Python：调整坐标到重心

Question

我有一个python脚本，我从两个单独的文本文件中导入三角形元素的坐标和元素定义。

坐标文件如下所示：

id,x,y,
  1,  0,   0
  2,  0,   1
  3,  0,   2
  4,  1,   0
  5,  1,   1
  6,  1,   2
  7,  2,   0
  8,  2,   1
  9,  2,   2

元素文件如下所示：

id, n1, n2, n3
 1, 1, 2, 4
 2, 1, 2, 5
 3, 2, 3, 5
 4, 3, 5, 6
 5, 5, 6, 8
 6, 6, 8, 9
 7, 5, 7, 8
 8, 4, 5, 7

在脚本中，当三角形元素的两条边位于同一位置时，我定义一个新元素（矩形）。我首先为每个三角形元素定义唯一的节点（因此元素不再共享相同的节点）然后我通过角落中的四个节点定义一个新元素。 见下图

这很好用，但是新定义的元素的厚度为零。而且我确实希望它们具有一种物理厚度。因此，我想调整三角形元素节点的坐标，并将它们稍微移动到元素的重心位置。

如何找到三角形单元的重心，然后在元素的重心方向上更改水平值为0.001，垂直距离为0.001的节点坐标？

我目前拥有的脚本如下：

    #!/usr/bin/env python


open("D://Documents//SkyDrive//afstuderen//99 EEM - Abaqus 6.11.2//scripting//_COORDINATEN.txt", "r")
import csv
import itertools

with open("_COORDINATEN.txt") as file:
    data = csv.reader(file)
    next(data)
    coords = []
    coords = ([[float(x) for x in line[1:]] for line in data])


open("D://Documents//SkyDrive//afstuderen//99 EEM - Abaqus 6.11.2//scripting//_ELEMENTEN.txt", "r")
import csv
import itertools

with open("_ELEMENTEN.txt") as file:
    data2 = csv.reader(file)
    next(data2)
    elems = []
    elems = ([[int(x)-1 for x in line[1:]] for line in data2])


#Flip the original elements if required
for i,elem in enumerate(elems):
    ecoords = [coords[e] for e in elem]

    a = [x2-x1 for x1,x2 in zip(ecoords[0],ecoords[1])]
    b = [x2-x1 for x1,x2 in zip(ecoords[1],ecoords[2])]

    n = a[0]*b[1]-a[1]*b[0]

    if n < 0:
        elems[i] = [ elem[0], elem[2], elem[1] ]

#bewerking elementen
newcoords = []
newelems  = []
for elem in elems:
    ecoords = [coords[e] for e in elem]
    newelem = range( len(newcoords), len(newcoords)+len(ecoords) )

    newcoords += ecoords
    newelems.append( newelem )

cohelems = []
for e,elem in enumerate(elems):
  for edge in [[0,1],[1,2],[2,0]]:

    eedge = [elem[i] for i in edge]

    for e2,elem2 in enumerate(elems[e+1:]):

      e2 += e+1

      for edge2 in [[0,1],[1,2],[2,0]]:

        eedge2 = [elem2[i] for i in edge2]

        if all([i in eedge2 for i in eedge]):

          newedge  = [newelems[e][i] for i in edge ]
          newedge += [newelems[e2][i] for i in edge2]

          cohelems.append( newedge[-1::-1] )

Answer 1

我不会尝试使其与您的变量名完全一致。相反，我将举例说明如何进行你想要的收缩。你应该能够将它应用到你自己的东西上。我正在使用Michael Mauderer链接的页面中的一个公式。

问题只是矢量代数。如果您不打算一般使用矢量类来表示点，那么至少有助于定义一些矢量操作：

def add_vectors(*points):
  new_x = 0.0
  new_y = 0.0
  for point in points:
    new_x += point[0]
    new_y += point[1]
  return [new_x, new_y]

def subtract_vectors(a, b):
  new_x = a[0] - b[0]
  new_y = a[1] - b[1]
  return [new_x, new_y]


def mul_by_scalar(vector, scalar):
  new_x = vector[0] * scalar
  new_y = vector[1] * scalar
  return [new_x, new_y]

通过这些，其余部分变得更容易：

triangle = [[0,0], [1,0], [1,1]]

# finding the center of mass:
#   CM = (1/3) * (a + b + c)
# CM:       position vector to the center of mass
# a, b, c:  position vectors to the corners

CM = mul_by_scalar(add_vectors(*triangle), 1.0/3)

# For every point of the triangle, find a vector that points towards its CM.
# Scale the vectors to 10% (in this instance).

point_to_CM_vectors = []
for point in triangle:
  point_to_CM_vectors.append(subtract_vectors(CM, point))

# Make a new triangle, contracted by 10%.

new_triangle = []
for point, motion in zip(triangle, point_to_CM_vectors):
  new_triangle.append(add_vectors(point, mul_by_scalar(motion, 0.10)))

您可以非常轻松地了解如何内联add_vectors，subtract_vectors和mul_by_scalar的功能来“手动”执行操作，但您将不断重复自己代码会令人困惑。