ConvexHull和QHull:秩/维不是最大的

Question

我正在尝试使用库Scipy和ConvexHull创建一个凸赫尔。据我所知，它叫QHull。

当我想要添加的点没有“完全维度”时，问题就出现了。示例：

from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)

民政事务总署产出：

Traceback (most recent call last):
  File "C:/folder/vertices_scipy2.py", line 5, in <module>
hull = ConvexHull(points)
  File "scipy\spatial\qhull.pyx", line 2230, in scipy.spatial.qhull.ConvexHull.__init__ (scipy\spatial\qhull.c:20317)
  File "scipy\spatial\qhull.pyx", line 328, in scipy.spatial.qhull._Qhull.__init__ (scipy\spatial\qhull.c:3639)
QhullError: Qhull error

然而，如果我加一个额外的点，使凸包有完整的尺寸：

from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,0],[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)

那么一切都正常。一个例子和另一个例子的区别(我已经做了很多其他的例子，所以我可以肯定)是，在第一种情况下，凸包在二维空间中是一维的，而在第二种情况下，在二维空间(即全维)中是二维的。

有什么想法吗？我认为从qhull_options开始传递一些文档就表明了这一点，正如在回答中提到的那样：

当Qhull遇到错误条件时引发QHullError，例如不启用解析选项时的几何简并。

然而，我读过许多QHull中的选项，似乎没有一个能解决这个问题。我随机尝试了其中的一些，但没有取得什么效果。

任何帮助都会有帮助。我正在做一个程序，创造数百个这样的船体，其中有些不是全维度的。

Answer 1

ConvexHull似乎不支持退化凸壳。

点的数目至少必须是维数加上一个具有非退化凸壳的数。

例如，在一个平面上，你需要3分才能有一个非退化的船体:3点的凸包是一个三角形，而退化的船体是两点之间的段。

事实上，文档提到：

引发:当Qhull遇到错误条件时引发QhullError，例如当未启用解析选项时的几何简并。

Answer 2

我不能评论，所以这不是真正的回答，但是您可以通过以下方法获得更好的错误描述：

>>> points2 = np.append([[0,0],[1,1]],[[2,2]],axis=0)
>>> hull = ConvexHull(points2)
QH6154 qhull precision error: initial facet 1 is coplanar with the interior point
ERRONEOUS FACET:
- f1
    - flags: bottom simplicial flipped
    - normal:   -0.7071   0.7071
    - offset:         -0
    - vertices: p2(v1) p0(v0)
    - neighboring facets: f2 f3

While executing:  | qhull i Qt
Options selected for Qhull 2012.1 2012/02/18:
  run-id 972186139  incidence  Qtriangulate  _pre-merge  _zero-centrum
  _max-width  2  Error-roundoff 1.7e-15  _one-merge 8.6e-15
  _near-inside 4.3e-14  Visible-distance 3.4e-15  U-coplanar-distance 3.4e-15
  Width-outside 6.9e-15  _wide-facet 2.1e-14

The input to qhull appears to be less than 2 dimensional, or a
computation has overflowed.

Qhull could not construct a clearly convex simplex from points:
- p1(v2):     1     1
- p2(v1):     2     2
- p0(v0):     0     0

The center point is coplanar with a facet, or a vertex is coplanar
with a neighboring facet.  The maximum round off error for
computing distances is 1.7e-15.  The center point, facets and distances
to the center point are as follows:

center point        1        1

facet p2 p0 distance=    0
facet p1 p0 distance=    0
facet p1 p2 distance=    0

These points either have a maximum or minimum x-coordinate, or
they maximize the determinant for k coordinates.  Trial points
are first selected from points that maximize a coordinate.

The min and max coordinates for each dimension are:
  0:         0         2  difference=    2
  1:         0         2  difference=    2

If the input should be full dimensional, you have several options that
may determine an initial simplex:
  - use 'QJ'  to joggle the input and make it full dimensional
  - use 'QbB' to scale the points to the unit cube
  - use 'QR0' to randomly rotate the input for different maximum points
  - use 'Qs'  to search all points for the initial simplex
  - use 'En'  to specify a maximum roundoff error less than 1.7e-15.
  - trace execution with 'T3' to see the determinant for each point.

If the input is lower dimensional:
  - use 'QJ' to joggle the input and make it full dimensional
  - use 'Qbk:0Bk:0' to delete coordinate k from the input.  You should
    pick the coordinate with the least range.  The hull will have the
    correct topology.
  - determine the flat containing the points, rotate the points
    into a coordinate plane, and delete the other coordinates.
  - add one or more points to make the input full dimensional.
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "qhull.pyx", line 2230, in scipy.spatial.qhull.ConvexHull.__init__ (scipy/spatial/qhull.c:19173)
  File "qhull.pyx", line 328, in scipy.spatial.qhull._Qhull.__init__ (scipy/spatial/qhull.c:3670)
scipy.spatial.qhull.QhullError: Qhull error
>>>