{"id":607,"date":"2008-12-05T12:19:38","date_gmt":"2008-12-05T11:19:38","guid":{"rendered":"http:\/\/www.navision-blog.de\/2008\/12\/05\/distance-on-the-surface-of-the-earth-in-fsharp\/"},"modified":"2023-01-05T14:06:49","modified_gmt":"2023-01-05T14:06:49","slug":"distance-on-the-surface-of-the-earth-in-fsharp","status":"publish","type":"post","link":"http:\/\/www.navision-blog.de\/blog\/2008\/12\/05\/distance-on-the-surface-of-the-earth-in-fsharp\/","title":{"rendered":"The distance of two cities on the surface of the earth in F#"},"content":{"rendered":"

If we want to calculate the distance between two objects, we need some sort of distance function. I recently showed how we can compute the “edit distance” between two strings (see Damerau-Levenshtein-Distance in F# – part I<\/a>, part II<\/a> and part III<\/a>). This time I will consider the distance between two points in the plane and on the surface of the earth. <\/p>\n

First of all we need some sort of location type, which stores information about the coordinates (I used this type before<\/a>). I will use the “Units of Measure”-feature in F# to distinct between <degree> vs. <radian> and <m> vs. <km>. If you are not familiar with this concept see Andrew Kennedy’s excellent blog series about Units of Measures in F#<\/a>.<\/p>\n

open <\/span>Microsoft.FSharp.Math.SI\n  \n[<Measure>]\ntype <\/span>degree\n\n[<Measure>]\ntype <\/span>radian =\n  static member <\/span>per_degree = Math.PI\/180.0<degree\/radian>\n  \n[<Measure>]\ntype <\/span>km =  \n  <\/font>static member <\/span>per_meter = 1000.<m\/km><\/pre>\n
type <\/span>Location =\n  {Latitude:float<degree>; \n   Longitude:float<degree> }\n    \n  member <\/span>x.YPos = x.Longitude\n  member <\/span>x.XPos = x.Latitude        \n  member <\/span>x.Longitude_radian = x.Longitude * radian.per_degree  \n  member <\/span>x.Latitude_radian = x.Latitude * radian.per_degree   \n  member <\/span>x.Coordinates = (x.Longitude,x.Latitude)  \n  \n  static member <\/span>CreateLocation(latitude, longitude) = \n    {new <\/span>Location with\n<\/span>      <\/span>Latitude = latitude and\n      <\/span>Longitude = longitude}<\/pre>\n
Now we can easily compute the Euclidean distance<\/a> for two points in the plane.<\/p>\n
let <\/span>sq x = x * x\nlet <\/span>CalcEuclideanDistance (s:Location) (t:Location) =\n
<\/p>  let <\/span>d1 = (t.Longitude - s.Longitude) \/ 1.<degree> \n  let <\/span>d2 = (t.Latitude - s.Latitude) \/ 1.<degree>\n  ((sq d1 + sq d2) |> Math.Sqrt) * 1.<m><\/pre>\n
If we want to approximate the distance of two cities on the surface of earth, we can use the “Great circle distance<\/a>“.<\/p>\n<\/p>\n
\n
“The great-circle distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere’s interior)” – Wikipedia<\/a><\/p>\n<\/blockquote>\n
let <\/span>kmFactor = 6372.795<km>\nlet <\/span>sin_rad x = Math.Sin(x \/ 1.<radian>)\nlet <\/span>cos_rad x = Math.Cos(x \/ 1.<radian>)\n\n\/\/\/ Great Circle Distance \n<\/span>let <\/span>CalcGreatCircleDistance (s:Location) (t:Location)=\n  if <\/span>s = t then\n    <\/span>0.<m>\n  else\n    let <\/span>factor = kmFactor * km.per_meter\n    let <\/span>b =\n         sin_rad s.Latitude_radian * sin_rad t.Latitude_radian +\n         cos_rad s.Latitude_radian * cos_rad t.Latitude_radian *\n           cos_rad (t.Longitude_radian - s.Longitude_radian) \n    Math.Acos(b) * factor<\/pre>\n
https:\/\/apotheekpillen.nl<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"
If we want to calculate the distance between two objects, we need some sort of distance function. I recently showed how we can compute the “edit distance” between two strings (see Damerau-Levenshtein-Distance in F# – part I, part II and part III). This time I will consider the distance between two points in the plane […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[23,448,8],"tags":[480,482,664,481],"_links":{"self":[{"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/posts\/607"}],"collection":[{"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/comments?post=607"}],"version-history":[{"count":4,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/posts\/607\/revisions"}],"predecessor-version":[{"id":2054,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/posts\/607\/revisions\/2054"}],"wp:attachment":[{"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/media?parent=607"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/categories?post=607"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.navision-blog.de\/blog\/wp-json\/wp\/v2\/tags?post=607"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}