User:Travelling salesman/gpx reduce
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This is a python script that removes (almost) unnecessary points from gpx-files. Set your gps receiver to the highest point density available (e.g. 1s) and use this script on your gpx-files before osm-upload. The script yields highly optimized results.
The script must be saved to a file (gpx_reduce.py) and the executable flag should be set. Then it can be executed from the command line. For more documentation, type
./gpx_reduce.py --help
If the script produces an output that looks non-optimal, this might be because of the third dimension. Otherwise leave me a message.
Requirements
On a debian based linux distribution (such as Ubuntu) you can install these with:
sudo apt-get install python python-scipy python-lxml python-matplotlib
Algorithm
gpx_reduce finds the track that globally optimizes a given cost function under the restriction that no original point may be further away from the resulting track than a certain limit. Points can be deleted but will never be moved or inserted.
The cost function can be easily modified. In the standard setting it consists of the number of remaining points plus (normalized) squared distances to removed points, plus a penalty for large-angle kinks at the remaining trackpoints.
The number of possible tracks is huge and not all of them could be explored individually to find the optimum. Instead the a modified version of the Dijkstra algorithm is utilized. It successively finds the shortest route to each point and then only has to trace back to all possible predecessor points instead of routes. Therefore the best trace is found and the task is performed in a reasonable amount of time. However if the track is very long and offers many possibilities, it may still take several seconds to compute.
Points will never become separated beyond a certain limit (200m by default), since josm would not show lines between further separated points with default settings. There is an additional speed-dependent distance-limit that keeps points more evenly spaced.
Code
#!/usr/bin/env python
# -*- coding: utf8 -*-
'''
gpx_reduce v1.8: removes points from gpx-files to reduce filesize and
tries to keep introduced distortions to the track at a minimum.
Copyright (C) 2011,2012,2013,2015,2016,2017 travelling_salesman on OpenStreetMap
changelog: v1.2: clarity refractoring + speedup for identical points
v1.3: new track weighting functions, progress display
v1.4: new track weighting function, restructuring for memory saving
v1.5: algorithm speedup by roughly a factor of 2 by eliminating some cases.
v1.6: presets for train etc.
v1.7: introduced weighting function for elevation errors
v1.8: speed-dependent distance limit
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
'''
import datetime
import sys
import time
import pylab as pl
import scipy as sc
import numpy.linalg as la
from math import *
from lxml import etree
from optparse import OptionParser
parser = OptionParser('usage: %prog [options] input-file.gpx')
parser.add_option('-v', '--verbose', action='store', type='int',
dest='verbose', default=1, help='verbose=[0,1]')
parser.add_option('-p', '--plot', action='store_true', dest='plot',
default=False, help='Show a plot of the result at the end.')
parser.add_option('-d', '--dist', action='store', type='float', dest='max_dist',
default=0.5, help='Maximum distance of line from original points in meters')
parser.add_option('-o', '--out', action='store', type='string',
dest='ofname', default=None, help='Output file name')
parser.add_option('-m', '--maxsep', action='store', type='float', dest='max_sep',
default=200.0, help='Absolute maximum separation of points. No points will be deleted where the resulting distance would become greater than maxsep. Standard JOSM settings will not display points spaced more than 200m. -1 means no limit.')
parser.add_option('-n', '--maxsep0', action='store', type='float', dest='max_sep0',
default=4.0, help='Maximum separation of points at zero speed.')
parser.add_option('-t', '--maxseptime', action='store', type='float', dest='max_sep_time',
default=3.0, help='Maximum time separation of points, which will be added to maxsep0. Maximum allowed point separation will be min(m, n + t*v) where v is the speed in m/s.')
parser.add_option('-e', '--ele-weight', action='store', type='float',
dest='ele_weight', default=0.0,
help='Weighting of elevation errors vs. horizontal errors. Default is 0.')
parser.add_option('-b', '--bend', action='store', type='float', dest='bend',
default=1.0, help='Penalty value for large bending angles at each trackpoint. Larger values (1 or more) make the track smoother.')
parser.add_option('-w', '--weighting', action='store', type='string',
dest='weighting', default='exp',
help='''Weighting function to be minimized for track reduction:
pnum (number of points),
sqrdistsum (number of points plus sum of squared distances to leftout points),
sqrdistmax (number of points plus sum of squared distances to each maximally separated leftout point per new line segment),
sqrlength (number of points plus sum of squared new line segment lengths normalized by maxsep),
mix (number of points plus sum of squared distances to each maximally separated leftout point per new line segment weighted with corresponding segment length),
exp (number of points plus sum of squared distances to leftout points with exponential weighting of 1/2, 1/4, 1/8... from furthest to closest point). exp=standard''')
(options, args) = parser.parse_args()
if len(args) < 1:
parser.print_usage()
exit(2)
# use the WGS-84 ellipsoid
rE = 6356752.314245 # earth's radius
a = 6378137.0
b = 6356752.314245179
timeformat = '%Y-%m-%dT%H:%M:%SZ'
def distance(p1_, pm_, p2_, ele_weight=1.0):
# returns distance of pm from line between p1 and p2
p1, pm, p2 = sc.array(p1_), sc.array(pm_), sc.array(p2_)
h1, hm, h2 = la.norm(p1), la.norm(pm), la.norm(p2)
if ele_weight != 1.0 and min(h1, hm, h2) > 0.0:
hmean = (h1 + hm + h2) / 3.0
p1 *= (ele_weight + (1.0 - ele_weight) * hmean / h1)
pm *= (ele_weight + (1.0 - ele_weight) * hmean / hm)
p2 *= (ele_weight + (1.0 - ele_weight) * hmean / h2)
line = p2 - p1
linel = la.norm(line)
vm = pm - p1
if linel == 0.0:
return la.norm(vm)
linem = line / linel
position = pl.dot(vm, linem) / linel
if position < 0.0:
return la.norm(vm)
elif position > 1.0:
return la.norm(pm - p2)
else:
return la.norm(vm - line * position)
def rotate(x, y, phi):
return x*cos(phi) - y*sin(phi), x*sin(phi) + y*cos(phi)
def project_to_meters(lat, lon, latm, lonm):
# azimuthal map projection centered at average track coordinate
lon -= lonm
xyz = latlonele_to_xyz(lat, lon, 0.0)
zy = rotate(xyz[2], xyz[1], radians(90 - latm))
lat2 = atan2(zy[0], la.norm([zy[1], xyz[0]]))
lon2 = atan2(xyz[0], -zy[1])
x_meters = rE * sin(lon2) * (pi / 2.0 - lat2)
y_meters = -rE * cos(lon2) * (pi / 2.0 - lat2)
return x_meters, y_meters
def latlonele_to_xyz(lat, lon, ele):
s = sin(radians(lat))
c = cos(radians(lat))
r = ele + a * b / la.norm([s*a, c*b])
lon = radians(lon)
return r * c * sin(lon), r * c * (-cos(lon)), r * s
def xyz_to_latlonele(x, y, z):
r = la.norm([x, y, z])
if (r == 0):
return 0.0, 0.0, 0.0
lat = degrees(atan2(z, la.norm([x, y])))
lon = degrees(atan2(x, -y))
ele = r * (1.0 - a * b / la.norm([a*z, b*x, b*y]))
return lat, lon, ele
def reduced_track_indices(coordinate_list, timesteps=None):
# returns a list of indices of trackpoints that constitute the reduced track
# takes a list of kartesian coordinate tuples
m = len(coordinate_list)
if (m == 0): return []
if timesteps != None and len(timesteps) != len(coordinate_list):
timesteps = None
# number of dimensions
d = len(coordinate_list[0])
# remove identical entries (can speed up algorithm considerably)
original_indices = [0]
points = [{'p': coordinate_list[0], 'weight':1}]
if timesteps != None: points[0]['t'] = timesteps[0]
for i in range(1, m):
if False in [coordinate_list[i-1][j] == coordinate_list[i][j] for j in range(d)]:
original_indices.append(i)
points.append({'p': coordinate_list[i], 'weight':1})
if timesteps != None: points[-1]['t'] = timesteps[i]
else:
points[-1]['weight'] += 1
n = len(points)
# progress printing initialisations
progress_printed = False
progress = None
tprint = time.time()
# execute Dijkstra-like algorithm on points
points[0]['cost'] = 1.0
points[0]['prev'] = -1
for i2 in range(1, n):
penalties = {}
imin = None
costmin = float('inf')
for i1 in reversed(range(i2)):
p1 = sc.array(points[i1]['p'])
p2 = sc.array(points[i2]['p'])
seglength = la.norm(p2 - p1)
# estimate speed between p1 and p2
if timesteps != None:
dt = (points[i2]['t'] - points[i1]['t']).total_seconds()
v = seglength / max(0.1, dt)
else:
v = seglength / float(i2 - i1) # assume 1s time spacing
max_sep = options.max_sep0 + v * options.max_sep_time
if options.max_dist >= 0:
max_sep = min(max_sep, options.max_sep)
if (seglength >= max_sep and i1 != i2 - 1):
# point separation is too far
# but always accept direct predecessor i1 = i2 - 1
if (seglength >= max_sep + options.max_dist):
# no chance to find a valid earlier predecessor point
break
else:
continue
if points[i1]['cost'] + 1.0 > costmin:
# the possible predecessor i1 is already too bad.
continue
i1_i2_segment_valid = True
lower_i1_possible = True
distance_squaremax = 0.0
distance_squaresum = 0.0
distances_squared = []
# iterate all medium points between i1 and i2
for im in range(i1+1, i2):
pm = sc.array(points[im]['p'])
d = distance(p1, pm, p2, options.ele_weight)
if (d <= options.max_dist):
d_sq = (d / options.max_dist) ** 2
distance_squaremax = max(distance_squaremax, d_sq)
distance_squaresum += points[im]['weight'] * d_sq
distances_squared.append(d_sq)
else:
i1_i2_segment_valid = False
# check if connection to any further point i1 is impossible
d1 = pl.dot(p1 - p2, p1 - p2)
d2 = pl.dot(pm - p2, pm - p2)
dd = options.max_dist ** 2
d1d2 = pl.dot(p1 - p2, pm - p2)
# formula from cosines of point separation angle and cone-opening angles around points
if (d1 > dd and d2 > dd and (d1d2 + dd)**2 < (d2 - dd) * (d1 - dd)):
lower_i1_possible = False
break
if (lower_i1_possible == False):
break
if i1_i2_segment_valid:
if options.weighting == 'sqrdistmax':
penalties[i1] = distance_squaremax
elif options.weighting == 'sqrdistsum':
penalties[i1] = distance_squaresum
elif options.weighting == 'sqrlength':
penalties[i1] = (seglength / max_sep) ** 2
elif options.weighting == 'mix':
penalties[i1] = (distance_squaremax * (1.0 + seglength / max_sep))
elif options.weighting == 'exp':
penalties[i1] = 0.5 * sum([0.5**i * d for i, d in
enumerate(sorted(distances_squared, reverse=True))])
else:
penalties[i1] = 0.0
# add a penalty for kinks
if options.bend > 0.:
if points[i1]['prev'] != -1:
p0 = sc.array(points[points[i1]['prev']]['p'])
v0 = p1 - p0
v1 = p2 - p1
if la.norm(v0) > 0. and la.norm(v1) > 0.:
v0 /= la.norm(v0)
v1 /= la.norm(v1)
kink = (1.0 - sc.dot(v0, v1)) / 2.0
penalties[i1] += options.bend * kink
# find best predecessor
imin = None
costmin = float('inf')
for prev, penalty in penalties.iteritems():
# cost function is sum of points used (1.0) plus penalties
cost = points[prev]['cost'] + 1.0 + penalty
if cost < costmin:
imin = prev
costmin = cost
points[i2]['cost'] = costmin
points[i2]['prev'] = imin
# print progess
if options.verbose == 1 and (100 * i2) / n > progress and time.time() >= tprint + 1:
tprint = time.time()
progress = (100 * i2) / n
print '\r', progress, '%',
sys.stdout.flush()
progress_printed = True
if progress_printed:
print '\r',
# trace route backwards to collect final points
final_pnums = []
i = n-1
while i >= 0:
final_pnums = [i] + final_pnums
i = points[i]['prev']
return [original_indices[i] for i in final_pnums]
############################## main function #################################
for fname in args:
# initialisations
tracksegs_old = []
tracksegs_new = []
sumx, sumy, sumz = 0.0, 0.0, 0.0
# import xml data from files
print 'opening file', fname
infile = open(fname)
tree = etree.parse(infile)
infile.close()
gpx = tree.getroot()
if gpx.nsmap.has_key(None):
nsmap = '{' + gpx.nsmap[None] + '}'
else:
nsmap = ''
# extract data from xml
for trkseg in gpx.findall('.//' + nsmap + 'trkseg'):
trkpts = trkseg.findall(nsmap + 'trkpt')
n = len(trkpts)
# extract coordinate values
lats = [float(trkpt.get('lat')) for trkpt in trkpts]
lons = [float(trkpt.get('lon')) for trkpt in trkpts]
eles = [float(trkpt.find(nsmap + 'ele').text) for trkpt in trkpts]
try:
times = [datetime.datetime.strptime(trkpt.find(nsmap + 'time'
).text, timeformat) for trkpt in trkpts]
except Exception as e:
print e
times = None
# save original trackseg for plotting
if options.plot:
tracksegs_old.append([[lats[i], lons[i], eles[i]] for i in range(n)])
# calculate projected points to work on
coords = []
for i in range(n):
x, y, z = latlonele_to_xyz(lats[i], lons[i], eles[i])
coords.append((x, y, z))
sumx += x
sumy += y
sumz += z
# execute the reduction algorithm
final_pnums = reduced_track_indices(coords, times)
n_new = len(final_pnums)
print 'number of points:', n, '-', n - n_new, '=', n_new
# delete certain points from original data
delete_pnums = [i for i in range(n) if i not in final_pnums]
for i in reversed(delete_pnums):
del trkseg[trkseg.index(trkpts[i])]
# save reduced trackseg for plotting
if options.plot:
tracksegs_new.append([[float(trkpt.get('lat')),
float(trkpt.get('lon')), float(trkpt.find(nsmap + 'ele').text)]
for trkpt in trkseg.findall(nsmap + 'trkpt')])
# export data to file
if options.ofname != None:
ofname = options.ofname
elif fname.endswith('.gpx'):
ofname = fname[:-4] + '_reduced.gpx'
else:
ofname = fname + '_reduced.gpx'
outfile = open(ofname, 'w')
outfile.write(etree.tostring(tree, xml_declaration=True,
pretty_print=True, encoding='utf-8'))
outfile.close()
print 'modified copy written to', ofname
# plot result to screen
if options.plot:
latm, lonm, elesum = xyz_to_latlonele(sumx, sumy, sumz)
for trkseg in tracksegs_old:
y_old = []
x_old = []
for trkpt in trkseg:
xy = project_to_meters(trkpt[0], trkpt[1], latm, lonm)
x_old.append(xy[0])
y_old.append(xy[1])
pl.plot(x_old, y_old, 'r.-')
for trkseg in tracksegs_new:
y_new = []
x_new = []
for trkpt in trkseg:
xy = project_to_meters(trkpt[0], trkpt[1], latm, lonm)
x_new.append(xy[0])
y_new.append(xy[1])
pl.plot(x_new, y_new, 'b.-')
pl.grid()
pl.gca().set_aspect('equal')
pl.xlabel('x [m]')
pl.ylabel('y [m]')
pl.show()