英文:
How to color 3D BSplines based on weights
问题
给定一个包含记录的三轴加速度值的数据框，用于确定位置向量。在应用BSpline之后，有一条看起来相当平滑的曲线。
作为下一步，我想使用不同的颜色显示加速度的程度。
对此，https://stackoverflow.com/questions/42215777/matplotlib-line-color-in-3d 提供了一个很好的基础，尽管结果有点混乱，我无法确定根本原因：
这是CSV中的加速度值记录：
,Counter,Acc.X,Acc.Y,Acc.Z
18,18,9.71,0.51,4.41
19,19,9.69,0.65,4.34
20,20,9.67,0.6,4.3
21,21,9.6,0.59,4.33
22,22,9.34,0.11,4.63
23,23,6.01,-2.75,8.43
24,24,0.58,-5.01,6.18
25,25,2.16,-2.19,0.8
26,26,7.42,-1.84,-4.85
27,27,12.56,-5.04,-8.95
28,28,14.78,-9.62,-8.07
29,29,10.82,-7.58,-5.8
30,30,11.05,-8.45,-3.82
以下是代码：
import pandas as pd
import numpy as np
from scipy.interpolate import splrep, BSpline
from mpl_toolkits import mplot3d
%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from mpl_toolkits.mplot3d.art3d import Line3DCollection
from enum import Enum
class axis(Enum):
X = 1
Y = 2
Z = 3
records = pd.read_csv(filepath_or_buffer='input.csv', index_col=0, sep=',')
i = range(0, len(records.index)-1)
x = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.X'].to_numpy()
y = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Y'].to_numpy()
z = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Z'].to_numpy()
ii = np.linspace(i.start, i.stop)
tckx0 = splrep(i, x, s=0)
tckx = splrep(i, x, s=50)
tcky = splrep(i, y, s=50)
tckz = splrep(i, z, s=50)
ax = plt.figure(figsize=(50, 50)).add_subplot(projection='3d')
ax.plot(BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii), 'o--', color='green')
plt.show()
结果如下图所示：
应用颜色，首先使用简单的样式，比如'magma'：
# Coloring
points = np.array([BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii)]).transpose().reshape(-1,1,3)
segs = np.concatenate([points[:-1],points[1:]],axis=1)
lc = Line3DCollection(segs, cmap=plt.get_cmap('magma'))
lc.set_array(ii)
fig = plt.figure(figsize=(50, 50))
ax = fig.add_subplot(111, projection='3d')
ax.add_collection3d(lc)
plt.show()
图像完全混乱：
我无法确定根本原因，你能帮我吗？
英文:
Given a Dataframe with recorded acceleration values on 3-axis that are used to determine position vectors. After applying BSpline, there is a smooth curve which looks quite well.
As a next step, I want to show also the extent of acceleration using different colors.
For that, https://stackoverflow.com/questions/42215777/matplotlib-line-color-in-3d gives a good base, although the result is somehow messy, and I cannot identify the root cause:
Here is the record of acceleration values in CSV:
,Counter,Acc.X,Acc.Y,Acc.Z
18,18,9.71,0.51,4.41
19,19,9.69,0.65,4.34
20,20,9.67,0.6,4.3
21,21,9.6,0.59,4.33
22,22,9.34,0.11,4.63
23,23,6.01,-2.75,8.43
24,24,0.58,-5.01,6.18
25,25,2.16,-2.19,0.8
26,26,7.42,-1.84,-4.85
27,27,12.56,-5.04,-8.95
28,28,14.78,-9.62,-8.07
29,29,10.82,-7.58,-5.8
30,30,11.05,-8.45,-3.82
And the code:
import pandas as pd
import numpy as np
from scipy.interpolate import splrep, BSpline
from mpl_toolkits import mplot3d
%matplotlib inline
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from mpl_toolkits.mplot3d.art3d import Line3DCollection
from enum import Enum
class axis(Enum):
X = 1
Y = 2
Z = 3
records = pd.read_csv(filepath_or_buffer='input.csv', index_col=0, sep=',')
i = range(0, len(records.index)-1)
x = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.X'].to_numpy()
y = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Y'].to_numpy()
z = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Z'].to_numpy()
ii = np.linspace(i.start, i.stop);
tckx0 = splrep(i, x, s=0)
tckx = splrep(i, x, s=50)
tcky = splrep(i, y, s=50)
tckz = splrep(i, z, s=50)
ax = plt.figure(figsize=(50, 50)).add_subplot(projection='3d')
ax.plot(BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii), 'o--', color='green')
plt.show()
It results the following figure:
Applying colors, firstly just a simple style such as 'magma':
# Coloring
points = np.array([BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii)]).transpose().reshape(-1,1,3)
segs = np.concatenate([points[:-1],points[1:]],axis=1)
lc = Line3DCollection(segs, cmap=plt.get_cmap('magma'))
lc.set_array(ii)
fig = plt.figure(figsize=(50, 50))
ax = fig.add_subplot(111, projection='3d')
ax.add_collection3d(lc)
plt.show()
The figure is completely messed:
I cannot identify the root cause, could you please help me?
答案1
得分: 0
我认为你正在插值错误的内容。
要插值一个3D曲线，你需要使用scipy的splprep（参见这个问题）。
要插值一个1D曲线，你需要使用scipy的splrep。
在以下代码中，我还绘制了初始的x, y, z数据，以便你可以将你的结果与我的结果进行比较。
from scipy.interpolate import splrep, BSpline, splev, splprep
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from mpl_toolkits.mplot3d.art3d import Line3DCollection
import numpy as np
from enum import Enum
class axis(Enum):
X = 1
Y = 2
Z = 3
from io import StringIO
import pandas as pd
mystr = StringIO("""Counter,Acc.X,Acc.Y,Acc.Z
18,18,9.71,0.51,4.41
19,19,9.69,0.65,4.34
20,20,9.67,0.6,4.3
21,21,9.6,0.59,4.33
22,22,9.34,0.11,4.63
23,23,6.01,-2.75,8.43
24,24,0.58,-5.01,6.18
25,25,2.16,-2.19,0.8
26,26,7.42,-1.84,-4.85
27,27,12.56,-5.04,-8.95
28,28,14.78,-9.62,-8.07
29,29,10.82,-7.58,-5.8
30,30,11.05,-8.45,-3.82
""")
records = pd.read_csv(mystr, sep=",")
i = range(0, len(records.index)-1)
x = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.X'].to_numpy()
y = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Y'].to_numpy()
z = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Z'].to_numpy()
ii = np.linspace(i.start, i.stop)
tckx0 = splrep(i, x, s=0)
tckx = splrep(i, x, s=50)
tcky = splrep(i, y, s=50)
tckz = splrep(i, z, s=50)
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.plot(x, y, z, 'ko', label="true data")
ax.plot(BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii),
color='green', label="your interpolation")
# 3D曲线的样条插值
tck, u = splprep([x, y, z], s=2)
ii = np.linspace(0, 1)
xs, ys, zs = splev(ii, tck)
# 1D曲线的样条插值
a_x = records["Acc.X"].to_numpy()[:-1]
a_y = records["Acc.Y"].to_numpy()[:-1]
a_z = records["Acc.Z"].to_numpy()[:-1]
# 根据加速度的大小着色
a = np.sqrt(a_x**2 + a_y**2 + a_z**2)
tcka = splrep(np.linspace(0, 1, len(a)), a, s=0)
parameter = splev(ii, tcka)
ax.plot(xs, ys, zs, 'r.', label="new interpolation")
def get_segments(x, y, z):
points = np.ma.array([x, y, z]).T.reshape(-1, 1, 3)
return np.ma.concatenate([points[:-1], points[1:]], axis=1)
line = Line3DCollection(get_segments(xs, ys, zs), cmap="magma", array=parameter)
ax.add_collection(line)
fig.colorbar(line, label="acceleration")
ax.legend()
plt.show()
<details>
<summary>英文:</summary>
I think you are interpolating the wrong things.
To interpolate a 3D curve you have to use scipy's `splprep` ([see this question](https://stackoverflow.com/questions/18962175/spline-interpolation-coefficients-of-a-line-curve-in-3d-space)).
To interpolate a 1D curve you have to use scipy's `splrep`.
In the following code I also plotted the initial `x, y, z` data so that you can compare your result with what I come up.
```py
from scipy.interpolate import splrep, BSpline, splev, splprep
from mpl_toolkits import mplot3d
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
from mpl_toolkits.mplot3d.art3d import Line3DCollection
import numpy as np
from enum import Enum
class axis(Enum):
X = 1
Y = 2
Z = 3
from io import StringIO
import pandas as pd
mystr = StringIO("""Counter,Acc.X,Acc.Y,Acc.Z
18,18,9.71,0.51,4.41
19,19,9.69,0.65,4.34
20,20,9.67,0.6,4.3
21,21,9.6,0.59,4.33
22,22,9.34,0.11,4.63
23,23,6.01,-2.75,8.43
24,24,0.58,-5.01,6.18
25,25,2.16,-2.19,0.8
26,26,7.42,-1.84,-4.85
27,27,12.56,-5.04,-8.95
28,28,14.78,-9.62,-8.07
29,29,10.82,-7.58,-5.8
30,30,11.05,-8.45,-3.82
""")
records = pd.read_csv(mystr, sep=",")
i = range(0, len(records.index)-1)
x = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.X'].to_numpy()
y = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Y'].to_numpy()
z = (records.iloc[1:].values-records.iloc[:-1]).loc[:,'Acc.Z'].to_numpy()
ii = np.linspace(i.start, i.stop);
tckx0 = splrep(i, x, s=0)
tckx = splrep(i, x, s=50)
tcky = splrep(i, y, s=50)
tckz = splrep(i, z, s=50)
fig = plt.figure()
ax = fig.add_subplot(projection='3d')
ax.plot(x, y, z, 'ko', label="true data")
ax.plot(BSpline(*tckx)(ii),BSpline(*tcky)(ii),BSpline(*tckz)(ii),
color='green', label="your interpolation")
# spline interpolation of a 3D curve
tck, u = splprep([x, y, z], s=2)
ii = np.linspace(0, 1)
xs, ys, zs = splev(ii, tck)
# spline interpolation of a 1D curve
a_x = records["Acc.X"].to_numpy()[:-1]
a_y = records["Acc.Y"].to_numpy()[:-1]
a_z = records["Acc.Z"].to_numpy()[:-1]
# color by magnitude of acceleration
a = np.sqrt(a_x**2 + a_y**2 + a_z**2)
tcka = splrep(np.linspace(0, 1, len(a)), a, s=0)
parameter = splev(ii, tcka)
ax.plot(xs, ys, zs, 'r.', label="new interpolation")
def get_segments(x, y, z):
points = np.ma.array([x, y, z]).T.reshape(-1, 1, 3)
return np.ma.concatenate([points[:-1], points[1:]], axis=1)
line = Line3DCollection(get_segments(xs, ys, zs), cmap="magma", array=parameter)
ax.add_collection(line)
fig.colorbar(line, label="acceleration")
ax.legend()
plt.show()
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