问计算轨迹中的拐点/枢轴点(路径)

EN

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>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()

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

def first_derivative(x) :
    return x[2:] - x[0:-2]

def second_derivative(x) :
    return x[2:] - 2 * x[1:-1] + x[:-2]

def curvature(x, y) :
    x_1 = first_derivative(x)
    x_2 = second_derivative(x)
    y_1 = first_derivative(y)
    y_2 = second_derivative(y)
    return np.abs(x_1 * y_2 - y_1 * x_2) / np.sqrt((x_1**2 + y_1**2)**3)

def plot_turning_points(x, y, turning_points=10, smoothing_radius=3,
                        cluster_radius=10) :
    if smoothing_radius :
        weights = np.ones(2 * smoothing_radius + 1)
        new_x = scipy.ndimage.convolve1d(x, weights, mode='constant', cval=0.0)
        new_x = new_x[smoothing_radius:-smoothing_radius] / np.sum(weights)
        new_y = scipy.ndimage.convolve1d(y, weights, mode='constant', cval=0.0)
        new_y = new_y[smoothing_radius:-smoothing_radius] / np.sum(weights)
    else :
        new_x, new_y = x, y
    k = curvature(new_x, new_y)
    turn_point_idx = np.argsort(k)[::-1]
    t_points = []
    while len(t_points) < turning_points and len(turn_point_idx) > 0:
        t_points += [turn_point_idx[0]]
        idx = np.abs(turn_point_idx - turn_point_idx[0]) > cluster_radius
        turn_point_idx = turn_point_idx[idx]
    t_points = np.array(t_points)
    t_points += smoothing_radius + 1
    plt.plot(x,y, 'k-')
    plt.plot(new_x, new_y, 'r-')
    plt.plot(x[t_points], y[t_points], 'o')
    plt.show()

>>> x, y = np.genfromtxt('bla.data')
>>> plot_turning_points(x, y, turning_points=20, smoothing_radius=15,
...                     cluster_radius=75)

def convex_filter(points,k):
    new_points = []
    for pts in (points[i:i + k] for i in xrange(0, len(points), k)):
        hull = set(convex_hull(pts))
        for point in pts:
            if point in hull:
                new_points.append(point)
    return new_points

# How the points are obtained is a minor point, but they need to be in the right order.
x_coords = [float(x) for x in x.split()]
y_coords = [float(y) for y in y.split()]
points = zip(x_coords,y_coords)

k = 10

prev_length = 0
new_points = points

# Filter using the convex hull until no more points are removed
while len(new_points) != prev_length:
    prev_length = len(new_points)
    new_points = convex_filter(new_points,k)