Matplotlib - 如何在极坐标中绘制流线? [英] Matplotlib - How to plot streamlines in polar coordinates?

问题描述

我一直试图在matplotlib 1.4.3中在极轴上绘制流线.streamplot 函数从 1.2.0 开始就已经存在，并且被文档认为是功能性和稳定的.这是一个小测试脚本:

I have been trying to plot streamlines on a polar axis in matplotlib 1.4.3. The streamplot function has been around since 1.2.0 and is considered functional and stable by the documentation. Here is a little test script:

from matplotlib import pyplot as plt
import numpy as np

# Define polar grid
r = np.arange(0,2001,50)
theta = np.arange(-np.pi, np.pi+np.pi/180, 2*np.pi/180)
r2D, theta2D = np.meshgrid(r, theta)
# Define some data
u = -np.sin(theta2D)
v = np.cos(theta2D)
# Set up axes
fig = plt.figure()
ax = fig.add_axes([0.1, 0.1, 0.8, 0.8], polar=True)
# Plot streamlines
ax.streamplot(r, theta, u, v, color='k', density=1, linewidth=1)

此脚本因以下回溯而失败:

This script fails with the following traceback:

Traceback (most recent call last):
  File "streamline_test.py", line 15, in <module>
    ax.streamplot(r, theta, u, v, color='k', density=1, linewidth=1)
  File "python2.7/site-packages/matplotlib/axes/_axes.py", line 4204, in streamplot
    zorder=zorder)
  File "python2.7/site-packages/matplotlib/streamplot.py", line 167, in streamplot
    axes.add_patch(p)
  File "python2.7/site-packages/matplotlib/axes/_base.py", line 1568, in add_patch
    self._update_patch_limits(p)
  File "python2.7/site-packages/matplotlib/axes/_base.py", line 1586, in _update_patch_limits
    vertices = patch.get_path().vertices
  File "python2.7/site-packages/matplotlib/patches.py", line 4033, in get_path
    _path, fillable = self.get_path_in_displaycoord()
  File "python2.7/site-packages/matplotlib/patches.py", line 4054, in get_path_in_displaycoord
    shrinkB=self.shrinkB * dpi_cor
  File "python2.7/site-packages/matplotlib/patches.py", line 2613, in __call__
    shrinked_path = self._shrink(clipped_path, shrinkA, shrinkB)
  File "python2.7/site-packages/matplotlib/patches.py", line 2586, in _shrink
    left, right = split_path_inout(path, insideA)
  File "python2.7/site-packages/matplotlib/bezier.py", line 246, in split_path_inout
    ctl_points, command = next(path_iter)
StopIteration

很明显，streamplot会永远迭代，并且必须在某个时刻停止.我还尝试了一组应用于极轴的规则间隔的笛卡尔点，但以同样的方式失败.使用笛卡尔坐标轴进行极坐标图绘制不是一种选择，因为我需要一个极坐标网格，但是这样的网格在笛卡尔坐标中不是规则间隔的，流图需要规则间隔的点.

Apparently streamplot is iterating forever and has to stop at some point. I have also tried a set of regularly-spaced cartesian points applied to the polar axis, but that fails in the same way. Making a polar plot using cartesian axes is not an option as I need a polar grid, but such a grid is not regularly-spaced in cartesian coordinates, and streamplot requires regularly-spaced points.

有人知道如何让matplotlib在极坐标中绘制流线吗?

Does anybody know how to get matplotlib to plot streamlines in polar coordinates?

推荐答案

您只需要切换径向和方位角坐标.考虑下图，以及用于生成它的代码.注意 streamplot() 的第三个参数中的除以半径，它将线速度转换为角速度:

You simply need to switch the radial and azimuthal coordinates. Consider the following figure, and the code used to generate it. Note the division by radius in the third argument to streamplot(), which converts linear velocity to angular velocity:

import math
import numpy
import matplotlib
from matplotlib import pyplot

pyplot.gcf().add_axes([0.1, 0.1, 0.8, 0.8], polar=True)

# coordinates
r = numpy.linspace(0, 1, 11)
p = numpy.linspace(-math.pi, math.pi, 361)
rg, pg = numpy.meshgrid(r, p)

def repeat(x):
  return numpy.full_like(r, x)

epsilon = 1e-8

# cylindrical components of horizontal unit vector
xr =  numpy.cos(pg)
xp = -numpy.sin(pg)
# cylindrical components of vertical unit vector
yr =  numpy.sin(pg)
yp =  numpy.cos(pg)

# starting points of streamlines
sx = numpy.transpose([
  numpy.hstack([repeat(-math.pi/2), repeat(math.pi/2)]),
  numpy.hstack([r, r])
])
sy = numpy.transpose([
  numpy.hstack([repeat(-math.pi+epsilon), repeat(0), repeat(math.pi-epsilon)]),
  numpy.hstack([r, r, r])
])

# streamlines
pyplot.streamplot(
  pg.transpose(), rg.transpose(), (xp/rg).transpose(), xr.transpose(),
  color='red', start_points=sx)
pyplot.streamplot(
  pg.transpose(), rg.transpose(), (yp/rg).transpose(), yr.transpose(),
  color='blue', start_points=sy)

pyplot.ylim(0, 1)
pyplot.annotate(
  matplotlib.__version__,
  (0, 0), (1, 0), 'axes fraction', 'axes fraction',
  ha='left', va='top')
pyplot.savefig('stream.png')

这篇关于Matplotlib - 如何在极坐标中绘制流线?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！