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copied!<p>I suggest to approximate locally the Earth surface as a sphere with radius given by the WGS84 ellipsoid at the given latitude. I suspect that the exact computation of latMin and latMax would require elliptic functions and would not yield an appreciable increase in accuracy (WGS84 is itself an approximation).</p> <p>My implementation follows (It's written in Python; I have not tested it):</p> <pre class="lang-py prettyprint-override"><code># degrees to radians def deg2rad(degrees): return math.pi*degrees/180.0 # radians to degrees def rad2deg(radians): return 180.0*radians/math.pi # Semi-axes of WGS-84 geoidal reference WGS84_a = 6378137.0 # Major semiaxis [m] WGS84_b = 6356752.3 # Minor semiaxis [m] # Earth radius at a given latitude, according to the WGS-84 ellipsoid [m] def WGS84EarthRadius(lat): # http://en.wikipedia.org/wiki/Earth_radius An = WGS84_a*WGS84_a * math.cos(lat) Bn = WGS84_b*WGS84_b * math.sin(lat) Ad = WGS84_a * math.cos(lat) Bd = WGS84_b * math.sin(lat) return math.sqrt( (An*An + Bn*Bn)/(Ad*Ad + Bd*Bd) ) # Bounding box surrounding the point at given coordinates, # assuming local approximation of Earth surface as a sphere # of radius given by WGS84 def boundingBox(latitudeInDegrees, longitudeInDegrees, halfSideInKm): lat = deg2rad(latitudeInDegrees) lon = deg2rad(longitudeInDegrees) halfSide = 1000*halfSideInKm # Radius of Earth at given latitude radius = WGS84EarthRadius(lat) # Radius of the parallel at given latitude pradius = radius*math.cos(lat) latMin = lat - halfSide/radius latMax = lat + halfSide/radius lonMin = lon - halfSide/pradius lonMax = lon + halfSide/pradius return (rad2deg(latMin), rad2deg(lonMin), rad2deg(latMax), rad2deg(lonMax)) </code></pre> <p>EDIT: The following code converts (degrees, primes, seconds) to degrees + fractions of a degree, and vice versa (not tested):</p> <pre class="lang-py prettyprint-override"><code>def dps2deg(degrees, primes, seconds): return degrees + primes/60.0 + seconds/3600.0 def deg2dps(degrees): intdeg = math.floor(degrees) primes = (degrees - intdeg)*60.0 intpri = math.floor(primes) seconds = (primes - intpri)*60.0 intsec = round(seconds) return (int(intdeg), int(intpri), int(intsec)) </code></pre>

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