Scipy ConvexHull 和 QHull：rank/dimension 不是最大的
Scipy ConvexHull and QHull: rank/dimension is not maximal
我正在尝试使用库 Scipy 和 ConvexHull 创建一个 Convex Hull。据我所知，它调用QHull。
当我要添加的点没有'full dimension'时出现问题。示例：
from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)
具有输出：
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
但是，如果我添加一个额外的点，使凸包具有完整的维度：
from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,0],[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)
然后一切正常。一个例子和另一个例子的区别（我做过很多其他的例子，所以我很确定）是第一种情况下的凸包在2维space中是1维的，而在第二种情况下, 是 2-dimensional in 2-dimensional space （即全维）.
有什么想法吗？我想传递一些 qhull_options 因为 docs 表明，正如答案中提到的那样：
QHullError Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.
然而，我已经阅读了很多 options in QHull 和 none 似乎解决了这个问题。我随机尝试了其中一些，但收效甚微。
任何帮助都会有所帮助。我正在开发一个程序来创建数百个这样的外壳，其中一些不是全尺寸的。
ConvexHull好像不支持退化凸包
点数必须至少为维数加一才能具有非退化凸包。
例如在一个平面上，你需要 3 个点才能有一个非退化包：3 个点的凸包将是一个三角形，而退化包将是 2 个点之间的线段。
事实上 docs 提到：
Raises: QhullError Raised when Qhull encounters an error condition,
such as geometrical degeneracy when options to resolve are not
enabled.
我无法发表评论，所以这不是真正的答案，但您可以通过以下方式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
>>>
我正在尝试使用库 Scipy 和 ConvexHull 创建一个 Convex Hull。据我所知，它调用QHull。
当我要添加的点没有'full dimension'时出现问题。示例：
from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)
具有输出：
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
但是，如果我添加一个额外的点，使凸包具有完整的维度：
from scipy.spatial import ConvexHull
import numpy as np
points = np.append([[0,0],[0,2]],[[2,0]],axis=0)
hull = ConvexHull(points)
然后一切正常。一个例子和另一个例子的区别（我做过很多其他的例子，所以我很确定）是第一种情况下的凸包在2维space中是1维的，而在第二种情况下, 是 2-dimensional in 2-dimensional space （即全维）.
有什么想法吗？我想传递一些 qhull_options 因为 docs 表明，正如答案中提到的那样：
QHullError Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.
然而，我已经阅读了很多 options in QHull 和 none 似乎解决了这个问题。我随机尝试了其中一些，但收效甚微。
任何帮助都会有所帮助。我正在开发一个程序来创建数百个这样的外壳，其中一些不是全尺寸的。
ConvexHull好像不支持退化凸包
点数必须至少为维数加一才能具有非退化凸包。
例如在一个平面上，你需要 3 个点才能有一个非退化包：3 个点的凸包将是一个三角形，而退化包将是 2 个点之间的线段。
事实上 docs 提到：
Raises: QhullError Raised when Qhull encounters an error condition, such as geometrical degeneracy when options to resolve are not enabled.
我无法发表评论，所以这不是真正的答案，但您可以通过以下方式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
>>>