पाइथन

Question

में 3 डी वक्र के लिए टुकड़े की क्यूबिक इंटरपोलेशन को आकार-संरक्षित करना मेरे पास 3 डी स्पेस में वक्र है। मैं मैटलैब में पचिप के समान एक आकार-संरक्षित टुकड़े की क्यूबिक इंटरपोलेशन का उपयोग करना चाहता हूं। मैंने scipy.interpolate में प्रदान किए गए कार्यों का शोध किया, उदाहरण के लिए interp2d, लेकिन फ़ंक्शंस कुछ वक्र संरचनाओं के लिए काम करते हैं, न कि मेरे पास डेटा पॉइंट्स। इसे कैसे करना है इसके बारे में कोई विचार?

x,y,z 
0,0,0 
0,0,98.43 
0,0,196.85 
0,0,295.28 
0,0,393.7 
0,0,492.13 
0,0,590.55 
0,0,656.17 
0,0,688.98 
0,0,787.4 
0,0,885.83 
0,0,984.25 
0,0,1082.68 
0,0,1181.1 
0,0,1227.3 
0,0,1279.53 
0,0,1377.95 
0,0,1476.38 
0,0,1574.8 
0,0,1673.23 
0,0,1771.65 
0,0,1870.08 
0,0,1968.5 
0,0,2066.93 
0,0,2158.79 
0,0,2165.35 
0,0,2263.78 
0,0,2362.2 
0,0,2460.63 
0,0,2559.06 
0,0,2647.64 
-0.016,0.014,2657.48 
-1.926,1.744,2755.868 
-7.014,6.351,2854.041 
-15.274,13.83,2951.83 
-26.685,24.163,3049.031 
-41.231,37.333,3145.477 
-58.879,53.314,3240.966 
-79.6,72.076,3335.335 
-103.351,93.581,3428.386 
-130.09,117.793,3519.96 
-159.761,144.66,3609.864 
-192.315,174.136,3697.945 
-227.682,206.16,3784.018 
-254.441,230.39,3843.779 
-265.686,240.572,3868.036 
-304.369,275.598,3951.483 
-343.055,310.627,4034.938 
-358.167,324.311,4067.538 
-381.737,345.653,4118.384 
-420.424,380.683,4201.84 
-459.106,415.708,4285.286 
-497.793,450.738,4368.741 
-505.543,457.756,4385.461 
-509.077,460.955,4393.084 
-536.475,485.764,4452.188 
-575.162,520.793,4535.643 
-613.844,555.819,4619.09 
-624.393,565.371,4641.847 
-652.22,591.897,4702.235 
-689.427,631.754,4784.174 
-725.343,675.459,4864.702 
-759.909,722.939,4943.682 
-793.051,774.087,5020.95 
-809.609,801.943,5060.188 
-820.151,820.202,5085.314 
-824.889,828.407,5096.606 
-830.696,838.466,5110.448 
-846.896,867.72,5150.399 
-855.384,883.717,5172.081 
-884.958,939.456,5247.626 
-914.53,995.188,5323.163 
-944.104,1050.927,5398.708 
-973.675,1106.659,5474.246 
-1003.249,1162.398,5549.791 
-1032.821,1218.13,5625.328 
-1062.395,1273.869,5700.873 
-1091.966,1329.601,5776.411 
-1121.54,1385.34,5851.956 
-1151.112,1441.072,5927.493 
-1180.686,1496.811,6003.038 
-1210.257,1552.543,6078.576 
-1239.831,1608.282,6154.121 
-1269.403,1664.015,6229.658 
-1281.875,1687.521,6261.517 
-1298.67,1720.451,6304.797 
-1317.209,1760.009,6353.528 
-1326.229,1780.608,6377.639 
-1351.851,1844.711,6447.786 
-1375.462,1912.567,6515.035 
-1379.125,1923.997,6525.735 
-1397.002,1984.002,6579.217 
-1416.406,2058.808,6640.141 
-1433.629,2136.794,6697.655 
-1448.619,2217.744,6751.587 
-1453.008,2244.679,6768.334 
-1461.337,2301.426,6801.784 
-1471.745,2387.628,6848.122 
-1479.813,2476.093,6890.468 
-1485.519,2566.597,6928.713 
-1488.852,2658.874,6962.744 
-1489.801,2752.688,6992.481 
-1488.358,2847.765,7017.828 
-1484.534,2943.865,7038.72 
-1478.344,3040.704,7055.099 
-1469.806,3137.966,7066.915 
-1469.799,3138.035,7066.922 
-1458.925,3235.574,7074.155 
-1445.742,3333.07,7076.775 
-1444.753,3339.757,7076.785 
-1438.72,3380.321,7076.785 
-1431.268,3430.42,7076.785 
-1416.787,3527.779,7076.785 
-1402.308,3625.128,7076.785 
-1401.554,3630.192,7076.785 
-1387.827,3722.487,7076.785 
-1373.347,3819.836,7076.785 
-1358.866,3917.195,7076.785 
-1357.872,3923.882,7076.785 
-1353.32,3954.485,7076.785 
-1344.387,4014.544,7076.785 
-1329.906,4111.903,7076.785 
-1315.427,4209.252,7076.785 
-1300.946,4306.611,7076.785 
-1286.466,4403.96,7076.785 
-1271.985,4501.319,7076.785 
-1257.504,4598.678,7076.785 
-1243.025,4696.027,7076.785 
-1228.544,4793.386,7076.785 
-1214.065,4890.735,7076.785 
-1199.584,4988.094,7076.785 
-1185.104,5085.443,7076.785 
-1170.623,5182.802,7076.785 
-1156.144,5280.151,7076.785 
-1141.663,5377.51,7076.785 
-1127.183,5474.859,7076.785 
-1112.703,5572.218,7076.785 
-1098.223,5669.567,7076.785 
-1083.742,5766.926,7076.785 
-1069.263,5864.275,7076.785 
-1054.782,5961.634,7076.785 
-1040.302,6058.983,7076.785 
-1025.821,6156.342,7076.785 
-1011.342,6253.692,7076.785 
-996.861,6351.05,7076.785 
-982.382,6448.4,7076.785 
-967.901,6545.759,7076.785 
-953.421,6643.108,7076.785 
-938.94,6740.467,7076.785 
-924.461,6837.816,7076.785 
-909.98,6935.175,7076.785 
-895.499,7032.534,7076.785 
-895.234,7034.314,7076.785 
-883.075,7130.158,7076.785 
-874.925,7228.243,7076.785 
-871.062,7326.579,7076.785 
-871.491,7425,7076.785 
-876.213,7523.299,7076.785 
-885.218,7621.308,7076.785 
-898.489,7718.822,7076.785 
-916.003,7815.673,7076.785 
-937.722,7911.659,7076.785 
-963.61,8006.615,7076.785 
-993.613,8100.342,7076.785 
-1027.678,8192.681,7076.785 
-1065.735,8283.437,7076.785 
-1083.912,8323.221,7076.785 
-1107.12,8372.742,7076.785 
-1148.885,8461.861,7076.785 
-1190.655,8550.989,7076.785 
-1232.42,8640.108,7076.785 
-1274.19,8729.236,7076.785 
-1315.955,8818.354,7076.785 
-1357.724,8907.482,7076.785 
-1399.49,8996.601,7076.785 
-1441.259,9085.729,7076.785 
-1483.024,9174.848,7076.785 
-1486.296,9181.829,7076.785 
-1510.499,9231.861,7076.785 
-1526.189,9263.304,7076.785 
-1570.139,9351.377,7076.785 
-1614.085,9439.441,7076.785 
-1658.035,9527.514,7076.785 
-1701.98,9615.578,7076.785 
-1745.93,9703.651,7076.785 
-1789.876,9791.715,7076.785 
-1833.826,9879.788,7076.785 
-1877.771,9967.852,7076.785 
-1921.721,10055.925,7076.785 
-1965.667,10143.989,7076.785 
-2009.625,10232.059,7076.785 
-2053.585,10320.115,7076.785 
-2097.551,10408.18,7076.785 
-2141.512,10496.237,7076.785 
-2185.477,10584.302,7076.785 
-2229.438,10672.359,7076.785 
-2273.403,10760.424,7076.785 
-2317.364,10848.481,7076.785 
-2352.213,10918.285,7076.785 

Answer 1

आप शायद splprep() and splev(), इस तरह उपयोग करना चाहते हैं (टिप्पणी में बुनियादी explaination):

import scipy 
from scipy import interpolate 
import numpy as np 

#This is your data, but we're 'zooming' into just 5 data points 
#because it'll provide a better visually illustration 
#also we need to transpose to get the data in the right format 
data = data[100:105].transpose() 

#now we get all the knots and info about the interpolated spline 
tck, u= interpolate.splprep(data) 
#here we generate the new interpolated dataset, 
#increase the resolution by increasing the spacing, 500 in this example 
new = interpolate.splev(np.linspace(0,1,500), tck) 

#now lets plot it! 
from mpl_toolkits.mplot3d import Axes3D 
import matplotlib.pyplot as plt 
fig = plt.figure() 
ax = Axes3D(fig) 
ax.plot(data[0], data[1], data[2], label='originalpoints', lw =2, c='Dodgerblue') 
ax.plot(new[0], new[1], new[2], label='fit', lw =2, c='red') 
ax.legend() 
plt.savefig('junk.png') 
plt.show() 

का उत्पादन:

यहाँ डेटा अंक हैं

जो अच्छा और चिकना है, यह भी काम करता है फिन ई आपके पूर्ण पोस्ट किए गए डेटासेट के लिए।

Answer 2

मुझे एक ऐसे व्यक्ति से an email मिला जो Matlab के pchip() फ़ंक्शन के देशी-पायथन संस्करण की भी तलाश कर रहा था। उन्होंने his code संलग्न किया जो दुर्भाग्य से 'अनुलग्नक -001.बीबी' के रूप में डाउनलोड करना चाहता है। यदि आप फ़ाइल को सहेजते हैं और इसे pychip.py पर पुनर्नामित करते हैं तो आप पाएंगे कि यह वही है जो आप पूछ रहे हैं।

Answer 3

SciPy pchipscipy.interpolate में है --- लेकिन, उह, कोई दस्तावेज में यह सूची भूल गया:

import numpy as np 
import matplotlib.pyplot as plt 
from scipy.interpolate import pchip 
x = np.linspace(0, 1, 20) 
y = np.random.rand(20) 
xi = np.linspace(0, 1, 200) 
yi = pchip(x, y)(xi) 
plt.plot(x, y, '.', xi, yi) 

3-डी डेटा के लिए, सिर्फ 3 में से प्रत्येक को जोड़ अलग से समन्वय करता है।

Answer 4

यहां एक और समाधान है जो मैं चाहता था (आकार-संरक्षण)।
समस्या यह है कि अंक जोड़ने के लिए कोई स्पष्ट सूत्र या समीकरण नहीं है। इसका जवाब एक नया डेटा सेट बनाने में निहित है जो विभिन्न बिंदुओं के लिए आम है। यह नया डेटा सेट पथ (मानक) के साथ लंबाई है। फिर हम प्रत्येक सेट को इंटरपोल करने के लिए इंटरप 1 का उपयोग करते हैं।

import numpy as np 
import matplotlib as mpl 
from matplotlib import pyplot as plt 
from mpl_toolkits.mplot3d import Axes3D 

# read data from a file 
# as x, y , z 

# create a new array to hold the norm (distance along path) 
npts = len(x) 
s = np.zeros(npts, dtype=float) 
for j in range(1, npts): 
    dx = x[j] - x[j-1] 
    dy = y[j] - y[j-1] 
    dz = z[j] - z[j-1] 
    vec = np.array([dx, dy, dz]) 
    s[j] = s[j-1] + np.linalg.norm(vec) 

# create a new data with finer coords 
xvec = np.linspace(s[0], s[-1], 5000) 

# Call the Scipy cubic spline interpolator 
from scipy.interpolate import interpolate 

# Create new interpolation function for each axis against the norm 
f1 = interpolate.interp1d(s, x, kind='cubic') 
f2 = interpolate.interp1d(s, y, kind='cubic') 
f3 = interpolate.interp1d(s, z, kind='cubic') 

# create new fine data curve based on xvec 
xs = f1(xvec) 
ys = f2(xvec) 
zs = f3(xvec) 

# now let's plot to compare 
#1st, reverse z-axis for plotting 
z = z*-1 
zs = zs*-1 

dpi = 75 
fig = plt.figure(dpi=dpi, facecolor = '#617f8a') 
threeDPlot = fig.add_subplot(111, projection='3d') 
fig.subplots_adjust(left=0.03, bottom=0.02, right=0.97, top=0.98) 
mpl.rcParams['legend.fontsize'] = 10 

threeDPlot.scatter(x, y, z, color='r') # Original data as a scatter plot 
threeDPlot.plot3D(xs, ys, zs, label='Curve Fit', color='b', linewidth=1) 
threeDPlot.legend() 
plt.show() 

परिणाम दिखाया गया है कि वह नीचे आ गया है। नीली रेखा वक्र फिट डेटा है जबकि लाल बिंदु मूल डेटा सेट हैं। हालांकि, मैंने इस दृष्टिकोण के साथ एक बात ध्यान में रखी है, यह है कि यदि डेटा सेट लंबा है, तो interpolate.interp1d कुशल नहीं है और इसमें काफी समय लगता है।