如何粗粒xy坐标

Question

我有一个不均匀采样的gp坐标数组。这似乎很明显，但我想把它投射到网格上。这是我的上下文脚本：

import numpy as np
from matplotlib.mlab import griddata

gps_track = np.array([[0,0],[1.2,2.3],[1.9,3],[3.2,4.3],[4,2.9],[6.5,3.1]])
x = gps_track[:,0]
y = gps_track[:,1]

# define grid
binsize = 1
xmin, xmax = x.min(), x.max()
ymin, ymax = y.min(), y.max()
xi = np.arange(xmin, xmax+binsize, binsize)
yi = np.arange(ymin, ymax+binsize, binsize)

在给定（x，y）原始坐标的情况下，如何从这里开始在（xi，yi）网格上插入（xnew，ynew）值？

# grid the data
xnew, ynew = grid(x, y, xi, yi)

我以为我会使用与matplotlib函数griddata类似的东西：

zi = griddata(x, y, z, xi, yi)

我做不到的;我想网格坐标本身，而不是值z = f（x，y）。你知道有任何快速解决方案吗？

编辑： 这真的有帮助。你们好棒！为了更准确地按照我的要求，我已经拍摄了你生成的情节并标记了我希望用空心圆圈得到的（xnew，ynew）样本。它们落在（xi，yi）网格上。

Answer 1

import numpy as np
import matplotlib.pyplot as plt
import scipy.interpolate as interpolate

gps_track = np.array([[0,0],[1.2,2.3],[1.9,3],[3.2,4.3],[4,2.9],[6.5,3.1]])
x = gps_track[:,0]
y = gps_track[:,1]

binsize = 1.0
xmin, xmax = x.min(), x.max()
ymin, ymax = y.min(), y.max()
xi = np.arange(xmin, xmax+binsize, binsize)
yi = np.arange(ymin, ymax+binsize, binsize)

N = 1000
tckp, u = interpolate.splprep([x, y], s=0, k=2, nest=-1)
xx, yy = interpolate.splev(np.linspace(0, 1, N), tckp)

# find integer indices where the xx fall between xi values
x_idx = np.searchsorted(xi, xx)
# find where the x_idx indices change. This is where the curve crosses a grid line 
x_mask = np.diff(x_idx) != 0
# do the same for y
y_idx = np.searchsorted(yi, yy)
y_mask = np.diff(y_idx) != 0

fig, ax = plt.subplots()
line, = ax.plot(xx, yy)
ax.scatter(xx[x_mask], yy[x_mask], color='red')
ax.scatter(xx[y_mask], yy[y_mask], color='red')

# make sure the grid lines fall on xi and yi
ax.set_xticks(xi)
ax.set_yticks(yi)
ax.grid()
plt.show()

的产率

---

xi，yi定义您的网格。

xx，yy是插值路径上的点。

要在垂直网格线上找到点，请先使用np.searchsorted进行查找 索引（xi）其中 xx中的每个值（x数据）都适合排序的数组xi（网格）。

In [88]: x_idx = np.searchsorted(xi, xx)
In [89]: x_idx
Out[89]: 
array([0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
       1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
       3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
       4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,
       6, 6, 6, 6, 7, 7, 7, 7])

然后我们可以得出相邻值的差异：

In [91]: np.diff(x_idx)
Out[91]: 
array([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0,
       0, 0, 0, 1, 0, 0, 0])

如果值为非零，则表示路径已越过网格线。

In [93]: x_mask = (np.diff(x_idx) != 0)

In [94]: x_mask
Out[94]: 
array([ True, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False,  True, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False,  True, False, False, False, False, False, False,
       False, False, False, False, False, False, False,  True, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
        True, False, False, False, False, False, False, False, False,
       False, False, False, False,  True, False, False, False, False,
       False, False, False, False, False,  True, False, False, False], dtype=bool)

然后可以使用x_mask来查找插值点上的x值 最接近网格线的路径：

In [95]: xx[x_mask]
Out[95]: 
array([ -6.93660834e-18,   9.65180188e-01,   1.95810449e+00,
         2.94969940e+00,   3.94167195e+00,   4.92607812e+00,
         5.99593850e+00])

当然我们可以类似地找到相应的y值：

In [96]: yy[x_mask]
Out[96]: 
array([ 0.        ,  2.02032307,  3.06460807,  4.25374305,  2.97366674,
        2.4770819 ,  2.79951527])

上面我已经走过了用于找到垂直网格线交叉点的步骤;在代码中对水平网格线也是如此。

Answer 2

我希望下面的修订有助于...我添加了所需的评论。

from __future__ import division
import numpy as np
from matplotlib.mlab import griddata
from scipy.interpolate import InterpolatedUnivariateSpline 
from matplotlib import pyplot as plt

# Data
gps_track = np.array([[0,0],[1.2,2.3],[1.9,3],[3.2,4.3],[4,2.9],[6.5,3.1]])
x = gps_track[:,0]
y = gps_track[:,1]

# Define grid
binsize = 1
xmin, xmax = x.min(), x.max()
ymin, ymax = y.min(), y.max()
xi = np.arange(xmin, xmax+binsize, binsize)
yi = np.arange(ymin, ymax+binsize, binsize)

# Get mean values 
x_mean = np.mean(x)
y_mean = np.mean(y)

# Create the fit data for spline
x_fit_data = x/x_mean
y_fit_data = y/y_mean

# A spline of 3. degree
factor = 1000 # arbitrary sampling factor
g = np.arange(0, len(x))
fx = InterpolatedUnivariateSpline(g, x_fit_data, k=3)
fy = InterpolatedUnivariateSpline(g, y_fit_data, k=3)

# Get new data points
gg = np.linspace(0, len(x), len(x)*factor)
x_new = fx(gg) * x_mean
y_new = fy(gg) * y_mean

# Plot
fig = plt.figure()
plt.axis('equal') # optional. To set equal aspect ratio
ax = fig.add_subplot(111)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_xlim(xmin,xmax)
ax.set_ylim(ymin,ymax)
ax.plot(x_new, y_new)
ax.plot(x, y, 'ro') # if you also want to plot the sampling points
ax.grid()
plt.show()

我认为你应该将你的问题分成两部分：插值和绘图。