polyline-ruler: Init from mapbox/cheap-ruler but more than that.
Install: pip install -U polyline-ruler
What is a ruler and what you can do with it¶
polyline-ruler originates from mapbox/cheap-ruler,
which provides fast approximations for common geodesic measurements:
A collection of very fast approximations to common geodesic measurements. Useful for performance-sensitive code that measures things on a city scale. Can be an order of magnitude faster than corresponding Turf methods.
The approximations are based on the WGS84 ellipsoid model of the Earth, projecting coordinates to a flat surface that approximates the ellipsoid around a certain latitude. For distances under 500 kilometers and not on the poles, the results are very precise — within 0.1% margin of error compared to Vincenti formulas, and usually much less for shorter distances.
Which means, you can quickly get distance between Shanghai and Suzhou, like this:
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from polyline_ruler import PolylineRuler
gps_shanghai = [121.4952, 31.2419, 0.0]
gps_suzhou = [120.6747, 31.3189, 0.0]
distance = PolylineRuler._distance(gps_shanghai, gps_suzhou, is_wgs84=True)
print(f'distance between Shanghai & Suzhou: {distance/1000:.1f}km (static method)')
ruler = PolylineRuler([gps_shanghai, gps_suzhou], is_wgs84=True)
print(f'or construct PolylineRuler first, then use member function: {ruler.length()/1e3:.1f}km (member function)')
from polyline_ruler import PolylineRuler
gps_shanghai = [121.4952, 31.2419, 0.0]
gps_suzhou = [120.6747, 31.3189, 0.0]
distance = PolylineRuler._distance(gps_shanghai, gps_suzhou, is_wgs84=True)
print(f'distance between Shanghai & Suzhou: {distance/1000:.1f}km (static method)')
ruler = PolylineRuler([gps_shanghai, gps_suzhou], is_wgs84=True)
print(f'or construct PolylineRuler first, then use member function: {ruler.length()/1e3:.1f}km (member function)')
distance between Shanghai & Suzhou: 78.6km (static method) or construct PolylineRuler first, then use member function: 78.6km (member function)
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from ipyleaflet import Map, GeoJSON, basemaps, WidgetControl
from ipywidgets import Layout
import numpy as np
def show_geojson(*, geojson, center = None, zoom=10, layout=None, basemap=basemaps.Esri.WorldStreetMap):
if center is None:
coords = np.array([np.array(f['geometry']['coordinates']).reshape(-1)[:2] for f in geojson['features']])
center = coords.mean(axis=0)
lon, lat = center[:2]
m = Map(
center=[lat, lon],
zoom=zoom,
scroll_wheel_zoom=True,
max_zoom=30,
basemap=basemap,
)
if layout is not None:
m.layout = layout
m.add_layer(GeoJSON(data=geojson))
return m
show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': [gps_shanghai, gps_suzhou]},
'properties': {'distance': distance},
}
]}, zoom=9)
from ipyleaflet import Map, GeoJSON, basemaps, WidgetControl
from ipywidgets import Layout
import numpy as np
def show_geojson(*, geojson, center = None, zoom=10, layout=None, basemap=basemaps.Esri.WorldStreetMap):
if center is None:
coords = np.array([np.array(f['geometry']['coordinates']).reshape(-1)[:2] for f in geojson['features']])
center = coords.mean(axis=0)
lon, lat = center[:2]
m = Map(
center=[lat, lon],
zoom=zoom,
scroll_wheel_zoom=True,
max_zoom=30,
basemap=basemap,
)
if layout is not None:
m.layout = layout
m.add_layer(GeoJSON(data=geojson))
return m
show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': [gps_shanghai, gps_suzhou]},
'properties': {'distance': distance},
}
]}, zoom=9)
Map(center=[31.2419, 121.4952], controls=(ZoomControl(options=['position', 'zoom_in_text', 'zoom_in_title', 'z…
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beauty_feet = [
[120.74827946135764, 31.448204795366777],
[120.74620885411491, 31.444671808351146],
[120.74783575980638, 31.442526715525744],
[120.74162393807808, 31.4339458532],
[120.73940543031875, 31.430664727645606],
[120.73629951945532, 31.423597297964193],
[120.73378521065985, 31.420568236465343],
[120.7287565930717, 31.417539077136567],
[120.72431957755157, 31.416529335620908],
[120.72313637341284, 31.41539336342359],
[120.71529764599455, 31.41362626821943],
[120.71204383461452, 31.40946084068321],
[120.7142623423739, 31.403022998034828],
[120.71056482944107, 31.392544780517753],
[120.71263543668385, 31.388125904492398],
[120.7144102428905, 31.38698958847614],
[120.71722035272069, 31.391787273682],
[120.71500184495983, 31.395322253295006],
[120.73511631531659, 31.419179883916897],
[120.74103233600874, 31.423723506736835],
[120.74443404790827, 31.424102132035657],
[120.74620885411491, 31.427888300943067],
[120.74931476497972, 31.428519314231295],
[120.7589282986047, 31.439119702465206],
[120.76144260740017, 31.444040903794075],
[120.75108957118778, 31.448330971010606]
]
show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': beauty_feet},
'properties': {'distance': distance},
}
]}, zoom=13, center=[120.735122, 31.4213], layout=Layout(width='80%', height='800px'))
beauty_feet = [
[120.74827946135764, 31.448204795366777],
[120.74620885411491, 31.444671808351146],
[120.74783575980638, 31.442526715525744],
[120.74162393807808, 31.4339458532],
[120.73940543031875, 31.430664727645606],
[120.73629951945532, 31.423597297964193],
[120.73378521065985, 31.420568236465343],
[120.7287565930717, 31.417539077136567],
[120.72431957755157, 31.416529335620908],
[120.72313637341284, 31.41539336342359],
[120.71529764599455, 31.41362626821943],
[120.71204383461452, 31.40946084068321],
[120.7142623423739, 31.403022998034828],
[120.71056482944107, 31.392544780517753],
[120.71263543668385, 31.388125904492398],
[120.7144102428905, 31.38698958847614],
[120.71722035272069, 31.391787273682],
[120.71500184495983, 31.395322253295006],
[120.73511631531659, 31.419179883916897],
[120.74103233600874, 31.423723506736835],
[120.74443404790827, 31.424102132035657],
[120.74620885411491, 31.427888300943067],
[120.74931476497972, 31.428519314231295],
[120.7589282986047, 31.439119702465206],
[120.76144260740017, 31.444040903794075],
[120.75108957118778, 31.448330971010606]
]
show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': beauty_feet},
'properties': {'distance': distance},
}
]}, zoom=13, center=[120.735122, 31.4213], layout=Layout(width='80%', height='800px'))
Map(center=[31.4213, 120.735122], controls=(ZoomControl(options=['position', 'zoom_in_text', 'zoom_in_title', …
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ruler = PolylineRuler(np.c_[beauty_feet, np.zeros(len(beauty_feet))], is_wgs84=True)
ruler = PolylineRuler(np.c_[beauty_feet, np.zeros(len(beauty_feet))], is_wgs84=True)
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# APIs:
# https://github.com/cubao/polyline-ruler/blob/master/src/polyline_ruler.hpp
from pprint import pprint
pprint({
'shape': ruler.polyline().shape,
'N': ruler.N(),
'is_wgs84': ruler.is_wgs84(),
'ranges': ruler.ranges(),
'ranges.shape': ruler.ranges().shape,
'length': ruler.length(),
})
# APIs:
# https://github.com/cubao/polyline-ruler/blob/master/src/polyline_ruler.hpp
from pprint import pprint
pprint({
'shape': ruler.polyline().shape,
'N': ruler.N(),
'is_wgs84': ruler.is_wgs84(),
'ranges': ruler.ranges(),
'ranges.shape': ruler.ranges().shape,
'length': ruler.length(),
})
{'N': 26,
'is_wgs84': True,
'length': 18042.970237876994,
'ranges': array([ 0. , 438.39371091, 722.09042528, 1841.84479117,
2262.34694775, 3099.73384723, 3511.94406245, 4096.13828784,
4532.50404611, 4701.36361104, 5471.80115866, 6027.64874941,
6771.95703552, 7985.75141991, 8513.75899485, 8724.31722722,
9319.5691501 , 9764.64655417, 13028.55274995, 13783.55654807,
14109.61893727, 14562.04879782, 14865.45712118, 16354.24121552,
16949.93602344, 18042.97023788]),
'ranges.shape': (26,),
'shape': (26, 3)}
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# range (mileage in meters) interpolation
help(ruler.range)
print(ruler.range(0)) # range of first point (always 0.0)
print(ruler.range(1)) # range of second point (length of first segment)
print(ruler.range(segment_index=0, t=0.5)) # middle of first segment
print(ruler.length(), ruler.range(ruler.N() - 1)) # length of polyline
# range (mileage in meters) interpolation
help(ruler.range)
print(ruler.range(0)) # range of first point (always 0.0)
print(ruler.range(1)) # range of second point (length of first segment)
print(ruler.range(segment_index=0, t=0.5)) # middle of first segment
print(ruler.length(), ruler.range(ruler.N() - 1)) # length of polyline
Help on method range in module polyline_ruler:
range(...) method of polyline_ruler.PolylineRuler instance
range(*args, **kwargs)
Overloaded function.
1. range(self: polyline_ruler.PolylineRuler, segment_index: int) -> float
2. range(self: polyline_ruler.PolylineRuler, *, segment_index: int, t: float) -> float
0.0
438.3937109139941
219.19685545699704
18042.970237876994 18042.970237876994
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# dirs in ENU
dirs = ruler.dirs()
print(dirs, dirs.shape)
dx = dirs[:, 0]
dy = dirs[:, 1]
heading = np.degrees(np.arctan2(dx, dy)) # https://en.wikipedia.org/wiki/Atan2
heading[heading < 0] += 360.0
# clockwise heading angle, north: 0, east:90, ...
print(heading)
# dirs in ENU
dirs = ruler.dirs()
print(dirs, dirs.shape)
dx = dirs[:, 0]
dy = dirs[:, 1]
heading = np.degrees(np.arctan2(dx, dy)) # https://en.wikipedia.org/wiki/Atan2
heading[heading < 0] += 360.0
# clockwise heading angle, north: 0, east:90, ...
print(heading)
[[-0.44895912 -0.8935523 0. ] [ 0.54510663 -0.83836673 0. ] [-0.52731437 -0.84967026 0. ] [-0.50149443 -0.86516087 0. ] [-0.35256258 -0.93578824 0. ] [-0.57979338 -0.81476355 0. ] [-0.81820992 -0.57491959 0. ] [-0.96652629 -0.25656759 0. ] [-0.66605087 -0.74590632 0. ] [-0.96712255 -0.25431077 0. ] [-0.55642936 -0.83089492 0. ] [ 0.28332277 -0.95902461 0. ] [-0.2895596 -0.95715999 0. ] [ 0.37276143 -0.92792722 0. ] [ 0.80122059 -0.59836909 0. ] [ 0.44874113 0.89366179 0. ] [-0.47380408 0.88063028 0. ] [ 0.58579319 0.81046057 0. ] [ 0.74482447 0.66726045 0. ] [ 0.99167693 0.12875117 0. ] [ 0.37288341 0.9278782 0. ] [ 0.97304939 0.23059679 0. ] [ 0.61379694 0.78946394 0. ] [ 0.40120671 0.91598754 0. ] [-0.9003417 0.43518367 0. ]] (25, 3) [206.676922 146.96804966 211.82417663 210.09891997 200.64413419 215.43601144 234.90599886 255.13350781 221.76299614 255.26725097 213.8092218 163.54138119 196.83159168 158.11397732 126.75318138 26.66294468 331.71848782 35.85904525 48.14402443 82.60256705 21.89355517 76.66779001 37.86455558 23.65363746 295.79698158]
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print(ruler.range(1))
print(ruler.dir(100)) # dir at range=100m, should be like first dir (heading=206.67922)
print(ruler.along(100)) # postion at range=100m
print(ruler.range(1))
print(ruler.dir(100)) # dir at range=100m, should be like first dir (heading=206.67922)
print(ruler.along(100)) # postion at range=100m
438.3937109139941 [-0.44895912 -0.8935523 0. ] [120.74780714 31.4473989 0. ]
arrows¶
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from polyline_ruler.tf import ecef2lla
'''
x
^
|
y |
<-----+
'''
def arrow():
return [
[0, -10, 0],
[200, -10, 0],
[200, -50, 0],
[300, 0, 0],
[200, 50, 0],
[200, 10, 0],
[0, 10, 0],
]
arrow = np.array(arrow()) * 2.0
import ipywidgets as widgets
slider = widgets.IntSlider(0, min=-1000, max=ruler.length() + 1000, step=10)
output = widgets.Output()
def show_map(range_meters):
T_ecef_frenet = ruler.local_frame(range_meters)
ecef = (T_ecef_frenet[:3, :3] @ arrow.T + T_ecef_frenet[:3, 3][:, np.newaxis]).T
llas = ecef2lla(ecef)
return show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': beauty_feet},
'properties': {'distance': distance},
},
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': llas.tolist()},
'properties': {},
},
]}, zoom=13, center=[120.735122, 31.4213], layout=Layout(width='80%', height='800px'))
def handle_slider_change(change):
with output:
output.clear_output()
display(show_map(range_meters=change.new))
slider.observe(handle_slider_change, names='value')
display(slider, output)
from polyline_ruler.tf import ecef2lla
'''
x
^
|
y |
<-----+
'''
def arrow():
return [
[0, -10, 0],
[200, -10, 0],
[200, -50, 0],
[300, 0, 0],
[200, 50, 0],
[200, 10, 0],
[0, 10, 0],
]
arrow = np.array(arrow()) * 2.0
import ipywidgets as widgets
slider = widgets.IntSlider(0, min=-1000, max=ruler.length() + 1000, step=10)
output = widgets.Output()
def show_map(range_meters):
T_ecef_frenet = ruler.local_frame(range_meters)
ecef = (T_ecef_frenet[:3, :3] @ arrow.T + T_ecef_frenet[:3, 3][:, np.newaxis]).T
llas = ecef2lla(ecef)
return show_geojson(geojson={'type': 'FeatureCollection', 'features': [
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': beauty_feet},
'properties': {'distance': distance},
},
{
'type': 'Feature',
'geometry': {'type': 'LineString', 'coordinates': llas.tolist()},
'properties': {},
},
]}, zoom=13, center=[120.735122, 31.4213], layout=Layout(width='80%', height='800px'))
def handle_slider_change(change):
with output:
output.clear_output()
display(show_map(range_meters=change.new))
slider.observe(handle_slider_change, names='value')
display(slider, output)
IntSlider(value=0, max=19042, min=-1000, step=10)
Output()
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print(ruler.extended_along(-1000)) # backwards 1km
print(ruler.at(0)) # start point
print(ruler.arrow(0)) # start point, direction
print(ruler.extended_along(-1000)) # backwards 1km
print(ruler.at(0)) # start point
print(ruler.arrow(0)) # start point, direction
[120.75300263 31.45626373 0. ] [120.74827946 31.4482048 0. ] (array([120.74827946, 31.4482048 , 0. ]), array([-0.44895912, -0.8935523 , 0. ]))
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ranges, llas, dirs = ruler.arrows([0, 100, 200, 400, 800])
print(ranges)
print(llas)
print(dirs)
ranges, llas, dirs = ruler.arrows([0, 100, 200, 400, 800])
print(ranges)
print(llas)
print(dirs)
[ 0. 100. 200. 400. 800.] [[120.74827946 31.4482048 0. ] [120.74780714 31.4473989 0. ] [120.74733483 31.44659301 0. ] [120.74639019 31.44498122 0. ] [120.74740356 31.44192968 0. ]] [[-0.44895912 -0.8935523 0. ] [-0.44895912 -0.8935523 0. ] [-0.44895912 -0.8935523 0. ] [-0.44895912 -0.8935523 0. ] [-0.52731437 -0.84967026 0. ]]
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ranges, llas, dirs = ruler.arrows(1000) # every 1km
print(ranges)
print(llas)
print(dirs)
ranges, llas, dirs = ruler.arrows(1000) # every 1km
print(ranges)
print(llas)
print(dirs)
[ 0. 1000. 2000. 3000. 4000. 5000. 6000. 7000. 8000. 9000. 10000. 11000. 12000. 13000. 14000. 15000. 16000. 17000. 18000. 18042.97023788] [[120.74827946 31.4482048 0. ] [120.74629406 31.44039705 0. ] [120.74078953 31.43271179 0. ] [120.73666944 31.42443904 0. ] [120.72958413 31.41803757 0. ] [120.72009793 31.4147084 0. ] [120.71220568 31.40966804 0. ] [120.71356767 31.40105439 0. ] [120.71062071 31.39242553 0. ] [120.71571171 31.38921157 0. ] [120.71645226 31.39704258 0. ] [120.72261496 31.40435211 0. ] [120.72877765 31.41166164 0. ] [120.73494035 31.41897118 0. ] [120.74329043 31.42397484 0. ] [120.75018355 31.42947728 0. ] [120.75664085 31.43659745 0. ] [120.76096841 31.4442374 0. ] [120.75149658 31.44816232 0. ] [120.75108957 31.44833097 0. ]] [[-0.44895912 -0.8935523 0. ] [-0.52731437 -0.84967026 0. ] [-0.50149443 -0.86516087 0. ] [-0.35256258 -0.93578824 0. ] [-0.81820992 -0.57491959 0. ] [-0.96712255 -0.25431077 0. ] [-0.55642936 -0.83089492 0. ] [-0.2895596 -0.95715999 0. ] [ 0.37276143 -0.92792722 0. ] [ 0.44874113 0.89366179 0. ] [ 0.58579319 0.81046057 0. ] [ 0.58579319 0.81046057 0. ] [ 0.58579319 0.81046057 0. ] [ 0.58579319 0.81046057 0. ] [ 0.99167693 0.12875117 0. ] [ 0.61379694 0.78946394 0. ] [ 0.61379694 0.78946394 0. ] [-0.9003417 0.43518367 0. ] [-0.9003417 0.43518367 0. ] [-0.9003417 0.43518367 0. ]]
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import k3d
import numpy as np
import k3d
import numpy as np
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# from pybind11_geobuf import Decoder, Encoder
# encoder = Encoder(max_precision=int(10**8))
# encoder.encode(geojson='cloverleaf.json', geobuf='cloverleaf.pbf')
# decoder = Decoder()
# decoder.decode(geobuf='cloverleaf.pbf', geojson='cloverleaf.pbf.json', indent=True, sort_keys=True)
# from pybind11_geobuf import Decoder, Encoder
# encoder = Encoder(max_precision=int(10**8))
# encoder.encode(geojson='cloverleaf.json', geobuf='cloverleaf.pbf')
# decoder = Decoder()
# decoder.decode(geobuf='cloverleaf.pbf', geojson='cloverleaf.pbf.json', indent=True, sort_keys=True)
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import json
with open('cloverleaf.pbf.json') as f:
geojson = json.load(f)
show_geojson(geojson=geojson, basemap=basemaps.Gaode.Normal, zoom=16)
import json
with open('cloverleaf.pbf.json') as f:
geojson = json.load(f)
show_geojson(geojson=geojson, basemap=basemaps.Gaode.Normal, zoom=16)
Map(center=[31.32049390261476, 120.68722507964208], controls=(ZoomControl(options=['position', 'zoom_in_text',…
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polylines = [f['geometry']['coordinates'] for f in geojson['features'] if f['properties'].get('type') == 'lane_border']
print(f'#polylines: {len(polylines)}')
polylines = [f['geometry']['coordinates'] for f in geojson['features'] if f['properties'].get('type') == 'lane_border']
print(f'#polylines: {len(polylines)}')
#polylines: 808
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# filter out some polylines, for faster visualization
from shapely import Polygon, LineString
bbox = [[120.68778, 31.31983], [120.68778, 31.31827], [120.68933, 31.31827], [120.68933, 31.31983], [120.68778, 31.31983]]
polygon = Polygon(bbox)
polylines = [p for p in polylines if not polygon.disjoint(LineString(p))]
print(f'#polylines: {len(polylines)} (filter by bbox)')
# filter out some polylines, for faster visualization
from shapely import Polygon, LineString
bbox = [[120.68778, 31.31983], [120.68778, 31.31827], [120.68933, 31.31827], [120.68933, 31.31983], [120.68778, 31.31983]]
polygon = Polygon(bbox)
polylines = [p for p in polylines if not polygon.disjoint(LineString(p))]
print(f'#polylines: {len(polylines)} (filter by bbox)')
#polylines: 113 (filter by bbox)
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# convert to ENU
from polyline_ruler.tf import lla2enu
anchor = polylines[0][0]
polylines = [lla2enu(llas, anchor_lla=anchor).astype(np.float32) for llas in polylines]
# convert to ENU
from polyline_ruler.tf import lla2enu
anchor = polylines[0][0]
polylines = [lla2enu(llas, anchor_lla=anchor).astype(np.float32) for llas in polylines]
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import k3d
import numpy as np
plot = k3d.plot()
for polyline in polylines:
plot += k3d.line(polyline)
plot.display()
import k3d
import numpy as np
plot = k3d.plot()
for polyline in polylines:
plot += k3d.line(polyline)
plot.display()
Output()
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id2feature = {f['properties']['id']: f for f in geojson['features']}
left_lane_border = id2feature.get('w1268')
print(left_lane_border)
coords = lla2enu(left_lane_border['geometry']['coordinates'], anchor_lla=anchor)
print(coords)
ruler = PolylineRuler(coords)
print(ruler.length())
scanlines = []
for r in np.arange(0, ruler.length(), 10):
ls = ruler.scanline(range=r, min=-10, max=10)
scanlines.append(ls)
plot = k3d.plot()
for polyline in polylines:
plot += k3d.line(polyline)
for line in scanlines:
plot += k3d.line(line, color=0xff0000)
plot.display()
id2feature = {f['properties']['id']: f for f in geojson['features']}
left_lane_border = id2feature.get('w1268')
print(left_lane_border)
coords = lla2enu(left_lane_border['geometry']['coordinates'], anchor_lla=anchor)
print(coords)
ruler = PolylineRuler(coords)
print(ruler.length())
scanlines = []
for r in np.arange(0, ruler.length(), 10):
ls = ruler.scanline(range=r, min=-10, max=10)
scanlines.append(ls)
plot = k3d.plot()
for polyline in polylines:
plot += k3d.line(polyline)
for line in scanlines:
plot += k3d.line(line, color=0xff0000)
plot.display()
{'geometry': {'coordinates': [[120.68743528, 31.3198304, 3.403], [120.68749578, 31.3198145, 3.693], [120.68754678, 31.3197994, 3.932], [120.68759647, 31.3197833, 4.163], [120.68764497, 31.3197662, 4.387], [120.68769227, 31.3197481, 4.608], [120.68773856, 31.3197292, 4.826], [120.68781206, 31.3196965, 5.185], [120.68786916, 31.3196683, 5.479], [120.68794345, 31.3196281, 5.869], [120.68799645, 31.3195969, 6.141], [120.68802185, 31.3195811, 6.264], [120.68809194, 31.3195345, 6.561], [120.68813924, 31.3194999, 6.704], [120.68820293, 31.3194497, 6.84], [120.68826313, 31.319398, 6.907], [120.68830553, 31.3193585, 6.915], [120.68835772, 31.3193056, 6.875], [120.68841782, 31.3192382, 6.732], [120.68845902, 31.3191888, 6.559]], 'type': 'LineString'}, 'properties': {'id': 'w1268', 'length': 123.181, 'stroke': '#ffffff', 'type': 'lane_border'}, 'type': 'Feature'}
[[-185.22038027 208.81189271 2.269 ]
[-179.46163204 207.04898108 2.559 ]
[-174.60715006 205.37476941 2.798 ]
[-169.87736164 203.5896828 3.029 ]
[-165.26084446 201.69372124 3.253 ]
[-160.75855039 199.68688473 3.474 ]
[-156.3523941 197.59134827 3.692 ]
[-149.3562289 193.96573757 4.051 ]
[-143.9211128 190.83906412 4.345 ]
[-136.84975071 186.38189133 4.735 ]
[-131.80489689 182.92259304 5.007 ]
[-129.3871745 181.17076891 5.13 ]
[-122.71559328 176.00399647 5.427 ]
[-118.21329921 172.16772338 5.57 ]
[-112.15090789 166.60180114 5.706 ]
[-106.42071544 160.86956648 5.773 ]
[-102.38483238 156.49000615 5.781 ]
[ -97.41707915 150.62472156 5.741 ]
[ -91.69640529 143.15175027 5.598 ]
[ -87.77474534 137.67452798 5.425 ]]
123.1789731671867
Output()
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