F# and Path Reduction

1. F# and Path Reduction Kit Eason - @kitlovesfsharp – www.kiteason.com – kit.eason@gmail.com

2. Norway – way too complicated!

3. Way, way too complicated!

4. Ramer–Douglas–Peucker

5. A record type type Point = {Long: double; Lat: double}

6. Distance from line letprivatefindPerpendicularDistance p p1 p2 = if (p1.Long = p2.Long) then abs(p.Long- p1.Long) else let slope = (p2.Lat - p1.Lat) / (p2.Long - p1.Long) let intercept = p1.Lat - (slope * p1.Long) abs(slope *p.Long-p.Lat+ intercept) /sqrt((pown slope 2) +1.)

7. Recursive algorithm letrec Reduce epsilon (points : Point[]) = ifpoints.Length<3|| epsilon =0.then points else letfirstPoint= points.[0] letlastPoint= points.[points.Length-1] letmutable index =-1 letmutabledist=0.0 foriin1..points.Length-1do letcDist=findPerpendicularDistance points.[i] firstPointlastPoint if (cDist>dist) then dist<-cDist index <-i if (dist> epsilon) then let l1 = points.[0..index] let l2 = points.[index..] let r1 = Reduce epsilon l1 let r2 = Reduce epsilon l2 Array.append (r1.[0..r1.Length-2]) r2 else [|firstPoint; lastPoint|]

8. letrec Reduce epsilon (points : Point[]) = ifpoints.Length<3|| epsilon =0.then points else letfirstPoint= points.[0] letlastPoint= points.[points.Length-1] letmutable index =-1 letmutabledist=0.0 foriin1..points.Length-1do letcDist=findPerpendicularDistance points.[i] firstPointlastPoint if (cDist>dist) then dist<-cDist index <-i if (dist> epsilon) then let l1 = points.[0..index] let l2 = points.[index..] let r1 = Reduce epsilon l1 let r2 = Reduce epsilon l2 Array.append (r1.[0..r1.Length-2]) r2 else [|firstPoint; lastPoint|]

9. The data nan nan 8.299972 54.778750 8.300778 54.778278 8.300806 54.775778 8.302417 54.775000 8.302444 54.772472 8.300778 54.771611 8.300750 54.767444 nan nan 8.277417 54.764111 8.277417 54.775750 8.279083 54.776611 8.279111 54.797444

10. Reading the data letprivateReadDatafileName= fileName |>File.ReadAllLines |>Array.breakOn (fun line -> line ="nan nan") |>Array.Parallel.mapToPoints |>FilterCount100

11. Breaking into arrays letbreakOn (f :'a -> bool) (a : array<'a>) = [| let result =ResizeArray() for x in a do if f x then yield result |>Array.ofSeq result.Clear() else result.Add(x) yield result |>Array.ofSeq |]

12. Converting to points letprivateToPoints (lines : array<string>) = lines |>Array.Parallel.map (fun line ->line.Split [|'\t'|]) |>Array.Parallel.map (fun items -> items |>Array.mapDouble.Parse) |>Array.choose (fun doubles ->match doubles with | [|long; lat|] -> Some {Long=long; Lat=lat} | _ -> None)

13. Eliminating tiny islands (and lakes!) letprivateFilterCountminCount groups = groups |>Array.filter (fun g ->Array.length g >minCount)

14. Calling the RDP algorithm let Simplify e polyLines= polyLines |>Array.Parallel.map (fun p -> p |>Reduce.Reduce e)

15. ε = 0

16. ε = 0.001

17. ε = 0.01

18. ε = 0.1

19. ε = 1

20. Out-takes

21. Resources • www.github.com/misterspeedy/coastline • www.fsharp.org • www.fsharpforfunandprofit.com • Chris Smith’s “Animal Guide”