Geek Answers Handbook

Scipy ConvexHull and QHull: rank / size not maximum

I am trying to create a convex hull using the Scipy and ConvexHull libraries. As far as I know, he calls QHull.

The problem occurs when the points that I want to add do not have a “full dimension”. Example:

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

Has for output:

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

However, if I add extra points, so that the convex hull has full dimension:

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

then everything works. The difference between one example and another (I made many other examples, so I'm sure) is that the convex hull in the first case is one-dimensional in two-dimensional space, and in the second - 2-dimensional in two-dimensional space (i.e., full the size).

Any ideas? I thought to skip some qhull_options as the docs indicate, as mentioned in the answers, which:

QHullError Raised when Qhull detects an error condition, such as geometric degeneration, when resolution options are not enabled.

However, I read many options in QHull , and none of them seem to fix this problem. I tried some of them at random, with little success.

Any help would be helpful. I am working on a program that creates hundreds of these buildings, and some of them are not full-sized.

+4
source share
2 answers

The convex hull does not seem to support degenerate convex hulls.

The number of points must be at least the number of dimensions plus one in order to have a non-degenerate convex hull.

, 3 , : , .

docs , :

: QhullError , Qhull , , .

+4

, , :

>>> 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
>>>
+1

More articles:


All Articles