title: Extend line to smoothly connect with another line
body: <p>I have two curves that look like this:</p>
  
  <p><img src="https://i.stack.imgur.com/PeUem.png" alt="fig1"></p>
  
  <p>I'm looking for a way to smoothly <em>connect</em> the blue curve with the red one by extending the former (blue line) <strong>upwards and to the right</strong>, while leaving the latter (red line) untouched. The direction is important, I mention this because it looks as if it would be easier to continue the blue line to the left. I can't do this (it wouldn't make sense in my larger code) so it has to be upwards and to the right.</p>
  
  <p>Here's what I've managed to do so far (the section where the two lines get close is zoomed in):</p>
  
  <p><img src="https://i.stack.imgur.com/ABmLz.png" alt="fig2"></p>
  
  <p>Basically I'm interpolating a new curve using a sample of points from both curves (the black dots) The <code>MWE</code> code to obtain this plot is below.</p>
  
  <p>What I need to do now is find a way to trim the green line from the point where it meets the red line to the point where it meets the blue line and <em>extend</em> the blue line replacing the little last segment that is now no longer necessary.</p>
  
  <p>This is how the blue line should look after the changes above are applied (made by hand):</p>
  
  <p><img src="https://i.stack.imgur.com/dkPZ3.png" alt="fig3"></p>
  
  <p>where the trimmed section of the green line is now a part of the blue line. Notice that I have:</p>
  
  <ol>
  <li>discarded the extra points of the green line that extend beyond the intersection with the red line</li>
  <li>discarded the extra points of the green line that extend beyond the intersection with the blue line.</li>
  <li>attached the remaining section of the green line to the blue line after discarding the portion of the blue line that extended to the left beyond the intersection of the green and blue lines.</li>
  </ol>
  
  <p>Since I already have the interpolating curve (the green line), all I need is a way to:</p>
  
  <ol>
  <li>Trim it up to the points where it intersects the other two curves as explained above.</li>
  <li>Replace the last portion of the blue line with this trimmed portion of the new interpolated line.</li>
  </ol>
  
  <p>In this particular example I've used fixed lists to plot and perform the calculations, but I have several pairs of lines for which I need to perform a similar operation, so the solution would have to be general enough to contemplate cases with similarly shaped but different curves. How could I do this?</p>
  
  <p>I'm open to solutions making use of <code>numpy</code>, <code>scipy</code> or whatever is necessary.</p>
  
  <p>Here's the <code>MWE</code>:</p>
  
  <pre><code>import numpy as np
  import matplotlib.pyplot as plt
  
  # Red line data.
  x1 = [0.01, 0.04, 0.08, 0.11, 0.15, 0.18, 0.22, 0.25, 0.29, 0.32, 0.35, 0.38, 0.41, 0.44, 0.46, 0.49, 0.51, 0.54, 0.56, 0.58]
  y1 = [2.04, 2.14, 2.24, 2.34, 2.44, 2.54, 2.64, 2.74, 2.84, 2.94, 3.04, 3.14, 3.24, 3.34, 3.44, 3.54, 3.64, 3.74, 3.84, 3.94]
  
  # Blue line data.
  x2 = [0.4634, 0.4497, 0.4375, 0.4268, 0.4175, 0.4095, 0.4027, 0.3971, 0.3925, 0.389, 0.3865, 0.3848, 0.384, 0.3839, 0.3845, 0.3857, 0.3874, 0.3896, 0.3922, 0.3951, 0.3982, 0.4016, 0.405, 0.4085, 0.412, 0.4154, 0.4186, 0.4215, 0.4242, 0.4265, 0.4283, 0.4297, 0.4304, 0.4305, 0.4298, 0.4284, 0.4261, 0.4228, 0.4185, 0.4132, 0.4067, 0.399, 0.39, 0.3796, 0.3679, 0.3546, 0.3397, 0.3232, 0.305, 0.285]
  y2 = [1.0252, 1.0593, 1.0934, 1.1275, 1.1616, 1.1957, 1.2298, 1.2639, 1.298, 1.3321, 1.3662, 1.4003, 1.4344, 1.4685, 1.5026, 1.5367, 1.5708, 1.6049, 1.639, 1.6731, 1.7072, 1.7413, 1.7754, 1.8095, 1.8436, 1.8776, 1.9117, 1.9458, 1.9799, 2.014, 2.0481, 2.0822, 2.1163, 2.1504, 2.1845, 2.2186, 2.2527, 2.2868, 2.3209, 2.355, 2.3891, 2.4232, 2.4573, 2.4914, 2.5255, 2.5596, 2.5937, 2.6278, 2.6619, 2.696]
  
  x3, y3 = [], []
  
  # Store a small section of the blue line in these new lists: only those points
  # closer than 0.2 to the last point in this line.
  for indx,y2_i in enumerate(y2):
      if (y2[-1]-y2_i)&lt;=0.2:
          y3.append(y2_i)
          x3.append(x2[indx])
  
  # The same as above but for the red line: store only those points between
  # 0. and 0.4 in the y axis and with a larger x value than the last point in the
  # blue line.
  for indx,y1_i in enumerate(y1):
      if 0. &lt;(y1_i-y2[-1])&lt;=0.4 and x1[indx] &gt; x2[-1]:
          y3.append(y1_i)
          x3.append(x1[indx])
  
  # Find interpolating curve that joins both segments stored in x3,y3.
  poli_order = 3 # Order of the polynome.
  poli = np.polyfit(y3, x3, poli_order)
  y_pol = np.linspace(min(y3), max(y3), 50)
  p = np.poly1d(poli)
  x_pol = [p(i) for i in y_pol]
  
  plt.plot(x1,y1, 'r')
  plt.plot(x2,y2, 'b')
  plt.plot(x_pol,y_pol, 'g')
  plt.scatter(x3,y3,c='k')
  
  plt.show()
  </code></pre>