0.5788554735638641, -0.17364817766693033 ],
  [ 0.3043223318729779, 0.9366078308002487, -0.17364817766693033 ],
  [ 0.5000000000000001, -0.5, 0.7071067811865475 ],
  [ -0.5, -0.5000000000000001, 0.7071067811865475 ],
  [ -0.5000000000000001, 0.5, 0.7071067811865475 ],
  [ 0.4999999999999999, 0.5000000000000001, 0.7071067811865475 ],
  [ 6.123233995736766e-17, 0, 1 ] 
]

来自 quickhull3d 的三角形： 暗淡 = 36x3

    trianglesqh = [ 
  [ 0, 1, 11 ],
  [ 0, 9, 18 ],
  [ 0, 10, 9 ],
  [ 0, 11, 10 ],
  [ 0, 15, 1 ],
  [ 0, 18, 15 ],
  [ 1, 2, 11 ],
  [ 1, 15, 2 ],
  [ 2, 12, 11 ],
  [ 2, 15, 16 ],
  [ 2, 16, 12 ],
  [ 3, 6, 17 ],
  [ 3, 7, 14 ],
  [ 3, 13, 6 ],
  [ 3, 14, 13 ],
  [ 3, 17, 7 ],
  [ 4, 5, 13 ],
  [ 4, 12, 16 ],
  [ 4, 13, 12 ],
  [ 4, 16, 17 ],
  [ 4, 17, 5 ],
  [ 5, 6, 13 ],
  [ 5, 17, 6 ],
  [ 7, 8, 14 ],
  [ 7, 17, 18 ],
  [ 7, 18, 8 ],
  [ 8, 9, 10 ],
  [ 8, 10, 14 ],
  [ 8, 18, 9 ],
  [ 10, 11, 12 ],
  [ 10, 12, 14 ],
  [ 12, 13, 14 ],
  [ 15, 18, 19 ],
  [ 15, 19, 16 ],
  [ 16, 19, 17 ],
  [ 17, 19, 18 ] 
]

来自 MATlab 的三角形： 暗淡 = 36x3

trianglesm = [
  [ 0, 1, 11 ],
  [ 0, 9, 18 ],
  [ 0, 10, 9 ],
  [ 0, 11, 10 ],
  [ 0, 15, 1 ],
  [ 0, 18, 15 ],
  [ 1, 2, 11 ],
  [ 1, 18, 2 ],
  [ 2, 3, 11 ],
  [ 2, 15, 16 ],
  [ 2, 16, 3 ],
  [ 3, 4, 12 ],
  [ 3, 12, 11 ],
  [ 3, 16, 4 ],
  [ 4, 5, 12 ],
  [ 4, 17, 5 ],
  [ 5, 8, 13 ],
  [ 5, 13, 12 ],
  [ 5, 16, 17 ],
  [ 5, 17, 6 ],
  [ 6, 7, 14 ],
  [ 6, 14, 13 ],
  [ 6, 17, 7 ],
  [ 7, 8, 14 ],
  [ 7, 17, 18 ],
  [ 7, 18, 8 ],
  [ 8, 9, 10 ],
  [ 8, 10, 14 ],
  [ 8, 18, 9 ],
  [ 10, 11, 14 ],
  [ 11, 12, 13 ],
  [ 11, 13, 14 ],
  [ 15, 18, 19 ],
  [ 15, 19, 16 ],
  [ 16, 19, 17 ],
  [ 17, 19, 18 ]
]

Answer 1

您可以尝试 Bowyer-Watson 算法，但使用外接球和四面体：https://en.m.wikipedia.org/wiki/Bowyer%E2%80%93Watson_algorithm。