2016 Update
This commit is contained in:
Tina Müller
parent
948b86eafa
commit
dcf5d15da3
7965 changed files with 139854 additions and 31002 deletions
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@ -1,13 +1,19 @@
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{{Wikipedia}}The '''haversine formula''' is an equation important in navigation,
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giving great-circle distances between two points on a sphere
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from their longitudes and latitudes.
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It is a special case of a more general formula in spherical trigonometry,
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the '''law of haversines''', relating the sides and angles of spherical "triangles".
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{{Wikipedia}}
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'''Task:''' Implement a great-circle distance function, or use a library function,
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to show the great-circle distance between Nashville International Airport (BNA)
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in Nashville, TN, USA: N 36°7.2', W 86°40.2' (36.12, -86.67)
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and Los Angeles International Airport (LAX) in Los Angeles, CA, USA: N 33°56.4', W 118°24.0' (33.94, -118.40).
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<br>
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The '''haversine formula''' is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.
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It is a special case of a more general formula in spherical trigonometry, the '''law of haversines''', relating the sides and angles of spherical "triangles".
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;Task:
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Implement a great-circle distance function, or use a library function,
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to show the great-circle distance between:
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* Nashville International Airport (BNA) in Nashville, TN, USA, which is:
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<big><big> '''N''' 36°7.2', '''W''' 86°40.2' (36.12, -86.67) </big></big> -and-
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* Los Angeles International Airport (LAX) in Los Angeles, CA, USA, which is:
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<big><big> '''N''' 33°56.4', '''W''' 118°24.0' (33.94, -118.40) </big></big>
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<br>
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<pre>
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User Kaimbridge clarified on the Talk page:
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@ -40,3 +46,4 @@ examples in real applications, it is better to use the
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6371 km. This value is recommended by the International Union of
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Geodesy and Geophysics and it minimizes the RMS relative error between the
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great circle and geodesic distance.
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<br><br>
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@ -1,9 +1,22 @@
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DATA : lat1 TYPE char20 VALUE '36.12' ,
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lon1 TYPE char20 VALUE '-86.67' ,
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lat2 TYPE char20 VALUE '33.94' ,
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lon2 TYPE char20 VALUE '-118.4' ,
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distance TYPE p DECIMALS 1 .
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CONSTANTS : pi TYPE char20 VALUE '3.141592654',
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earth_radius TYPE char20 VALUE '6372.8' ."in km
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distance = earth_radius * acos( cos( ( 90 - lat1 ) * ( pi / 180 ) ) * cos( ( 90 - lat2 ) * ( pi / 180 ) ) + sin( ( 90 - lat1 ) * ( pi / 180 ) ) * sin( ( 90 - lat2 ) * ( pi / 180 ) ) * cos( ( lon1 - lon2 ) * ( pi / 180 ) ) ) .
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DATA: X1 TYPE F, Y1 TYPE F,
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X2 TYPE F, Y2 TYPE F, YD TYPE F,
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PI TYPE F,
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PI_180 TYPE F,
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MINUS_1 TYPE F VALUE '-1'.
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PI = ACOS( MINUS_1 ).
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PI_180 = PI / 180.
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LATITUDE1 = 36,12 . LONGITUDE1 = -86,67 .
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LATITUDE2 = 33,94 . LONGITUDE2 = -118,4 .
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X1 = LATITUDE1 * PI_180.
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Y1 = LONGITUDE1 * PI_180.
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X2 = LATITUDE2 * PI_180.
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Y2 = LONGITUDE2 * PI_180.
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YD = Y2 - Y1.
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DISTANCE = 20000 / PI *
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ACOS( SIN( X1 ) * SIN( X2 ) + COS( X1 ) * COS( X2 ) * COS( YD ) ).
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WRITE : 'Distance between given points = ' , distance , 'km .' .
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21
Task/Haversine-formula/AMPL/haversine-formula.ampl
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21
Task/Haversine-formula/AMPL/haversine-formula.ampl
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@ -0,0 +1,21 @@
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set location;
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set geo;
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param coord{i in location, j in geo};
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param dist{i in location, j in location};
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data;
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set location := BNA LAX;
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set geo := LAT LON;
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param coord:
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LAT LON :=
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BNA 36.12 -86.67
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LAX 33.94 -118.4
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;
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let dist['BNA','LAX'] := 2 * 6372.8 * asin (sqrt(sin(atan(1)/45*(coord['LAX','LAT']-coord['BNA','LAT'])/2)^2 + cos(atan(1)/45*coord['BNA','LAT']) * cos(atan(1)/45*coord['LAX','LAT']) * sin(atan(1)/45*(coord['LAX','LON'] - coord
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['BNA','LON'])/2)^2));
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printf "The distance between the two points is approximately %f km.\n", dist['BNA','LAX'];
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3
Task/Haversine-formula/APL/haversine-formula.apl
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3
Task/Haversine-formula/APL/haversine-formula.apl
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@ -0,0 +1,3 @@
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r←6371
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hf←{(p q)←○⍺ ⍵÷180 ⋄ 2×rׯ1○(+/(2*⍨1○(p-q)÷2)×1(×/2○⊃¨p q))*÷2}
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36.12 ¯86.67 hf 33.94 ¯118.40
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36
Task/Haversine-formula/JavaScript/haversine-formula-2.js
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36
Task/Haversine-formula/JavaScript/haversine-formula-2.js
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@ -0,0 +1,36 @@
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((x, y) => {
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'use strict';
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// haversine :: (Num, Num) -> (Num, Num) -> Num
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let haversine = ([lat1, lon1], [lat2, lon2]) => {
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// Math lib function names
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let [pi, asin, sin, cos, sqrt, pow, round] =
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['PI', 'asin', 'sin', 'cos', 'sqrt', 'pow', 'round']
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.map(k => Math[k]),
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// degrees as radians
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[rlat1, rlat2, rlon1, rlon2] = [lat1, lat2, lon1, lon2]
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.map(x => x / 180 * pi),
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dLat = rlat2 - rlat1,
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dLon = rlon2 - rlon1,
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radius = 6372.8; // km
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// km
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return round(
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radius * 2 * asin(
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sqrt(
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pow(sin(dLat / 2), 2) +
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pow(sin(dLon / 2), 2) *
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cos(rlat1) * cos(rlat2)
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)
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) * 100
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) / 100;
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};
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// TEST
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return haversine(x, y);
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// --> 2887.26
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})([36.12, -86.67], [33.94, -118.40]);
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@ -0,0 +1,6 @@
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Add-Type -AssemblyName System.Device
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$BNA = New-Object System.Device.Location.GeoCoordinate 36.12, -86.67
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$LAX = New-Object System.Device.Location.GeoCoordinate 33.94, -118.40
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$BNA.GetDistanceTo( $LAX ) / 1000
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28
Task/Haversine-formula/PowerShell/haversine-formula-2.psh
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28
Task/Haversine-formula/PowerShell/haversine-formula-2.psh
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@ -0,0 +1,28 @@
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function Get-GreatCircleDistance ( $Coord1, $Coord2 )
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{
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# Convert decimal degrees to radians
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$Lat1 = $Coord1[0] / 180 * [math]::Pi
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$Long1 = $Coord1[1] / 180 * [math]::Pi
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$Lat2 = $Coord2[0] / 180 * [math]::Pi
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$Long2 = $Coord2[1] / 180 * [math]::Pi
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# Mean Earth radius (km)
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$R = 6371
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# Haversine formula
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$ArcLength = 2 * $R *
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[math]::Asin(
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[math]::Sqrt(
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[math]::Sin( ( $Lat1 - $Lat2 ) / 2 ) *
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[math]::Sin( ( $Lat1 - $Lat2 ) / 2 ) +
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[math]::Cos( $Lat1 ) *
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[math]::Cos( $Lat2 ) *
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[math]::Sin( ( $Long1 - $Long2 ) / 2 ) *
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[math]::Sin( ( $Long1 - $Long2 ) / 2 ) ) )
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return $ArcLength
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}
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$BNA = 36.12, -86.67
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$LAX = 33.94, -118.40
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Get-GreatCircleDistance $BNA $LAX
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@ -1,59 +1,53 @@
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/*REXX program calculates distance between Nashville and Los Angles airports.*/
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call pi; numeric digits length(pi)%2 /*use ½ of the decimal digs that PI has*/
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/*REXX program calculates the distance between Nashville and Los Angles airports.*/
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call pi; numeric digits length(pi)%2 /*use half of decimal digits of PI. */
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say " Nashville: north 36º 7.2', west 86º 40.2' = 36.12º, -86.67º"
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say " Los Angles: north 33º 56.4', west 118º 24.0' = 33.94º, -118.40º"
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@using_radius='using the mean radius of the earth as ' /*literal for SAY.*/
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radii.=.; radii.1=6372.8; radii.2=6371 /*mean radii of the earth in kilometers*/
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say; m=1/0.621371192237 /*M: length of one mile in kilometers.*/
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do radius=1 while radii.radius\==. /*calc. distance using specific radius.*/
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d=surfaceDistance( 36.12, -86.67, 33.94, -118.4, radii.radius)
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say
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say center(@using_radius radii.radius ' kilometers', 75, '─')
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say ' Distance between: ' format(d/1 ,,2) " kilometers,"
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say ' or ' format(d/m ,,2) " statute miles,"
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say ' or ' format(d/m*5280/6076.1,,2) " nautical (or air miles)."
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end /*radius*/ /*only display └───◄ 2 digits of dist.*/
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exit /*stick a fork in it, we're all done. */
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/*────────────────────────────────────────────────────────────────────────────*/
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surfaceDistance: arg th1,ph1,th2,ph2,r /*use haversine formula for distance.*/
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numeric digits digits()*2 /*double the number of decimal digits. */
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ph1 = d2r(ph1-ph2) /*convert degrees ──► radians & reduce.*/
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th1 = d2r(th1); th2 = d2r(th2) /* " " " " " " */
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x = cos(ph1) * cos(th1) - cos(th2)
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y = sin(ph1) * cos(th1)
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z = sin(th1) - sin(th2)
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return Asin( sqrt( x**2 + y**2 + z**2) / 2 ) * r * 2
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/*═════════════════════════════general subroutines════════════════════════════*/
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d2d: return arg(1) // 360 /*normalize degrees to a unit circle. */
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d2r: return r2r(arg(1)*pi() / 180) /*normalize and convert deg ──► radians*/
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r2d: return d2d((arg(1)*180 / pi())) /*normalize and convert rad ──► degrees*/
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r2r: return arg(1) // (pi()*2) /*normalize radians to a unit circle. */
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p: return word(arg(1),1) /*pick the first of two words (numbers)*/
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pi: pi=3.141592653589793238462643383279502884197169399375105820975; return pi
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Acos: procedure; parse arg x; if x<-1 | x>1 then call $81r -1,1,x,"ACOS"
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return .5*pi()-Asin(x) /*$81R says argument X is out of range,*/
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/* ··· and the sub isn't included here.*/
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Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
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if a>1 then call $81r -1,1,x,"ASIN" /*X argument is out of range.*/
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if a>=sqrt(2)*.5 then return sign(x) * Acos(sqrt(1-aa), '-ASIN')
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do j=2 by 2 until p=z; p=z; o=o*aa*(j-1)/j; z=z+o/(j+1); end
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return z /* [↑] compute until no more noise. */
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@using_radius= 'using the mean radius of the earth as ' /*a literal for SAY.*/
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radii.=.; radii.1=6372.8; radii.2=6371 /*mean radii of the earth in kilometers*/
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say; m=1/0.621371192237 /*M: one statute mile in " */
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do radius=1 while radii.radius\==. /*calc. distance using specific radius.*/
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d=surfaceDistance( 36.12, -86.67, 33.94, -118.4, radii.radius); say
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say center(@using_radius radii.radius ' kilometers', 75, '─')
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say ' Distance between: ' format(d/1 ,,2) " kilometers,"
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say ' or ' format(d/m ,,2) " statute miles,"
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say ' or ' format(d/m*5280/6076.1,,2) " nautical (or air miles)."
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end /*radius*/ /*these └───◄ displays 2 decimal digs.*/
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exit /*stick a fork in it, we're all done. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Acos: return .5*pi() - aSin( arg(1) )
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d2d: return arg(1) // 360 /*normalize degrees to a unit circle. */
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d2r: return r2r(arg(1)*pi() / 180) /*normalize and convert deg ──► radians*/
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r2d: return d2d((arg(1)*180 / pi())) /*normalize and convert rad ──► degrees*/
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r2r: return arg(1) // (pi()*2) /*normalize radians to a unit circle. */
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p: return word(arg(1),1) /*pick the first of two words (numbers)*/
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pi: pi=3.141592653589793238462643383279502884197169399375105820975; return pi
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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surfaceDistance: parse arg th1,ph1,th2,ph2,r /*use haversine formula for distance.*/
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numeric digits digits() * 2 /*double the number of decimal digits. */
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ph1= d2r(ph1 - ph2) /*convert degrees ──► radians & reduce.*/
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th1= d2r(th1); th2 = d2r(th2) /* " " " " " " */
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x= cos(ph1) * cos(th1) - cos(th2)
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y= sin(ph1) * cos(th1)
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z= sin(th1) - sin(th2)
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return Asin( sqrt( x**2 + y**2 + z**2) / 2 ) * r * 2
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a
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if a>=sqrt(2) * .5 then return sign(x) * Acos(sqrt(1-aa))
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do j=2 by 2 until p=z; p=z; o=o*aa*(j-1)/j; z=z+o/(j+1); end /*j*/
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return z /* [↑] compute until no more noise. */
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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cos: procedure; parse arg x; x=r2r(x); a=abs(x); Hpi=pi*.5
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numeric fuzz min(6,digits()-3); if a=pi() then return -1
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if a=Hpi | a=Hpi*3 then return 0; if a=pi()/3 then return .5
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if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1)
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, digits()-3)
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if abs(x)=pi() then return 0; return .sinCos(x,x,1)
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.sinCos: parse arg z,_,i; q=x*x; p=z; do k=2 by 2; _=-_*q/(k*(k+i)); z=z+_
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if z=p then leave; p=z; end; return z /*used by SIN & COS*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9
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numeric digits 9; numeric form; h=d+6; if x<0 then do; x=-x; i='i'; end
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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numeric digits d; return (g/1)i /*make complex if X < 0.*/
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if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1)
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sin: procedure; parse arg x; x=r2r(x); numeric fuzz min(5, digits()-3)
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if abs(x)=pi() then return 0; return .sinCos(x,x,1)
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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.sinCos: parse arg z 1 p,_,i; q=x*x
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do k=2 by 2; _=-_*q/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z
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/*──────────────────────────────────────────────────────────────────────────────────────*/
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
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numeric digits; parse value format(x,2,1,,0) 'E0' with g "E" _ .; g=g * .5'e'_ % 2
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do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
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do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/
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19
Task/Haversine-formula/Rust/haversine-formula.rust
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19
Task/Haversine-formula/Rust/haversine-formula.rust
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use std::f64;
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static R: f64 = 6372.8;
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fn haversine_dist(mut th1: f64, mut ph1: f64, mut th2: f64, ph2: f64) -> f64 {
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ph1 -= ph2;
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ph1 = ph1.to_radians();
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th1 = th1.to_radians();
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th2 = th2.to_radians();
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let dz: f64 = th1.sin() - th2.sin();
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let dx: f64 = ph1.cos() * th1.cos() - th2.cos();
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let dy: f64 = ph1.sin() * th1.cos();
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((dx * dx + dy * dy + dz * dz).sqrt() / 2.0).asin() * 2.0 * R
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}
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fn main() {
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let d: f64 = haversine_dist(36.12, -86.67, 33.94, -118.4);
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println!("Distance: {} km ({} mi)", d, d / 1.609344);
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}
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16
Task/Haversine-formula/XQuery/haversine-formula.xquery
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16
Task/Haversine-formula/XQuery/haversine-formula.xquery
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declare namespace xsd = "http://www.w3.org/2001/XMLSchema";
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declare namespace math = "http://www.w3.org/2005/xpath-functions/math";
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declare function local:haversine($lat1 as xsd:float, $lon1 as xsd:float, $lat2 as xsd:float, $lon2 as xsd:float)
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as xsd:float
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{
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let $dlat := ($lat2 - $lat1) * math:pi() div 180
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let $dlon := ($lon2 - $lon1) * math:pi() div 180
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let $rlat1 := $lat1 * math:pi() div 180
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let $rlat2 := $lat2 * math:pi() div 180
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let $a := math:sin($dlat div 2) * math:sin($dlat div 2) + math:sin($dlon div 2) * math:sin($dlon div 2) * math:cos($rlat1) * math:cos($rlat2)
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let $c := 2 * math:atan2(math:sqrt($a), math:sqrt(1-$a))
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return xsd:float($c * 6371.0)
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};
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local:haversine(36.12, -86.67, 33.94, -118.4)
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10 LET diam=2*6372.8
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20 LET Lg1m2=FN r((-86.67)-(-118.4))
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30 LET Lt1=FN r(36.12)
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40 LET Lt2=FN r(33.94)
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50 LET dz=SIN (Lt1)-SIN (Lt2)
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60 LET dx=COS (Lg1m2)*COS (Lt1)-COS (Lt2)
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70 LET dy=SIN (Lg1m2)*COS (Lt1)
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80 LET hDist=ASN ((dx*dx+dy*dy+dz*dz)^0.5/2)*diam
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90 PRINT "Haversine distance: ";hDist;" km."
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100 STOP
|
||||
1000 DEF FN r(a)=a*0.017453293: REM convert degree to radians
|
||||
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Reference in a new issue