kopia lustrzana https://github.com/projecthorus/horus-gui
84 wiersze
3.0 KiB
Python
84 wiersze
3.0 KiB
Python
from math import radians, degrees, sin, cos, atan2, sqrt, pi
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# Earthmaths code by Daniel Richman (thanks!)
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# Copyright 2012 (C) Daniel Richman; GNU GPL 3
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def position_info(listener, balloon):
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"""
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Calculate and return information from 2 (lat, lon, alt) tuples
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Returns a dict with:
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- angle at centre
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- great circle distance
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- distance in a straight line
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- bearing (azimuth or initial course)
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- elevation (altitude)
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Input and output latitudes, longitudes, angles, bearings and elevations are
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in degrees, and input altitudes and output distances are in meters.
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"""
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# Earth:
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radius = 6371000.0
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(lat1, lon1, alt1) = listener
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(lat2, lon2, alt2) = balloon
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lat1 = radians(lat1)
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lat2 = radians(lat2)
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lon1 = radians(lon1)
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lon2 = radians(lon2)
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# Calculate the bearing, the angle at the centre, and the great circle
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# distance using Vincenty's_formulae with f = 0 (a sphere). See
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# http://en.wikipedia.org/wiki/Great_circle_distance#Formulas and
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# http://en.wikipedia.org/wiki/Great-circle_navigation and
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# http://en.wikipedia.org/wiki/Vincenty%27s_formulae
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d_lon = lon2 - lon1
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sa = cos(lat2) * sin(d_lon)
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sb = (cos(lat1) * sin(lat2)) - (sin(lat1) * cos(lat2) * cos(d_lon))
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bearing = atan2(sa, sb)
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aa = sqrt((sa ** 2) + (sb ** 2))
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ab = (sin(lat1) * sin(lat2)) + (cos(lat1) * cos(lat2) * cos(d_lon))
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angle_at_centre = atan2(aa, ab)
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great_circle_distance = angle_at_centre * radius
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# Armed with the angle at the centre, calculating the remaining items
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# is a simple 2D triangley circley problem:
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# Use the triangle with sides (r + alt1), (r + alt2), distance in a
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# straight line. The angle between (r + alt1) and (r + alt2) is the
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# angle at the centre. The angle between distance in a straight line and
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# (r + alt1) is the elevation plus pi/2.
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# Use sum of angle in a triangle to express the third angle in terms
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# of the other two. Use sine rule on sides (r + alt1) and (r + alt2),
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# expand with compound angle formulae and solve for tan elevation by
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# dividing both sides by cos elevation
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ta = radius + alt1
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tb = radius + alt2
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ea = (cos(angle_at_centre) * tb) - ta
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eb = sin(angle_at_centre) * tb
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elevation = atan2(ea, eb)
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# Use cosine rule to find unknown side.
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distance = sqrt((ta ** 2) + (tb ** 2) - 2 * tb * ta * cos(angle_at_centre))
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# Give a bearing in range 0 <= b < 2pi
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if bearing < 0:
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bearing += 2 * pi
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return {
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"listener": listener, "balloon": balloon,
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"listener_radians": (lat1, lon1, alt1),
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"balloon_radians": (lat2, lon2, alt2),
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"angle_at_centre": degrees(angle_at_centre),
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"angle_at_centre_radians": angle_at_centre,
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"bearing": degrees(bearing),
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"bearing_radians": bearing,
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"great_circle_distance": great_circle_distance,
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"straight_distance": distance,
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"elevation": degrees(elevation),
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"elevation_radians": elevation
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}
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