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    <p>You could use the <a href="http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm" rel="noreferrer">Ramer-Douglas-Peucker (RDP) algorithm</a> to simplify the path. Then you could compute the change in directions along each segment of the simplified path. The points corresponding to the greatest change in direction could be called the turning points:</p> <p>A Python implementation of the RDP algorithm can be found <a href="https://github.com/sebleier/RDP/" rel="noreferrer">on github</a>.</p> <pre><code>import matplotlib.pyplot as plt import numpy as np import os import rdp def angle(dir): """ Returns the angles between vectors. Parameters: dir is a 2D-array of shape (N,M) representing N vectors in M-dimensional space. The return value is a 1D-array of values of shape (N-1,), with each value between 0 and pi. 0 implies the vectors point in the same direction pi/2 implies the vectors are orthogonal pi implies the vectors point in opposite directions """ dir2 = dir[1:] dir1 = dir[:-1] return np.arccos((dir1*dir2).sum(axis=1)/( np.sqrt((dir1**2).sum(axis=1)*(dir2**2).sum(axis=1)))) tolerance = 70 min_angle = np.pi*0.22 filename = os.path.expanduser('~/tmp/bla.data') points = np.genfromtxt(filename).T print(len(points)) x, y = points.T # Use the Ramer-Douglas-Peucker algorithm to simplify the path # http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_algorithm # Python implementation: https://github.com/sebleier/RDP/ simplified = np.array(rdp.rdp(points.tolist(), tolerance)) print(len(simplified)) sx, sy = simplified.T # compute the direction vectors on the simplified curve directions = np.diff(simplified, axis=0) theta = angle(directions) # Select the index of the points with the greatest theta # Large theta is associated with greatest change in direction. idx = np.where(theta&gt;min_angle)[0]+1 fig = plt.figure() ax =fig.add_subplot(111) ax.plot(x, y, 'b-', label='original path') ax.plot(sx, sy, 'g--', label='simplified path') ax.plot(sx[idx], sy[idx], 'ro', markersize = 10, label='turning points') ax.invert_yaxis() plt.legend(loc='best') plt.show() </code></pre> <p><img src="https://i.stack.imgur.com/yiExE.png" alt="enter image description here"></p> <p>Two parameters were used above:</p> <ol> <li>The RDP algorithm takes one parameter, the <code>tolerance</code>, which represents the maximum distance the simplified path can stray from the original path. The larger the <code>tolerance</code>, the cruder the simplified path.</li> <li>The other parameter is the <code>min_angle</code> which defines what is considered a turning point. (I'm taking a turning point to be any point on the original path, whose angle between the entering and exiting vectors on the simplified path is greater than <code>min_angle</code>).</li> </ol>
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    1. POcalculate turning points / pivot points in trajectory (path)
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    1. POcalculate turning points / pivot points in trajectory (path)
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    1. COThis seems like what I was trying to achieve with the convex hull approach, as I kinda had quick-hull in mind. +1 and will have to remember this one. My only issue is that it should probably be based on a minimum angle to be considered a turn instead of number of points.
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    2. CO@MC: Excellent idea. Thank you. (The change has been made.)
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