Question

我有一套K层面标准病媒,而(K-1)-Simplex则对这些病媒作了界定。我想将这一简单因素分成几个小节,这些小节将最初的简单轴线分为Barycentric子。

例如,在K = 3时,简单x的三vert分别为[1,00]、[0,1,0]和[0,1]。如果你用 b子子子子子把 this子 sub在est子里,那么你可以做到如下:

Find the mid point of each edge: [1/2, 1/2, 0], [1/2, 0, 1/2],[0, 1/2, 1/2]
Find the barycentric point: [1/3, 1/3, 1/3]

以下清单提供了每一次小节的所有vert点,这些小节将原来的简单X分开:

[[[1,0,0], [1/2, 1/2, 0] [1/3, 1/3, 1/3]]]
[[[1,0,0], [1/2, 0, 1/2] [1/3, 1/3, 1/3]]]
[[[0,1,0], [1/2, 1/2, 0] [1/3, 1/3, 1/3]]]
[[[0,1,0], [0, 1/2, 1/2] [1/3, 1/3, 1/3]]]
[[[0,0,1], [1/2, 0 ,1/2] [1/3, 1/3, 1/3]]]
[[[0,0,1], [0, 1/2, 1/2] [1/3, 1/3, 1/3]]]

在较低层面,这是一项容易完成的任务,然而,我想写出一种功能(通常是在平时,尽管我很灵活),它利用了原简单轴的vert和分裂程度,并将每一次简练清单清单及其vert弄。

我试图开发一个能够解决这一问题的算法,然而,我却不抱逻辑。每个次级项目将包含对(K-1)层面(例如,在此情况下是一点)、对面和表面的垂直。因此,我尝试了一种综合方法,但不能将其延伸到能够编入职能的N级。

Is anyone aware of a relevant package (or mathematical software?) that can help answer this question, or on how to write the logic into a python function.

Answer 1

You can try the following:

from itertools import permutations
import numpy as np
from sympy import Rational

k = 2 #dimension of the simplex

subdivision = []
for p in permutations(range(k+1)):
    n = len(p)
    fracs = np.array([Rational(1, i) for i in range(1, n+1)]).reshape(-1, 1)
    simplex = np.where(np.tile(p, (n, 1)) <= np.c_[:n], fracs, 0)
    subdivision.append(simplex)

for s in subdivision:
    print(*s)

它规定:

[1 0 0] [1/2 1/2 0] [1/3 1/3 1/3]
[1 0 0] [1/2 0 1/2] [1/3 1/3 1/3]
[0 1 0] [1/2 1/2 0] [1/3 1/3 1/3]
[0 0 1] [1/2 0 1/2] [1/3 1/3 1/3]
[0 1 0] [0 1/2 1/2] [1/3 1/3 1/3]
[0 0 1] [0 1/2 1/2] [1/3 1/3 1/3]

该法典将适用于任何单位,但既然一千imp(k+1)的血压子分层已经! 问题k的简单化,并不现实地将它们归为大的k价值。

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