如何将单纯形添加到 scipy Delaunay 三角剖分对象 [英] How to add simplices to a scipy Delaunay triangulation object

问题描述

我已经有一个由 scipy.spatial.Delaunay() 对象三角剖分的矩形.我设法拉伸和弯曲它，使它看起来像沿着一条线切割的环.下面是一些代码来制作具有相同拓扑的东西:

I already have a rectangle triangulated by a scipy.spatial.Delaunay() object. I manage to stretch and curve it around so that it looks like an annulus cut along a line. Here is some code to make something with the same topology:

from scipy.spatial import Delaunay

NR = 22
NTheta = 36

Rin = 1
Rout = 3
alphaFactor = 33/64
alpha = np.pi/alphaFactor # opening angle of wedge

u=np.linspace(pi/2, pi/2 + alpha, NTheta)
v=np.linspace(Rin, Rout, NR)
u,v=np.meshgrid(u,v)
u=u.flatten()
v=v.flatten()

#evaluate the parameterization at the flattened u and v
x=v*np.cos(u)
y=v*np.sin(u)

#define 2D points, as input data for the Delaunay triangulation of U
points2D=np.vstack([u,v]).T
xy0 = np.vstack([x,y]).T
triLattice = Delaunay(points2D) #triangulate the rectangle U
triSimplices = triLattice.simplices
plt.figure()
plt.triplot(x, y, triSimplices, linewidth=0.5)

从这个拓扑开始，我现在想把两个开放的边连接起来，做一个封闭的环(改变拓扑，就是这样).如何手动将新三角形添加到现有三角剖分中?

Starting from this topology, I now want to join up the two open edges, and make a closed annulus (change the topology, that is). How do I manually add new triangles to the existing triangulation?

推荐答案

解决方案是合并间隙周围的点.这是通过跟踪相应点的索引来做到这一点的一种方法:

A solution is to merge the points around the gap. Here is a way to do this, by keeping track of the indexes of the corresponding points:

import matplotlib.pylab as plt
from scipy.spatial import Delaunay
import numpy as np

NR = 4
NTheta = 16

Rin = 1
Rout = 3
alphaFactor = 33/64  # -- set to .5 to close the gap
alpha = np.pi/alphaFactor  # opening angle of wedge

u = np.linspace(np.pi/2, np.pi/2 + alpha, NTheta)
v = np.linspace(Rin, Rout, NR)
u_grid, v_grid = np.meshgrid(u, v)
u = u_grid.flatten()
v = v_grid.flatten()

# Get the indexes of the points on the first and last columns:
idx_grid_first = (np.arange(u_grid.shape[0]),
                  np.zeros(u_grid.shape[0], dtype=int))

idx_grid_last = (np.arange(u_grid.shape[0]),
                 (u_grid.shape[1]-1)*np.ones(u_grid.shape[0], dtype=int))

# Convert these 2D indexes to 1D indexes, on the flatten array:
idx_flat_first = np.ravel_multi_index(idx_grid_first, u_grid.shape)
idx_flat_last = np.ravel_multi_index(idx_grid_last, u_grid.shape)

# Evaluate the parameterization at the flattened u and v
x = v * np.cos(u)
y = v * np.sin(u)

# Define 2D points, as input data for the Delaunay triangulation of U
points2D = np.vstack([u, v]).T
triLattice = Delaunay(points2D) # triangulate the rectangle U
triSimplices = triLattice.simplices

# Replace the 'last' index by the corresponding 'first':
triSimplices_merged = triSimplices.copy()
for i_first, i_last in zip(idx_flat_first, idx_flat_last):
    triSimplices_merged[triSimplices == i_last] = i_first

# Graph
plt.figure(figsize=(7, 7))
plt.triplot(x, y, triSimplices, linewidth=0.5)
plt.triplot(x, y, triSimplices_merged, linewidth=0.5, color='k')
plt.axis('equal');

plt.plot(x[idx_flat_first], y[idx_flat_first], 'or', label='first')
plt.plot(x[idx_flat_last], y[idx_flat_last], 'ob', label='last')
plt.legend();

给出:

也许您必须调整 alphaFactor 的定义，以便间隙具有正确的大小.

Maybe you will have to adjust the definition of the alphaFactor so that the gap has the right size.

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