[英]Python: adjust coordinates to centre of gravity
我有一个python脚本,在其中导入三角形元素的坐标以及来自两个单独文本文件的元素定义。
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,当三角形元素的两个边在同一位置时,我定义了一个新元素(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),然后通过角落中的四个节点定义一个新元素。 见下图
这很好,但是新定义的元素的厚度为零。 而且我确实希望它们具有实际的厚度。 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。
如何找到三角形元素的重心,然后沿元素的重心方向将节点的坐标更改为水平方向的值0.001和垂直方向的值0.001?
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] )
我不会尝试使其与您的变量名完全对应。 相反,我将给出一个有关如何进行所需收缩的一般示例。 您应该能够将其应用于自己的东西。 我正在使用Michael Mauderer链接的页面上的公式之一。
问题只是矢量代数。 如果您一般不打算对这些点使用向量类,则至少有助于定义一些向量操作:
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]
有了这些,剩下的就变得容易一些了:
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)))
您可以很容易地看到如何内联add_vectors
, subtract_vectors
和mul_by_scalar
以“手动”执行操作,但是您将不断重复自己,并且代码将令人困惑。
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