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geoid.py
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geoid.py
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#!/usr/bin/python
# This file is mostly a straight translation of
# GeographicLib/src/Geoid.cpp from C++ to Python
# by Kim Vandry <vandry@TZoNE.ORG>
#
# /**
# * \file Geoid.cpp
# * \brief Implementation for GeographicLib::Geoid class
# *
# * Copyright (c) Charles Karney (2009) <charles@karney.com>
# * and licensed under the LGPL. For more information, see
# * http://geographiclib.sourceforge.net/
# **********************************************************************/
#
# Geoid height grade not supported
import os
import mmap
import struct
class GeoidBadDataFile(Exception):
pass
class GeoidHeight(object):
"""Calculate the height of the WGS84 geoid above the
ellipsoid at any given latitude and longitude
:param name: name to PGM file containing model info
download from http://geographiclib.sourceforge.net/1.18/geoid.html
"""
c0 = 240
c3 = (
( 9, -18, -88, 0, 96, 90, 0, 0, -60, -20),
( -9, 18, 8, 0, -96, 30, 0, 0, 60, -20),
( 9, -88, -18, 90, 96, 0, -20, -60, 0, 0),
(186, -42, -42, -150, -96, -150, 60, 60, 60, 60),
( 54, 162, -78, 30, -24, -90, -60, 60, -60, 60),
( -9, -32, 18, 30, 24, 0, 20, -60, 0, 0),
( -9, 8, 18, 30, -96, 0, -20, 60, 0, 0),
( 54, -78, 162, -90, -24, 30, 60, -60, 60, -60),
(-54, 78, 78, 90, 144, 90, -60, -60, -60, -60),
( 9, -8, -18, -30, -24, 0, 20, 60, 0, 0),
( -9, 18, -32, 0, 24, 30, 0, 0, -60, 20),
( 9, -18, -8, 0, -24, -30, 0, 0, 60, 20),
)
c0n = 372
c3n = (
( 0, 0, -131, 0, 138, 144, 0, 0, -102, -31),
( 0, 0, 7, 0, -138, 42, 0, 0, 102, -31),
( 62, 0, -31, 0, 0, -62, 0, 0, 0, 31),
(124, 0, -62, 0, 0, -124, 0, 0, 0, 62),
(124, 0, -62, 0, 0, -124, 0, 0, 0, 62),
( 62, 0, -31, 0, 0, -62, 0, 0, 0, 31),
( 0, 0, 45, 0, -183, -9, 0, 93, 18, 0),
( 0, 0, 216, 0, 33, 87, 0, -93, 12, -93),
( 0, 0, 156, 0, 153, 99, 0, -93, -12, -93),
( 0, 0, -45, 0, -3, 9, 0, 93, -18, 0),
( 0, 0, -55, 0, 48, 42, 0, 0, -84, 31),
( 0, 0, -7, 0, -48, -42, 0, 0, 84, 31),
)
c0s = 372
c3s = (
( 18, -36, -122, 0, 120, 135, 0, 0, -84, -31),
(-18, 36, -2, 0, -120, 51, 0, 0, 84, -31),
( 36, -165, -27, 93, 147, -9, 0, -93, 18, 0),
(210, 45, -111, -93, -57, -192, 0, 93, 12, 93),
(162, 141, -75, -93, -129, -180, 0, 93, -12, 93),
(-36, -21, 27, 93, 39, 9, 0, -93, -18, 0),
( 0, 0, 62, 0, 0, 31, 0, 0, 0, -31),
( 0, 0, 124, 0, 0, 62, 0, 0, 0, -62),
( 0, 0, 124, 0, 0, 62, 0, 0, 0, -62),
( 0, 0, 62, 0, 0, 31, 0, 0, 0, -31),
(-18, 36, -64, 0, 66, 51, 0, 0, -102, 31),
( 18, -36, 2, 0, -66, -51, 0, 0, 102, 31),
)
def __init__(self, name="egm2008-1.pgm"):
self.offset = None
self.scale = None
with open(name, "rb") as f:
line = f.readline()
if line != b"P5\012" and line != b"P5\015\012":
raise GeoidBadDataFile("No PGM header")
headerlen = len(line)
while True:
line = f.readline()
if len(line) == 0:
raise GeoidBadDataFile("EOF before end of file header")
headerlen += len(line)
if line.startswith(b'# Offset '):
try:
self.offset = int(line[9:])
except ValueError as e:
raise GeoidBadDataFile("Error reading offset", e)
elif line.startswith(b'# Scale '):
try:
self.scale = float(line[8:])
except ValueError as e:
raise GeoidBadDataFile("Error reading scale", e)
elif not line.startswith(b'#'):
try:
self.width, self.height = list(map(int, line.split()))
except ValueError as e:
raise GeoidBadDataFile("Bad PGM width&height line", e)
break
line = f.readline()
headerlen += len(line)
levels = int(line)
if levels != 65535:
raise GeoidBadDataFile("PGM file must have 65535 gray levels")
if self.offset is None:
raise GeoidBadDataFile("PGM file does not contain offset")
if self.scale is None:
raise GeoidBadDataFile("PGM file does not contain scale")
if self.width < 2 or self.height < 2:
raise GeoidBadDataFile("Raster size too small")
fd = f.fileno()
fullsize = os.fstat(fd).st_size
if fullsize - headerlen != self.width * self.height * 2:
raise GeoidBadDataFile("File has the wrong length")
self.headerlen = headerlen
self.raw = mmap.mmap(fd, fullsize, mmap.MAP_SHARED, mmap.PROT_READ)
self.rlonres = self.width / 360.0
self.rlatres = (self.height - 1) / 180.0
self.ix = None
self.iy = None
def _rawval(self, ix, iy):
if iy < 0:
iy = -iy
ix += self.width/2
elif iy >= self.height:
iy = 2 * (self.height - 1) - iy
ix += self.width/2
if ix < 0:
ix += self.width
elif ix >= self.width:
ix -= self.width
return struct.unpack_from('>H', self.raw,
(iy * self.width + ix) * 2 + self.headerlen
)[0]
def get(self, lat, lon, cubic=True):
if lon < 0:
lon += 360
fy = (90 - lat) * self.rlatres
fx = lon * self.rlonres
iy = int(fy)
ix = int(fx)
fx -= ix
fy -= iy
if iy == self.height - 1:
iy -= 1
if ix != self.ix or iy != self.iy:
self.ix = ix
self.iy = iy
if not cubic:
self.v00 = self._rawval(ix, iy)
self.v01 = self._rawval(ix+1, iy)
self.v10 = self._rawval(ix, iy+1)
self.v11 = self._rawval(ix+1, iy+1)
else:
v = (
self._rawval(ix , iy - 1),
self._rawval(ix + 1, iy - 1),
self._rawval(ix - 1, iy ),
self._rawval(ix , iy ),
self._rawval(ix + 1, iy ),
self._rawval(ix + 2, iy ),
self._rawval(ix - 1, iy + 1),
self._rawval(ix , iy + 1),
self._rawval(ix + 1, iy + 1),
self._rawval(ix + 2, iy + 1),
self._rawval(ix , iy + 2),
self._rawval(ix + 1, iy + 2)
)
if iy == 0:
c3x = GeoidHeight.c3n
c0x = GeoidHeight.c0n
elif iy == self.height - 2:
c3x = GeoidHeight.c3s
c0x = GeoidHeight.c0s
else:
c3x = GeoidHeight.c3
c0x = GeoidHeight.c0
self.t = [
sum([ v[j] * c3x[j][i] for j in range(12) ]) / float(c0x)
for i in range(10)
]
if not cubic:
a = (1 - fx) * self.v00 + fx * self.v01
b = (1 - fx) * self.v10 + fx * self.v11
h = (1 - fy) * a + fy * b
else:
h = (
self.t[0] +
fx * (self.t[1] + fx * (self.t[3] + fx * self.t[6])) +
fy * (
self.t[2] + fx * (self.t[4] + fx * self.t[7]) +
fy * (self.t[5] + fx * self.t[8] + fy * self.t[9])
)
)
return self.offset + self.scale * h