I'm working on modernizing Rosetta Code's infrastructure. Starting with communications. Please accept this time-limited open invite to RC's Slack.. --Michael Mol (talk) 20:59, 30 May 2020 (UTC)

# Weather routing

Weather routing is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

The weather routing problem has the following parts:

• a predicted surface wind direction and speed, at increments of longitude, latitude, and time
• an expected surface current direction and speed, at increments of longitude, latitude, and time
• 'polar data' describing maximum speed of a sailboat at points of sail for a given speed of wind over water
• regions for sailing (the open ocean) and not (the land, shallows, restricted areas, etc.)
• a starting location and time, and a destination

Given the above information and a specific path, progress and arrival time are determined. The weather routing problem, conversely, is to determine the path which results in the earliest arrival time.

## Go

Translation of: Julia

This runs in only 37 seconds which is surprisingly quick compared to Julia. However, I've just noticed that I'm using an out of date version of Julia (1.0.4) so hopefully the latest version will be able to close the gap.

`package main import (    "fmt"    "io/ioutil"    "log"    "math"    "strconv"    "strings") type matrixF = [][]float64type pred = func(float64) bool /*   Structure that represents a polar CSV file's data.   Note 0 degrees is directly into the wind, 180 degrees is directly downwind.*/type SailingPolar struct {    winds   []float64 // vector of windspeeds    degrees []float64 // vector of angles in degrees of direction relative to the wind    speeds  matrixF   // matrix of sailing speeds indexed by wind velocity and angle of boat to wind} /*   Structure that represents wind and surface current direction and velocity for a given position.   Angles in degrees, velocities in knots.*/type SurfaceParameters struct{ windDeg, windKts, currentDeg, currentKts float64 } // Checks for fatal errors.func check(err error) {    if err != nil {        log.Fatal(err)    }} // Reads a sailing polar CSV file and returns a SailingPolar struct containing the file data.// A sailing polar file is a CSV file, with ';' used as the comma separator instead of a comma.// The first line of file contains labels for the wind velocities that make up columns, and// the first entry of each row makes up a column of angle of sailing direction from wind in degrees.func getPolarData(fileName string) *SailingPolar {    content, err := ioutil.ReadFile(fileName)    check(err)    lines := strings.Split(string(content), "\n")    line0 := strings.TrimSpace(lines)    header := strings.Split(line0, ";")    var winds, degrees []float64    var speeds matrixF    for _, col := range header[1:] {        t, err := strconv.ParseFloat(col, 64)        check(err)        winds = append(winds, t)    }    for _, line := range lines[1:] {        line = strings.TrimSpace(line)        if line == "" {            break // ignore final blank line if there is one        }        cols := strings.Split(line, ";")        f, err := strconv.ParseFloat(cols, 64)        check(err)        degrees = append(degrees, f)        var temp []float64        for _, col := range cols[1:] {            t, err := strconv.ParseFloat(col, 64)            check(err)            temp = append(temp, t)        }        speeds = append(speeds, temp)    }    return &SailingPolar{winds, degrees, speeds}} const R = 6372800.0 // Earth's approximate radius in meters /* various helper methods which work with degrees rather than radians. */ // Converts degrees to radians.func deg2Rad(deg float64) float64 { return math.Mod(deg*math.Pi/180+2*math.Pi, 2*math.Pi) } // Converts radians to degrees.func rad2Deg(rad float64) float64 { return math.Mod(rad*180/math.Pi+360, 360) } // Trig functions.func sind(d float64) float64     { return math.Sin(deg2Rad(d)) }func cosd(d float64) float64     { return math.Cos(deg2Rad(d)) }func asind(d float64) float64    { return rad2Deg(math.Asin(d)) }func atand(x, y float64) float64 { return rad2Deg(math.Atan2(x, y)) } // Calculates the haversine function for two points on the Earth's surface.// Given two latitude, longitude pairs in degrees for a point on the Earth,// get distance in meters and the initial direction of travel in degrees for// movement from point 1 to point 2.func haversine(lat1, lon1, lat2, lon2 float64) (float64, float64) {    dlat := lat2 - lat1    dlon := lon2 - lon1    a := math.Pow(sind(dlat/2), 2) + cosd(lat1)*cosd(lat2)*math.Pow(sind(dlon/2), 2)    c := 2 * asind(math.Sqrt(a))    theta := atand(sind(dlon)*cosd(lat2), cosd(lat1)*sind(lat2)-sind(lat1)*cosd(lat2)*cosd(dlon))    theta = math.Mod(theta+360, 360)    return R * c * 0.5399565, theta} // Returns the index of the first element of 'a' for which 'p' returns true or -1 otherwise.func findFirst(a []float64, p pred) int {    for i, e := range a {        if p(e) {            return i        }    }    return -1} // Returns the index of the last element of 'a' for which 'p' returns true or -1 otherwise.func findLast(a []float64, p pred) int {    for i := len(a) - 1; i >= 0; i-- {        if p(a[i]) {            return i        }    }    return -1} // Calculate the expected sailing speed in a specified direction in knots,// given sailing polar data, a desired point of sail in degrees, and wind speed in knots.func boatSpeed(sp *SailingPolar, pointOfSail, windSpeed float64) float64 {    winds := sp.winds    degrees := sp.degrees    speeds := sp.speeds    udeg := findLast(degrees, func(t float64) bool { return t <= pointOfSail })    odeg := findFirst(degrees, func(t float64) bool { return t >= pointOfSail })    uvel := findLast(winds, func(t float64) bool { return t <= windSpeed })    ovel := findFirst(winds, func(t float64) bool { return t >= windSpeed })    if udeg == -1 || odeg == -1 || uvel == -1 || ovel == -1 {        return -1    }    var frac float64    switch {    case odeg == udeg && uvel == ovel:        frac = 1    case odeg == udeg:        frac = (windSpeed - winds[uvel]) / (winds[ovel] - winds[uvel])    case uvel == ovel:        frac = (pointOfSail - degrees[udeg]) / (degrees[odeg] - degrees[udeg])    default:        frac = ((pointOfSail-degrees[udeg])/(degrees[odeg]-degrees[udeg]) +            (windSpeed-winds[uvel])/(winds[ovel]-winds[uvel])) / 2    }    return speeds[udeg][uvel] + frac*(speeds[odeg][ovel]-speeds[udeg][uvel])} // Calculates the expected net boat speed in a desired direction versus the wind ('azimuth').// This is generally different from the actual boat speed in its actual direction.// Directions are in degrees ('pointos' is point of sail the ship direction from the wind),// and velocity of wind ('ws') is in knots.func sailingSpeed(sp *SailingPolar, azimuth, pointos, ws float64) float64 {    return boatSpeed(sp, pointos, ws) * cosd(math.Abs(pointos-azimuth))} // Calculates the net direction and velocity of a sailing ship.// Arguments are sailing polar data, direction of travel in degrees from north, wind direction in// degrees from north, wind velocity in knots, surface current direction in degrees, and// current velocity in knots.func bestVectorSpeed(sp *SailingPolar, dirTravel, dirWind, windSpeed, dirCur, velCur float64) (float64, float64) {    azimuth := math.Mod(dirTravel-dirWind, 360)    if azimuth < 0 {        azimuth += 360    }    if azimuth > 180 {        azimuth = 360 - azimuth    }    vmg := boatSpeed(sp, azimuth, windSpeed)    other := -1.0    idx := -1    for i, d := range sp.degrees {        ss := sailingSpeed(sp, azimuth, d, windSpeed)        if ss > other {            other = ss            idx = i        }    }    if other > vmg {        azimuth = sp.degrees[idx]        vmg = other    }    dirChosen := deg2Rad(dirWind + azimuth)    wx := vmg * math.Sin(dirChosen)    wy := vmg * math.Cos(dirChosen)    curX := velCur * math.Sin(deg2Rad(dirCur))    curY := velCur * math.Cos(deg2Rad(dirCur))    return rad2Deg(math.Atan2(wy+curY, wx+curX)), math.Sqrt(math.Pow(wx+curX, 2) + math.Pow(wy+curY, 2))} // Calculates the trip time in minutes from (lat1, lon1) to the destination (lat2, lon2).// Uses the data in SurfaceParameters for wind and current velocity and direction.func sailSegmentTime(sp *SailingPolar, p SurfaceParameters, lat1, lon1, lat2, lon2 float64) float64 {    distance, dir := haversine(lat1, lon1, lat2, lon2)    _, vel := bestVectorSpeed(sp, dir, p.windDeg, p.windKts, p.currentDeg, p.currentKts)    // minutes/s * m / (knots * (m/s / knot)) = minutes    return (1.0 / 60.0) * distance / (vel * 1.94384)} /* Structure that represents a point in 2-D space. */type Point2 struct{ x, y int } func (p Point2) add(p2 Point2) Point2  { return Point2{p.x + p2.x, p.y + p2.y} }func (p Point2) equals(p2 Point2) bool { return p.x == p2.x && p.y == p2.y }func (p Point2) String() string        { return fmt.Sprintf("[%d, %d]", p.x, p.y) } /*   Structure that consists of a tuple of latitude and longitude in degrees.   NB: This uses latitude (often considered to be y) first then longitude (often considered to be x).   This latitude, then longitude ordering is as per ISO 6709 (en.wikipedia.org/wiki/ISO_6709).*/type Position struct{ lat, lon float64 } /*  Structure that represents a Position with the SurfaceParameters of wind and current at the Position. */type GridPoint struct {    pt Position    sp SurfaceParameters}type MatrixG = [][]*GridPoint /*   Type alias for a matrix of GridPoints, each Position point with their SurfaceParameters.   A Vector of TimeSlice can give the surface characteristics for an ocean region over time.*/type TimeSlice = MatrixG /* Structure that represents a routing problem. */type RoutingProblem struct {    timeInterval    float64     // the minutes duration for each TimeSlice    timeFrame       []TimeSlice // a vector of sequential timeslices for the ocean region    obstacleIndices []Point2    // the Cartesian indices in each TimeSlice for    // obstacles, such as land or shoals, where the ship may not go    startIndex        int    // the TimeSlice position for time of starting    start             Point2 // starting location on grid of GridPoints    finish            Point2 // destination / finish location on grid of GridPoints    allowRepeatVisits bool   // whether the vessel may overlap its prior path, usually false} /* Structure that represents a timed path. */type TimedPath struct {    duration float64  // minutes total to travel the path    path     []Point2 // vector of Cartesian indices of points in grid for path to travel} func (t TimedPath) String() string           { return fmt.Sprintf("%g %v", t.duration, t.path) }func (t TimedPath) equals(t2 TimedPath) bool { return t.String() == t2.String() } func findMin(a []float64) (float64, int) {    min := a    idx := 0    for i, e := range a[1:] {        if e < min {            min = e            idx = i + 1        }    }    return min, idx} var ntuples = []int{{-1, -1}, {-1, 0}, {-1, 1}, {0, -1}, {0, 1}, {1, -1}, {1, 0}, {1, 1}}var neighbors = make([]Point2, len(ntuples)) func init() {    for i := 0; i < len(ntuples); i++ {        neighbors[i] = Point2{ntuples[i], ntuples[i]}    }} func contains(points []Point2, point Point2) bool {    for _, p := range points {        if p.equals(point) {            return true        }    }    return false} // Returns a list of points surrounding 'p' which are not otherwise excluded.func surround(p Point2, mat TimeSlice, excluded []Point2) []Point2 {    xmax := len(mat)    ymax := len(mat)    var res []Point2    for _, x := range neighbors {        q := x.add(p)        if (0 <= q.x && q.x < xmax) && (0 <= q.y && q.y < ymax) && !contains(excluded, q) {            res = append(res, q)        }    }    return res} // Get the route (as a TimedPath) that minimizes time from start to finish for a given// RoutingProblem (sea parameters) given sailing polar data (ship parameters).func minimumTimeRoute(rp *RoutingProblem, sp *SailingPolar, verbose bool) *TimedPath {    timedPaths := []*TimedPath{&TimedPath{0, []Point2{rp.start}}}    completed := false    minPath := &TimedPath{1000, []Point2{}}    for i := 0; i < 1000; i++ {        var newPaths []*TimedPath        if verbose {            fmt.Printf("Checking %d paths of length %d\n", len(timedPaths), len(timedPaths.path))        }        for _, tpath := range timedPaths {            le := len(tpath.path)            if tpath.path[le-1] == rp.finish {                completed = true                newPaths = append(newPaths, tpath)            } else {                p1 := tpath.path[le-1]                num := int(math.Round(tpath.duration))                den := int(math.Round(rp.timeInterval))                slice := rp.timeFrame[(num/den)%len(rp.timeFrame)]                for _, p2 := range surround(p1, slice, rp.obstacleIndices) {                    if !rp.allowRepeatVisits && contains(tpath.path, p2) {                        continue                    }                    gp1 := slice[p1.x][p1.y]                    gp2 := slice[p2.x][p2.y]                    lat1 := gp1.pt.lat                    lon1 := gp1.pt.lon                    lat2 := gp2.pt.lat                    lon2 := gp2.pt.lon                    t := sailSegmentTime(sp, gp1.sp, lat1, lon1, lat2, lon2)                    path := make([]Point2, len(tpath.path))                    copy(path, tpath.path)                    path = append(path, p2)                    newPaths = append(newPaths, &TimedPath{tpath.duration + t, path})                }            }        }        set := make(map[string]*TimedPath)        for _, np := range newPaths {            set[np.String()] = np        }        timedPaths = timedPaths[:0]        for k := range set {            timedPaths = append(timedPaths, set[k])        }        if completed {            var durations []float64            for _, x := range timedPaths {                durations = append(durations, x.duration)            }            minDur, _ := findMin(durations)            var finished []*TimedPath            for _, x := range timedPaths {                le := len(x.path)                if x.path[le-1] == rp.finish {                    finished = append(finished, x)                }            }            durations = durations[:0]            for _, x := range finished {                durations = append(durations, x.duration)            }            minFinDur, idx := findMin(durations)            if verbose {                fmt.Printf("Current finished minimum: %v, others %v\n", finished[idx], minDur)            }            if minDur == minFinDur {                minPath = finished[idx]                break            }        }    }    return minPath} /*   The data is selected so the best time path is slightly longer than the   shortest length path. The forbidden regions are x, representing land or reef.   The allowed sailing points are . and start and finish are S and F.    x  .  .  F  .  .  x  .  x   .  .  .  .  .  .  .  x  x   x  .  .  x  x  x  .  .  .   .  .  x  x  x  x  .  x  x   x  .  .  .  x  x  .  x  .   x  .  .  .  x  x  .  x  .   .  .  .  .  x  .  .  x  .   x  .  .  .  .  .  .  x  .   .  .  .  S  .  .  .  .  .*/ // These need to be changed to 0-based for Go.var ftuples = []int{    {1, 8}, {2, 1}, {2, 8}, {3, 5}, {3, 8}, {4, 1}, {4, 5}, {4, 6}, {4, 8}, {5, 1},    {5, 5}, {5, 6}, {5, 8}, {6, 3}, {6, 4}, {6, 5}, {6, 6}, {6, 8}, {6, 9}, {7, 1},    {7, 4}, {7, 5}, {7, 6}, {8, 8}, {8, 9}, {9, 1}, {9, 7}, {9, 9},} var forbidden = make([]Point2, len(ftuples)) func init() {    for i := 0; i < len(ftuples); i++ {        forbidden[i] = Point2{ftuples[i] - 1, ftuples[i] - 1}    }} // Create regional wind patterns on the map.func surfaceByLongitude(lon float64) SurfaceParameters {    switch {    case lon < -155.03:        return SurfaceParameters{-5, 8, 150, 0.5}    case lon < -155.99:        return SurfaceParameters{-90, 20, 150, 0.4}    default:        return SurfaceParameters{180, 25, 150, 0.3}    }} // Vary wind speeds over time.func mutateTimeSlices(slices []TimeSlice) {    i := 1    for _, slice := range slices {        for j := 0; j < len(slice); j++ {            for k := 0; k < len(slice[j]); k++ {                x := slice[j][k]                x.sp = SurfaceParameters{x.sp.windDeg, x.sp.windKts * (1 + 0.002*float64(i)),                    x.sp.currentDeg, x.sp.currentKts}            }        }        i++    }} func main() {    startPos := Point2{0, 3} // 0-based    endPos := Point2{8, 3}   // ditto    slices := make([]MatrixG, 200)    for s := 0; s < 200; s++ {        gpoints := make([][]*GridPoint, 9)        for i := 0; i < 9; i++ {            gpoints[i] = make([]*GridPoint, 9)            for j := 0; j < 9; j++ {                pt := Position{19.78 - 1.0/60.0 + float64(i)/60, -155.0 - 5.0/60.0 + float64(j)/60}                gpoints[i][j] = &GridPoint{pt, surfaceByLongitude(pt.lon)}            }        }        slices[s] = gpoints    }    mutateTimeSlices(slices)    routeProb := &RoutingProblem{10, slices, forbidden, 0, startPos, endPos, false}    fileName := "polar.csv"    sp := getPolarData(fileName)    tp := minimumTimeRoute(routeProb, sp, false)    fmt.Println("The route taking the least time found was:\n", tp.path, "\nwhich has duration",        int(tp.duration/60), "hours,", int(math.Round(math.Mod(tp.duration, 60))), "minutes.")}`
Output:
```The route taking the least time found was:
[[0, 3] [0, 4] [1, 5] [2, 6] [3, 6] [4, 6] [5, 6] [6, 6] [7, 5] [7, 4] [8, 3]]
which has duration 4 hours, 44 minutes.
```

## Julia

Brute force optimization search, practical for shorter path lengths, but would require a better algorithm for paths over twice this size.

`module SailingPolars using DelimitedFiles export SailingPolar, SurfaceParameters, getpolardata, deg2rad, rad2deg, cartesian2polarexport polar2cartesian, haversine, inverse_haversine, boatspeed, bestvectorspeedexport sailingspeed, sailsegmenttime """    Structure to represent a polar CSV file's data. Contains a matrix, speeds, of sailing speeds indexed by wind velocity and angle of boat to windwinds is a list of wind speedsdegrees is a list of angles in degrees of direction relative to the windNote 0.0 degrees is directly into the wind, 180 degrees is directly downwind."""struct SailingPolar    winds::Vector{Float32}    degrees::Vector{Float32}    speeds::Matrix{Float32} # speeds[wind direction degrees, windspeed knots]end """    struct SurfaceParameters Structure that represents wind and surface current direction and velocity for a given positionAngles in degrees, velocities in knots"""struct SurfaceParameters    winddeg::Float32    windkts::Float32    currentdeg::Float32    currentkts::Float32end """function getpolardata(filename) Read a sailing polar CSV file and return a SailingPolar containing the file data. A sailing polar file is a CSV file, with ';' used as the comma separator instead of a comma.The first line of file contains labels for the wind velocities that make up columns, andthe first entry of each row makes up a column of angle of sailing direction from wind in degrees"""function getpolardata(filename)    datacells, headercells = readdlm(filename, ';', header=true)    winds = map(x -> parse(Float32, x), headercells[2:end])    degrees = datacells[:, 1]    speeds = datacells[:, 2:end]    return SailingPolar(winds, degrees, speeds)end  const R = 6372800  # Earth's approximate radius in meters """    deg2rad(deg) Convert degrees to radians"""deg2rad(deg) = (deg * π / 180.0 + 2π) % 2π """    rad2deg(rad) Convert radians to degrees"""rad2deg(rad) = (rad * (180.0 / π) + 360.0) % 360.0 """    cartesian2polard(x, y) Convert x, y coordinates to polar coordinates with angle in degrees"""cartesian2polard(x, y) = sqrt(x * x + y * y), atand(x, y) """    polard2cartesian(r, deg) Convert polar coordinates in degrees to cartesian x, y coordinates"""polard2cartesian(r, deg) = r .* sincosd(deg) """    function haversine(lat1, lon1, lat2, lon2) Calculate the haversine function for two points on the Earth's surface. Given two latitude, longitude pairs in degrees for a point on the Earth,get distance in meters and the initial direction of travel in degrees formovement from point 1 to point 2."""function haversine(lat1, lon1, lat2, lon2)    dlat = lat2 - lat1    dlon = lon2 - lon1    a = sind(dlat / 2)^2 + cosd(lat1) * cosd(lat2) * sind(dlon / 2)^2    c = 2.0 * asind(sqrt(a))    theta = atand(sind(dlon) * cosd(lat2),        cosd(lat1) * sind(lat2) - sind(lat1) * cosd(lat2) * cosd(dlon))    theta = (theta + 360) % 360    return R * c * 0.5399565, thetaend """    function inverse_haversine(lat1, lon1, distance, direction) Calculate an inverse haversine function. Takes the point of origin in degrees (latitude, longitude), distance in meters, andinitial direction in degrees, and returns the latitude and longitude of the endpointin degrees after traveling the specified distance."""function inverse_haversine(lat1, lon1, distance, direction)    lat2 = asind(sind(lat1) * cos(distance / R) + cosd(lat1) * sin(distance / R) * cosd(direction))    lon2 = lon1 + atand(sind(direction) * sin(distance / R) * cosd(lat1),                       cos(distance / R) - sind(lat1) * sind(lat2))    return lat2, lon2end """    function boatspeed(sp::SailingPolar, pointofsail, windspeed) Calculate the expected sailing speed in a specified direction in knots,given sailing polar data, a desired point of sail in degrees, and wind speed in knots"""function boatspeed(sp::SailingPolar, pointofsail, windspeed)    winds, degrees, speeds = sp.winds, sp.degrees, sp.speeds    udeg = findlast(t -> t <= pointofsail, degrees)    odeg = findfirst(t -> t >= pointofsail, degrees)    uvel = findlast(t -> t <= windspeed, winds)    ovel = findfirst(t -> t >= windspeed, winds)    if any(t -> t == nothing, [udeg, odeg, uvel, ovel])        return -1.0    end    frac = (odeg == udeg && uvel == ovel) ? 1.0 :            (odeg == udeg) ? (windspeed - winds[uvel]) / (winds[ovel] - winds[uvel]) :            (uvel == ovel) ? (pointofsail - degrees[udeg]) / (degrees[odeg] - degrees[udeg]) :            ((pointofsail - degrees[udeg]) / (degrees[odeg] - degrees[udeg]) +            (windspeed - winds[uvel]) / (winds[ovel] - winds[uvel])) / 2    return speeds[udeg, uvel] + frac * (speeds[odeg, ovel] - speeds[udeg, uvel])end  """    sailingspeed(sp::SailingPolar, azimuth, pointos, ws) Calculate the expected net boat speed in a desired direction versus the wind (azimuth).This is generally different from the actual boat speed in its actual direction.Directions are in degrees (pointos is point of sail, the ship direction from wind),and velocity of wind (ws) is in knots."""sailingspeed(sp, azimuth, pointos, ws) = boatspeed(sp, pointos, ws) * cosd(abs(pointos - azimuth))  """    function bestvectorspeed(sp::SailingPolar, dirtravel, dirwind, windspeed, dircur, velcur) Calculate the net direction and velocity of a sailing ship. Arguments are sailing polar data, direction of travel in degrees from north, wind direction indegrees from north, wind velocity in knots, surface current direction in degrees, andcurrent velocity in knots."""function bestvectorspeed(sp::SailingPolar, dirtravel, dirwind, windspeed, dircur, velcur)    azimuth = (dirtravel - dirwind) % 360.0    azimuth = azimuth < 0 ? azimuth + 360.0 : azimuth    azimuth = azimuth > 180.0 ? 360.0 - azimuth : azimuth    VMG = boatspeed(sp, azimuth, windspeed)    other, idx = findmax([sailingspeed(sp, azimuth, x, windspeed) for x in sp.degrees])    if other > VMG        azimuth = sp.degrees[idx]        VMG = other    end    dirchosen = deg2rad(dirwind + azimuth)    wx, wy = VMG * sin(dirchosen), VMG * cos(dirchosen)    curx, cury = velcur * sin(deg2rad(dircur)), velcur * cos(deg2rad(dircur))    return rad2deg(atan(wy + cury, wx + curx)), sqrt((wx + curx)^2 + (wy + cury)^2)end """    function sailsegmenttime(sp::SailingPolar, p::SurfaceParameters, lat1, lon1, lat2, lon2) Calculate the trip time in minutes from (lat1, lon1) to the destination (lat2, lon2).Uses the data in SurfaceParameters for wind and current velocity and direction."""function sailsegmenttime(sp::SailingPolar, p::SurfaceParameters, lat1, lon1, lat2, lon2)    distance, dir = haversine(lat1, lon1, lat2, lon2)    dir2, vel = bestvectorspeed(sp, dir, p.winddeg, p.windkts, p.currentdeg, p.currentkts)    # minutes/s * m / (knots * (m/s / knot)) = minutes    return (1 / 60) * distance / (vel * 1.94384)end  end # module  module SailingNavigation export Position, lat, lon, GridPoint, TimeSlice, TimedPath, closestpoint, surroundexport RoutingProblem, minimumtimeroute using GeometryTypesusing ..SailingPolars # NB: This uses latitude (often considered to be y) first then longitude (often considered to be x).# This latitude, then longitude ordering is as per ISO 6709 (en.wikipedia.org/wiki/ISO_6709) # Position is a Float32 2-tuple of latitude and longitude in degreesPosition = Point2f0 # latitude from Positionlat(p::Position) = p # longitude from Positionlon(p::Position) = p # A GridPoint is a Position with the SurfaceParameters of wind and current at the Positionmutable struct GridPoint    pt::Position    sp::SurfaceParametersend """    TimeSlice A TimeSlice is a matrix of GridPoints, each Position point with their SurfaceParametersA Vector of TimeSlice can give the surface characteristics for an ocean region over time."""TimeSlice = Matrix{GridPoint} """    mutable struct RoutingProblem timeinterval: the minutes duration for each TimeSlicetimeframe: a vector of sequential timeslices for the ocean regionobstacleindices: the Cartesian indices in each timeslice for    obstacles, such as land or shoals, where the ship may not gostartindex: the timeslice position for time of startingstart: starting location on grid of GridPointsfinish: destination / finish location on grid of GridPointsallowrepeatvisits: whether the vessel may overlap its prior path, usually false"""mutable struct RoutingProblem    timeinterval::Float64 # minutes between timeframe slices    timeframe::Vector{TimeSlice}    obstacleindices::Vector{Point2{Int}}    startindex::Int    start::Point2{Int}    finish::Point2{Int}    allowrepeatvisits::Boolend """    mutable struct TimedPath duration: minutes total to travel the pathpath: vector of Cartesian indices of points in grid for path to travel"""mutable struct TimedPath    duration::Float64    path::Vector{Point2{Int}}end """    closestpoint(p, mat) Get the closest GridPoint in matrix mat to a given position p.p: Cartesian indices of a Position (latitude, longitude in degrees) in grid of GridPointsmat: matrix of Gridpoints"""closestpoint(p, mat) = findmin(gp -> haversine(p, p, gp.pt, gp.pt), mat) function surround(p, mat, excluded)    neighbors = Point2{Int}[(-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 1), (1, -1), (1, 0), (1, 1)]    (xmax, ymax) = size(mat)    return filter(q -> 1 <= q <= xmax && 1 <= q <= ymax && !(q in excluded),        [x + p for x in neighbors])end """    function minimumtimeroute(rp::RoutingProblem, sp::SailingPolar, verbose=false) Get the route (as a TimedPath) that minimizes time from start to finish for a givenRoutingProblem (sea parameters) given sailing polar data (ship parameters)."""function minimumtimeroute(rp::RoutingProblem, sp::SailingPolar, verbose=false)    timedpaths = [TimedPath(0.0, [rp.start])]    completed, mintime, minpath = false, 1000.0, TimedPath(1000.0, [])    for i in 1:1000        newpaths = TimedPath[]        verbose && println("Checking ", length(timedpaths), " paths of length ",            length(timedpaths.path) - 1)        for tpath in timedpaths            if tpath.path[end] == rp.finish                completed = true                push!(newpaths, tpath)            else                p1 = tpath.path[end]                slice = rp.timeframe[div(Int(round(tpath.duration)),                                     Int(round(rp.timeinterval))) %                                     length(rp.timeframe) + 1]                for p2 in surround([p1, p1], slice, rp.obstacleindices)                    !rp.allowrepeatvisits && p2 in tpath.path && continue                    gp1, gp2 = slice[p1, p1], slice[p2, p2]                    lat1, lon1, lat2, lon2 = gp1.pt, gp1.pt, gp2.pt, gp2.pt                    t = sailsegmenttime(sp, gp1.sp, lat1, lon1, lat2, lon2)                    path = deepcopy(tpath.path)                    push!(path, p2)                    push!(newpaths, TimedPath(tpath.duration + t, path))                end            end        end        timedpaths = unique(newpaths)        if completed            mindur = minimum(map(x -> x.duration, timedpaths))            finished = filter(x -> x.path[end] == rp.finish, timedpaths)            minfindur, idx = findmin(map(x -> x.duration, finished))            verbose && println("Current finished minimum: ", finished[idx], ", others \$mindur")            if mindur == minfindur                minpath = finished[idx]                break            end        end    end    return minpathend end # module using GeometryTypesusing .SailingNavigation, .SailingPolars #=The data is selected so the best time path is slightly longer than theshortest length path. The forbidden regions are x, representing land or reef.The allowed sailing points are . and start and finish are S and F. x  .  .  F  .  .  x  .  x.  .  .  .  .  .  .  x  xx  .  .  x  x  x  .  .  ..  .  x  x  x  x  .  x  xx  .  .  .  x  x  .  x  .x  .  .  .  x  x  .  x  ..  .  .  .  x  .  .  x  .x  .  .  .  .  .  .  x  ..  .  .  S  .  .  .  .  .=#const forbidden = Point2{Int}.([    [1, 8], [2, 1], [2, 8], [3, 5], [3, 8], [4, 1], [4, 5], [4, 6], [4, 8], [5, 1],    [5, 5], [5, 6], [5, 8], [6, 3], [6, 4], [6, 5], [6, 6], [6, 8], [6, 9], [7, 1],    [7, 4], [7, 5], [7, 6], [8, 8], [8, 9], [9, 1], [9, 7], [9, 9],]) # Create regional wind patterns on the map.function surfacebylongitude(lon)    return lon < -155.03 ? SurfaceParameters(-5.0, 8, 150, 0.5) :           lon < -155.99 ? SurfaceParameters(-90.0, 20, 150, 0.4) :                           SurfaceParameters(180.0, 25, 150, 0.3)end # Vary wind speeds over time.function mutatetimeslices!(slices)    for (i, slice) in enumerate(slices), x in slice        x.sp = SurfaceParameters(x.sp.winddeg, x.sp.windkts * (1 + 0.002 * i),            x.sp.currentdeg, x.sp.currentkts)    endend  const startpos = Point2{Int}(1, 4)const endpos = Point2{Int}(9, 4)const pmat  = [Position(19.78 - 1/60 + i/60, -155.0 - 5/60 + j/60) for i in 0:8, j in 0:8]const gpoints = map(pt -> GridPoint(pt, surfacebylongitude(lon(pt))), pmat)const slices = [deepcopy(gpoints) for _ in 1:200]mutatetimeslices!(slices) const routeprob = RoutingProblem(10.0, slices, forbidden, 1, startpos, endpos, false)const filename = "polar.csv"const sp = getpolardata(filename)const tp = minimumtimeroute(routeprob, sp) println("The route taking the least time found was:\n    ", tp.path,    "\nwhich has duration \$(div(tp.duration, 60)) hours, \$(rem(tp.duration, 60)) minutes.") `

The polar CSV file used for this solution, named polar.csv, is as follows. Note that this is a very detailed polar, chosen to stress the testing of the code. Most polar files are far smaller, with fewer choices for angle and wind speed.

```TWA\TWS;0;4;5;6;7;8;9;10;11;12;13;14;15;16;17;18;19;20;21;22;23;24;25;26;27;28;29;30;35;40;60;70
40;0;0.53;0.54;0.49;0.4;0.31;0.21;0.16;0.11;0.08;0.05;0.03;0.02;0.01;0;0;0;0;0;0;0;0;0;0;0;0;0;0;-0.01;-0.05;-0.1;-0.11
41;0;0.61;0.62;0.56;0.47;0.36;0.25;0.19;0.14;0.1;0.07;0.04;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;0;0;0;0;-0.04;-0.09;-0.1
44;0;0.89;0.91;0.82;0.69;0.56;0.42;0.33;0.24;0.18;0.13;0.08;0.05;0.03;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;0;0;-0.02;-0.06;-0.06
45;0;0.99;1.02;0.92;0.78;0.64;0.49;0.39;0.29;0.22;0.15;0.1;0.07;0.04;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;0;0;-0.01;-0.05;-0.05
46;0;1.11;1.14;1.02;0.87;0.73;0.57;0.45;0.35;0.26;0.18;0.13;0.08;0.05;0.03;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;0;-0.01;-0.04;-0.05
47;0;1.23;1.25;1.14;0.97;0.82;0.66;0.53;0.41;0.31;0.22;0.15;0.1;0.07;0.04;0.02;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;-0.01;-0.03;-0.04
48;0;1.37;1.37;1.26;1.08;0.93;0.76;0.61;0.48;0.36;0.26;0.19;0.13;0.08;0.05;0.03;0.02;0.01;0.01;0.01;0;0;0;0;0;0;0;0;0;0;-0.02;-0.03
49;0;1.5;1.5;1.39;1.2;1.05;0.87;0.71;0.56;0.42;0.31;0.22;0.15;0.1;0.07;0.04;0.03;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;0;-0.02;-0.02
50;0;1.65;1.64;1.52;1.33;1.18;1;0.81;0.65;0.49;0.37;0.26;0.19;0.13;0.08;0.05;0.04;0.03;0.02;0.01;0.01;0;0;0;0;0;0;0;0;0;-0.01;-0.02
51;0;1.79;1.77;1.67;1.46;1.32;1.13;0.92;0.74;0.57;0.43;0.31;0.22;0.15;0.1;0.07;0.05;0.03;0.02;0.02;0.01;0.01;0;0;0;0;0;0;0;0;-0.01;-0.02
53;0;2.1;2.07;1.99;1.76;1.62;1.4;1.14;0.95;0.74;0.57;0.43;0.31;0.22;0.16;0.1;0.08;0.06;0.04;0.03;0.02;0.01;0.01;0.01;0;0;0;0;0;0;-0.01;-0.01
54;0;2.26;2.22;2.16;1.92;1.78;1.55;1.28;1.06;0.84;0.65;0.5;0.37;0.27;0.19;0.13;0.1;0.07;0.06;0.04;0.03;0.02;0.01;0.01;0;0;0;0;0;0;0;-0.01
55;0;2.43;2.39;2.34;2.09;1.95;1.7;1.42;1.18;0.95;0.74;0.57;0.43;0.32;0.23;0.16;0.12;0.09;0.07;0.05;0.04;0.03;0.02;0.01;0.01;0;0;0;0;0;0;-0.01
60;0;3.29;3.33;3.33;3.08;2.93;2.64;2.29;1.98;1.66;1.36;1.1;0.88;0.68;0.53;0.39;0.32;0.26;0.21;0.17;0.13;0.1;0.07;0.05;0.04;0.03;0.02;0.01;0;0;0;0
70;0;5.2;5.53;5.74;5.59;5.5;5.22;4.84;4.46;3.94;3.51;3.08;2.65;2.26;1.9;1.55;1.38;1.22;1.06;0.92;0.78;0.66;0.55;0.46;0.37;0.3;0.24;0.18;0.03;0;0;0
80;0;6.8;7.43;7.97;8.02;8.23;8.34;8.2;7.9;7.37;6.91;6.43;5.9;5.32;4.72;4.12;3.83;3.55;3.25;2.96;2.67;2.4;2.13;1.88;1.65;1.43;1.22;1.04;0.37;0.09;0.01;0
90;0;7.59;8.5;9.4;9.73;10.4;11.16;11.53;11.56;11.3;11.05;10.77;10.44;9.83;9.07;8.34;8;7.65;7.27;6.88;6.46;6.04;5.61;5.15;4.74;4.33;3.88;3.51;1.72;0.67;0.12;0.03
100;0;7.34;8.25;9.16;9.86;10.5;11.95;12.79;13.5;14.02;14.4;14.37;14.5;14.4;13.92;13.52;13.19;12.79;12.51;12.1;11.66;11.22;10.77;10.26;9.72;9.2;8.58;8.01;4.87;2.51;0.7;0.23
110;0;7.09;7.97;8.84;9.74;10.09;11.85;12.75;13.84;14.99;16.02;16.33;17.1;17.83;17.99;18.32;18.14;17.81;17.84;17.6;17.3;17.05;16.83;16.53;16.03;15.59;15.03;14.37;10.26;6.41;2.32;0.86
120;0;6.59;7.42;8.3;9.1;9.56;10.83;11.6;13.1;13.87;14.66;15.75;16.67;17.63;18.43;19.62;20.17;20.6;21.12;21.55;21.75;21.91;22.07;21.9;21.58;21.29;20.92;20.29;16.47;12.03;5.49;2.26
129;0;6.14;6.93;7.83;8.52;9.09;9.89;10.57;12.42;12.87;13.43;15.23;16.16;17.08;18.07;19.48;20.35;21.22;21.93;22.85;23.44;23.98;24.55;24.59;24.55;24.51;24.46;24;21.56;17.75;9.64;4.25
130;0;6.07;6.87;7.76;8.44;9.02;9.8;10.48;12.29;12.73;13.27;15.08;16.03;16.97;17.96;19.36;20.25;21.15;21.88;22.82;23.44;24.03;24.6;24.66;24.68;24.67;24.64;24.24;22;18.33;10.11;4.5
135;0;5.72;6.57;7.36;8.02;8.65;9.38;10.11;11.52;11.97;12.55;13.85;15.31;16.31;17.33;18.54;19.48;20.35;21.28;22.3;23.08;24.09;24.63;24.69;24.78;24.79;24.91;24.82;23.74;20.98;12.39;5.78
136;0;5.66;6.5;7.28;7.93;8.57;9.3;10.04;11.34;11.82;12.42;13.62;15.06;16.17;17.2;18.35;19.29;20.15;21.12;22.15;22.96;24.07;24.6;24.67;24.76;24.75;24.85;24.81;23.98;21.45;12.8;6.03
139;0;5.42;6.31;6.92;7.67;8.34;9.08;9.86;10.86;11.32;12.03;12.99;14.3;15.73;16.76;17.76;18.71;19.53;20.6;21.66;22.54;23.92;24.44;24.53;24.64;24.58;24.65;24.67;24.47;22.68;13.79;6.73
140;0;5.35;6.22;6.79;7.59;8.26;9;9.8;10.72;11.16;11.89;12.79;14.06;15.5;16.62;17.57;18.51;19.32;20.43;21.49;22.4;23.84;24.36;24.46;24.58;24.51;24.57;24.61;24.56;23.02;14.08;6.96
141;0;5.29;6.12;6.67;7.48;8.18;8.93;9.74;10.57;11.02;11.77;12.62;13.82;15.26;16.47;17.38;18.32;19.04;20.28;21.31;22.07;23.53;24;24.21;24.29;24.43;24.48;24.55;24.61;23.33;14.31;7.18
142;0;5.23;6.02;6.57;7.39;8.1;8.86;9.67;10.43;10.88;11.64;12.45;13.59;15.03;16.24;17.14;18.06;18.77;19.98;21.01;21.75;23.18;23.65;23.86;23.95;24.34;24.39;24.48;24.61;23.61;14.54;7.4
143;0;5.16;5.93;6.45;7.3;8;8.78;9.54;10.27;10.75;11.5;12.28;13.36;14.8;16.01;16.9;17.81;18.5;19.69;20.72;21.43;22.84;23.31;23.52;23.61;24.05;24.27;24.41;24.57;23.85;14.8;7.6
144;0;5.09;5.83;6.33;7.23;7.92;8.66;9.41;10.13;10.62;11.39;12.13;13.13;14.57;15.78;16.65;17.56;18.24;19.41;20.43;21.12;22.5;22.97;23.19;23.28;23.73;24.08;24.33;24.49;24.04;15;7.8
145;0;5.02;5.73;6.23;7.15;7.85;8.55;9.28;9.98;10.51;11.27;11.98;12.92;14.35;15.56;16.42;17.31;17.97;19.13;20.14;20.82;22.17;22.64;22.87;22.96;23.42;23.81;24.23;24.41;24.19;15.14;7.98
146;0;4.96;5.64;6.12;7.07;7.77;8.43;9.15;9.84;10.38;11.16;11.83;12.71;14.12;15.35;16.19;17.07;17.72;18.86;19.86;20.51;21.84;22.31;22.56;22.65;23.12;23.48;23.94;24.33;24.3;15.3;8.16
148;0;4.82;5.45;5.91;6.9;7.59;8.21;8.89;9.55;10.14;10.89;11.55;12.29;13.7;14.92;15.74;16.6;17.23;18.32;19.3;19.91;21.2;21.67;21.95;22.05;22.53;22.87;23.38;24.13;24.39;15.52;8.46
149;0;4.76;5.35;5.81;6.78;7.49;8.09;8.78;9.42;10.01;10.76;11.41;12.1;13.48;14.71;15.52;16.36;16.98;18.06;19.03;19.63;20.89;21.37;21.67;21.77;22.26;22.61;23.12;23.98;24.37;15.57;8.58
150;0;4.69;5.26;5.7;6.67;7.37;7.96;8.64;9.26;9.86;10.6;11.24;11.89;13.26;14.48;15.29;16.11;16.73;17.79;18.74;19.33;20.55;21.04;21.37;21.48;21.98;22.34;22.83;23.69;24.11;15.6;8.67
155;0;4.33;4.74;5.16;6.16;6.79;7.33;7.96;8.51;9.15;9.81;10.4;10.85;12.14;13.37;14.1;14.87;15.48;16.42;17.3;17.8;18.88;19.39;19.86;20;20.54;20.97;21.45;22.25;22.77;15.38;8.89
160;0;4.09;4.41;4.83;5.77;6.39;6.94;7.55;8.04;8.67;9.28;9.83;10.24;11.46;12.69;13.39;14.11;14.73;15.6;16.41;16.87;17.85;18.4;18.97;19.15;19.72;20.2;20.65;21.35;21.84;14.95;8.74
162;0;4;4.29;4.69;5.62;6.23;6.77;7.38;7.86;8.48;9.07;9.6;10;11.18;12.42;13.1;13.81;14.43;15.27;16.06;16.5;17.43;18;18.62;18.81;19.39;19.89;20.33;20.99;21.48;14.76;8.61
168;0;3.74;3.93;4.35;5.15;5.75;6.31;6.93;7.34;7.92;8.45;8.95;9.35;10.44;11.68;12.32;12.99;13.63;14.39;15.11;15.5;16.31;16.94;17.7;17.92;18.53;19.08;19.49;19.99;20.46;14.34;8.3
170;0;3.69;3.85;4.27;5.04;5.65;6.22;6.82;7.23;7.8;8.31;8.8;9.22;10.27;11.51;12.15;12.81;13.45;14.19;14.9;15.28;16.06;16.7;17.51;17.73;18.34;18.91;19.31;19.77;20.22;14.24;8.24
174;0;3.57;3.69;4.11;4.83;5.43;6.01;6.62;7;7.55;8.03;8.5;8.93;9.95;11.19;11.81;12.45;13.11;13.81;14.48;14.84;15.57;16.24;17.11;17.35;17.98;18.57;18.95;19.33;19.77;14.03;8.13
180;0;3.51;3.6;4.03;4.71;5.31;5.91;6.51;6.88;7.41;7.88;8.33;8.79;9.78;11.02;11.63;12.26;12.93;13.61;14.26;14.61;15.31;15.99;16.9;17.15;17.79;18.39;18.77;19.09;19.52;13.87;8.07
```
Output:
```The route taking the least time found was:
Point{2,Int64}[[1, 4], [1, 5], [2, 6], [3, 7], [4, 7], [5, 7], [6, 7], [7, 7], [8, 6], [8, 5], [9, 4]]
which has duration 4.0 hours, 43.697879668707344 minutes.
```

## Nim

Translation of: Go

The Go version runs in about 44 seconds on my computer. This Nim version, compiled in release mode (which includes runtime checks), runs in 22 seconds (18 seconds if link time optimization is activated). When compiled without checks (“danger” mode), it runs in 15.5 seconds.

`import hashes, math, parsecsv, sequtils, sets, strutils, sugar type  MatrixF = seq[seq[float]]  Pred = float -> bool   # Structure that represents a polar CSV file's data.  # Note 0 degrees is directly into the wind, 180 degrees is directly downwind.  SailingPolar = object    winds: seq[float]     # Vector of windspeeds.    degrees: seq[float]   # Vector of angles in degrees of direction relative to the wind.    speeds: MatrixF       # Matrix of sailing speeds indexed by wind velocity and angle of boat to wind.   # Structure that represents wind and surface current direction and velocity for a given position.  # Angles in degrees, velocities in knots.  SurfaceParameters = tuple[windDeg, windKts, currentDeg, currentKts: float]  proc getPolarData(filename: string): SailingPolar =  ## Reads a sailing polar CSV file and returns a SailingPolar struct containing the file data.  ## A sailing polar file is a CSV file, with ';' used as the comma separator instead of a comma.  ## The first line of file contains labels for the wind velocities that make up columns, and  ## the first entry of each row makes up a column of angle of sailing direction from wind in degrees.  var parser: CsvParser  parser.open(filename, separator = ';')  parser.readHeaderRow()  for col in 1..parser.headers.high:    result.winds.add parser.headers[col].parseFloat()  while parser.readRow():    if parser.row.len == 0: break # Ignore final blank line if there is one.    result.degrees.add parser.row.parseFloat()    result.speeds.add @[]    for col in 1..parser.row.high:      result.speeds[^1].add parser.row[col].parseFloat()  const R = 6372800.0 # Earth's approximate radius in meters. template sind(d: float): float = sin(degToRad(d))template cosd(d: float): float = cos(degToRad(d))template asind(x: float): float = radToDeg(arcsin(x))template atand(x, y: float): float = radToDeg(arctan2(x, y))  func haversine(lat1, long1, lat2, long2: float): (float, float) =  ## Calculates the Haversine function for two points on the Earth's surface.  ## Given two latitude, longitude pairs in degrees for a point on the Earth,  ## get distance in meters and the initial direction of travel in degrees for  ## movement from point 1 to point 2.  let dlat = lat2 - lat1  let dlong = long2 - long1  let a = sind(dlat/2)^2 + cosd(lat1) * cosd(lat2) * sind(dlong/2)^2  let c = 2 * asind(sqrt(a))  var theta = atand(sind(dlong) * cosd(lat2),                    cosd(lat1) * sind(lat2) - sind(lat1) * cosd(lat2) * cosd(dlong))  theta = (theta + 360) mod 360  result = (R * c * 0.5399565, theta)  func findFirst(a: seq[float]; p: Pred): int =  ## Returns the index of the first element of 'a' for which 'p' returns true or -1 otherwise.  for i in 0..a.high:    if p(a[i]): return i  result = -1  func findLast(a: seq[float]; p: Pred): int =  ## Returns the index of the last element of 'a' for which 'p' returns true or -1 otherwise.  for i in countdown(a.high, 0):    if p(a[i]): return i  result = -1  func boatSpeed(sp: SailingPolar; pointOfSail, windSpeed: float): float =  ## Calculate the expected sailing speed in a specified direction in knots,  ## given sailing polar data, a desired point of sail in degrees, and wind speed in knots.  let    udeg = sp.degrees.findLast(t => t <= pointOfSail)    odeg = sp.degrees.findFirst(t => t >= pointOfSail)    uvel = sp.winds.findLast(t => t <= windSpeed)    ovel = sp.winds.findFirst(t => t >= windSpeed)  if udeg == -1 or odeg == -1 or uvel == -1 or ovel == -1: return -1  let frac = if odeg == udeg and uvel == ovel:               1.0             elif odeg == udeg:               (windSpeed - sp.winds[uvel]) / (sp.winds[ovel] - sp.winds[uvel])             elif uvel == ovel:               (pointOfSail - sp.degrees[udeg]) / (sp.degrees[odeg] - sp.degrees[udeg])             else:               ((pointOfSail - sp.degrees[udeg]) / (sp.degrees[odeg] - sp.degrees[udeg]) +               (windSpeed - sp.winds[uvel]) / (sp.winds[ovel] - sp.winds[uvel])) / 2  result = sp.speeds[udeg][uvel] + frac * (sp.speeds[odeg][ovel] - sp.speeds[udeg][uvel])  func sailingSpeed(sp: SailingPolar; azimuth, pointos, ws: float): float =  ## Calculates the expected net boat speed in a desired direction versus the wind ('azimuth').  ## This is generally different from the actual boat speed in its actual direction.  ## Directions are in degrees ('pointos' is point of sail the ship direction from the wind),  ## and velocity of wind ('ws') is in knots.  sp.boatSpeed(pointos, ws) * cosd(abs(pointos - azimuth))  func bestVectorSpeed(sp: SailingPolar;                     dirTravel, dirWind, windSpeed, dirCur, velCur: float): (float, float) =  ## Calculates the net direction and velocity of a sailing ship.  ## Arguments are sailing polar data, direction of travel in degrees from north, wind direction in  ## degrees from north, wind velocity in knots, surface current direction in degrees, and  ## current velocity in knots.  var azimuth = (dirTravel - dirWind) mod 360  if azimuth < 0: azimuth += 360  if azimuth > 180: azimuth = 360 - azimuth   var vmg = sp.boatSpeed(azimuth, windSpeed)  var other = -1.0  var idx = -1  for i, d in sp.degrees:    let ss = sp.sailingSpeed(azimuth, d, windSpeed)    if ss > other:      other = ss      idx = i  if other > vmg:    azimuth = sp.degrees[idx]    vmg = other   let    dirChosen = dirWind + azimuth    wx = vmg * sind(dirChosen)    wy = vmg * cosd(dirChosen)    curX = velCur * sind(dirCur)    curY = velCur * cosd(dirCur)  result = (atand(wy + curY, wx + curX), sqrt((wx + curX)^2 + (wy + curY)^2))  func sailSegmentTime(sp: SailingPolar; p: SurfaceParameters;                     lat1, long1, lat2, long2: float): float =  ## Calculates the trip time in minutes from (lat1, long1) to the destination (lat2, long2).  ## Uses the data in SurfaceParameters for wind and current velocity and direction.  let (distance, dir) = haversine(lat1, long1, lat2, long2)  let (_, vel) = sp.bestVectorSpeed(dir, p.windDeg, p.windKts, p.currentDeg, p.currentKts)  ## minutes/s * m / (knots * (m/s / knot)) = minutes  result = (1 / 60) * distance / (vel * 1.94384)  # Structure that represents a point in 2-D space.type Point2 = tuple[x, y: int] func `+`(p1, p2: Point2): Point2 = (p1.x + p2.x, p1.y + p2.y) func `\$`(p: Point2): string = "(\$1, \$2)".format(p.x, p.y)  type   # Tuple that consists of a tuple of latitude and longitude in degrees.  # NB: This uses latitude (often considered to be y) first then longitude (often considered to be x).  # This latitude, then longitude ordering is as per ISO 6709 (en.wikipedia.org/wiki/ISO_6709).  Position = tuple[lat, long: float]   # Tuple that represents a Position with the SurfaceParameters of wind and current at the Position.  GridPoint = tuple[pt: Position; sp: SurfaceParameters]   MatrixG = seq[seq[GridPoint]]   # Type alias for a matrix of GridPoints, each Position point with their SurfaceParameters.  # A vector of TimeSlice can give the surface characteristics for an ocean region over time.  TimeSlice = MatrixG   # Structure that represents a routing problem.  RoutingProblem = object    timeInterval: float           # The minutes duration for each TimeSlice.    timeFrame: seq[TimeSlice]     # A vector of sequential timeslices for the ocean region.    obstacleIndices: seq[Point2]  # The cartesian indices in each TimeSlice for obstacles                                  # such as land or shoals, where the ship may not go.    startIndex: int               # The TimeSlice position for time of starting.    start: Point2                 # Starting location on grid of GridPoints.    finish: Point2                # Destination / finish location on grid of GridPoints.    allowRepeatVisits: bool       # Whether the vessel may overlap its prior path, usually false.   # Structure that represents a timed path.  TimedPath = object    duration: float     # Minutes total to travel the path.    path: seq[Point2]   # Vector of cartesian indices of points in grid for path to travel.  func hash(t: TimedPath): Hash =  ## Hash function to allow building a set of TimedPath values.  result = t.duration.hash !& t.path.hash  result = !\$result  const Neighbors: seq[Point2] = @[(-1, -1), (-1,  0), (-1, 1), (0, -1),                                 ( 0,  1), ( 1, -1), ( 1, 0), (1,  1)] func surround(p: Point2; mat: TimeSlice; excluded: openArray[Point2]): seq[Point2] =  ## Returns a list of points surrounding 'p' which are not otherwise excluded.  let xmax = mat.len  let ymax = mat.len  for x in Neighbors:    let q = p + x    if q.x >= 0 and q.x < xmax and q.y >= 0 and q.y < ymax and q notin excluded:      result.add q  proc minimumTimeRoute(rp: RoutingProblem; sp: SailingPolar; verbose: bool): TimedPath =  ## Get the route (as a TimedPath) that minimizes time from start to finish for a given  ## RoutingProblem (sea parameters) given sailing polar data (ship parameters).   var timedPaths = @[TimedPath(duration: 0, path: @[rp.start])]  var completed = false  result = TimedPath(duration: 1000)  for _ in 1..1000:     var newPaths: seq[TimedPath]    if verbose:      echo "Checking \$1 paths of length \$2".format(timedPaths.len, timedPaths.path.len)    for tpath in timedPaths:      if tpath.path[^1] == rp.finish:        completed = true        newPaths.add tpath      else:        let p1 = tpath.path[^1]        let num = tpath.duration.toInt        let den = rp.timeInterval.toInt        let slice = rp.timeFrame[num div den mod rp.timeFrame.len]        for p2 in p1.surround(slice, rp.obstacleIndices):          if not rp.allowRepeatVisits and p2 in tpath.path:            continue          let gp1 = slice[p1.x][p1.y]          let gp2 = slice[p2.x][p2.y]          let (lat1, long1) = gp1.pt          let (lat2, long2) = gp2.pt          let t = sp.sailSegmentTime(gp1.sp, lat1, long1, lat2, long2)          let path = tpath.path & p2          newPaths.add TimedPath(duration: tpath.duration + t, path: path)     timedPaths = newPaths.toHashSet().toSeq()    if completed:      var durations = collect(newSeq, for t in timedPaths: t.duration)      let minDur = min(durations)      let finished = collect(newSeq):                       for t in timedPaths:                         if t.path[^1] == rp.finish: t      durations = collect(newSeq, for f in finished: f.duration)      let idx = minIndex(durations)      let minFinDur = durations[idx]      if verbose:        echo "Current finished minimum: \$1, others \$2".format(finished[idx], minDur)      if minDur == minFinDur:        result = finished[idx]        break  #[ The data is selected so the best time path is slightly longer than the   shortest length path. The forbidden regions are x, representing land or reef.   The allowed sailing points are . and start and finish are S and F.    x  .  .  F  .  .  x  .  x   .  .  .  .  .  .  .  x  x   x  .  .  x  x  x  .  .  .   .  .  x  x  x  x  .  x  x   x  .  .  .  x  x  .  x  .   x  .  .  .  x  x  .  x  .   .  .  .  .  x  .  .  x  .   x  .  .  .  .  .  .  x  .   .  .  .  S  .  .  .  .  .]#  const Forbidden: seq[Point2] = @[(0, 7), (1, 0), (1, 7), (2, 4), (2, 7), (3, 0), (3, 4),                                 (3, 5), (3, 7), (4, 0), (4, 4), (4, 5), (4, 7), (5, 2),                                 (5, 3), (5, 4), (5, 5), (5, 7), (5, 8), (6, 0), (6, 3),                                 (6, 4), (6, 5), (7, 7), (7, 8), (8, 0), (8, 6), (8, 8)]  func surfaceByLongitude(long: float): SurfaceParameters =  ## Create regional wind patterns on the map.  if long < -155.03:    (-5.0, 8.0, 150.0, 0.5)  elif long < -155.99:    (-90.0, 20.0, 150.0, 0.4)  else:    (180.0, 25.0, 150.0, 0.3)  func mutateTimeSlices(slices: var seq[TimeSlice]) =  var i = 1  for slice in slices.mitems:    for j in 0..slice.high:      for x in slice[j].mitems:        x.sp = (x.sp.windDeg, x.sp.windKts * (1 + 0.002 * float64(i)),                x.sp.currentDeg, x.sp.currentKts)    inc i  let startPos: Point2 = (0, 3)let endPos: Point2 = (8, 3)var slices = newSeq[MatrixG](200) for s in 0..slices.high:  var gpoints = newSeq[seq[GridPoint]](9)  for i in 0..<9:    gpoints[i].setLen(9)    for j in 0..<9:      let pt: Position = (19.78 - 1/60 + i/60, -155.0 - 5/60 + j/60)      gpoints[i][j] = (pt, surfaceByLongitude(pt.long))  slices[s] = move(gpoints) slices.mutateTimeSlices()let routeProb = RoutingProblem(timeInterval: 10, timeFrame: slices,                               obstacleIndices: Forbidden, startIndex: 0,                               start: startPos, finish: endPos, allowRepeatVisits: false)let fileName = "polar.csv"let sp = getPolarData(fileName)let tp = routeProb.minimumTimeRoute(sp, false)echo "The route taking the least time found was:"echo tp.pathecho "which has duration ", int(tp.duration / 60), " hours ", toInt(tp.duration mod 60), " minutes."`
Output:
```The route taking the least time found was:
@[(0, 3), (0, 4), (1, 5), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6), (7, 5), (7, 4), (8, 3)]
which has duration 4 hours 44 minutes.```

## Phix

`-- demo/rosetta/Weather_Routing.exwfunction to_numbers(sequence s)    for i=1 to length(s) do        s[i] = to_number(s[i])    end for    return send function function getpolardata(string s)---- A sailing polar file is a CSV file, with ';' used as the comma separator instead of a comma.-- The first line of the file contains labels for the wind velocities that make up columns, and-- the first entry of each row makes up a column of angle of sailing direction from wind in degrees--    sequence lines = split_any(s,"\r\n"),             winds = to_numbers(split(lines,";")[2..\$]),             degrees = {}, speeds = {}    for i=2 to length(lines) do        sequence l = to_numbers(split(lines[i],";"))        if length(l)!=length(winds)+1 then ?9/0 end if        degrees = append(degrees,l)        speeds = append(speeds,l[2..\$])    end for    return {winds, degrees, speeds}end function ---- winds is a list of wind speeds-- degrees is a list of angles in degrees of direction relative to the wind--  (note 0 degrees is directly into the wind, 180 degrees is directly downwind)-- each speeds[i] is an array of length(winds) for each degrees[i]--constant {winds, degrees, speeds} = getpolardata(get_text("polar.csv")) -- (note the distributed version uses a literal string constant instead)constant R = 6372800  -- Earth's approximate radius in metersconstant timeinterval = 10  -- the minutes duration for each TimeSlice function deg2rad(atom deg) return remainder(deg*PI/180+2*PI,2*PI) end functionfunction rad2deg(atom rad) return remainder (rad*(180/PI)+360,360) end functionfunction sind(atom deg) return sin(deg2rad(deg)) end functionfunction cosd(atom deg) return cos(deg2rad(deg)) end functionfunction asind(atom deg) return rad2deg(arcsin(deg)) end functionfunction atand(atom x,y) return rad2deg(atan2(x,y)) end function function haversine(atom lat1, lon1, lat2, lon2)---- Calculate the haversine function for two points on the Earth's surface.-- -- Given two latitude, longitude pairs in degrees for a point on the Earth,-- get distance in meters and the initial direction of travel in degrees for-- movement from point 1 to point 2.--    atom dlat = lat2 - lat1,         dlon = lon2 - lon1,         a = power(sind(dlat/2),2) + cosd(lat1)*cosd(lat2)*power(sind(dlon/2),2),         c = 2.0 * asind(sqrt(a)),         theta = atand(sind(dlon)*cosd(lat2),                       cosd(lat1)*sind(lat2) - sind(lat1)*cosd(lat2)*cosd(dlon))    theta = remainder(theta+360, 360)    return {R*c*0.5399565, theta}end function function find_range(atom v, sequence s)-- Returns the indexes of s of the first >=v, and the last <=v    for i=1 to length(s) do        if s[i]>=v then            for j=length(s) to 1 by -1 do                if s[j]<=v then return {i,j} end if            end for            exit        end if    end for    return {-1,-1}end function function boatspeed(atom pointofsail, windspeed)---- Calculate the expected sailing speed in a specified direction in knots,-- given a desired point of sail in degrees, and wind speed in knots (for-- the previously loaded sailing polar data)--    integer {ld,ud} = find_range(pointofsail, degrees),            {lv,uv} = find_range(windspeed, winds)    if find(-1,{ld, ud, lv, uv}) then return -1 end if    atom wu = winds[uv],         wl = winds[lv],         du = degrees[ud],         dl = degrees[ld],         f    if ld==ud then        f = iff(uv==lv ? 1 :            (wu-windspeed)/(wu-wl))    elsif uv==lv then        f = (du-pointofsail)/(du-dl)    else        f = ((du-pointofsail)/(du-dl)+             (wu-windspeed)/(wu-wl))/2    end if    atom su = speeds[ud,uv],         sl = speeds[ld,lv],         res = su - f*(su-sl)    return resend function function sailingspeed(atom azimuth, pointofsail, ws)---- Calculate the expected net boat speed in a desired direction versus the wind (azimuth).-- This is generally different from the actual boat speed in its actual direction.-- Directions are in degrees (pointofsail is the ship direction from wind),-- and velocity of wind (ws) is in knots.--    return boatspeed(pointofsail, ws) * cosd(abs(pointofsail-azimuth))end function struct SurfaceParameters---- wind and surface current, direction and velocity, for a given position-- directions are in degrees from north, and velocities are in knots.--    public atom winddirection,                windvelocity,                currentdirection,                currentvelocityend struct function bestvectorspeed(atom dirtravel, SurfaceParameters p)---- Calculate the net direction and velocity of a sailing ship.--    atom wd = p.winddirection,         wv = p.windvelocity,         cd = p.currentdirection,         cv = p.currentvelocity,         azimuth = remainder(dirtravel-wd,360)    if azimuth<0 then azimuth += 360 end if    if azimuth>180 then azimuth = 360-azimuth end if    atom vmg = boatspeed(azimuth, wv),         other = -1    integer idx = -1    for i=1 to length(degrees) do        atom ss = sailingspeed(azimuth, degrees[i], wv)        if ss>other then {other,idx} = {ss,i} end if    end for    if other>vmg then        azimuth = degrees[idx]        vmg = other    end if    atom dirchosen = deg2rad(wd + azimuth),         dircurrent = deg2rad(cd),         wx = vmg * sin(dirchosen),         wy = vmg * cos(dirchosen),         curx = cv * sin(dircurrent),         cury = cv * cos(dircurrent)    return sqrt(power(wx+curx,2) + power(wy+cury,2))end function function sailsegmenttime(SurfaceParameters p, atom lat1, lon1, lat2, lon2)---- Calculate the trip time in minutes from (lat1, lon1) to the destination (lat2, lon2).-- Uses the data in SurfaceParameters p for wind and current velocity and direction.--    atom {distance, direction} = haversine(lat1, lon1, lat2, lon2),         velocity = bestvectorspeed(direction, p)    -- minutes/s * m / (knots * (m/s / knot)) = minutes    atom res = (1/60) * distance / (velocity * 1.94384)    return resend function ----  The data is selected so the best time path is slightly longer than the--  shortest length path. The forbidden regions are x, representing land or reef.--  The allowed sailing points are . and start and finish are S and F.--   constant chart = split("""...S.....x......x.....x..x.x...xx.x.x...xx.x...xxxx.xxx..xxx..........xxx..F..x.x""",'\n') function minimum_time_route(sequence timeframe, start, finish)---- Get the fastest route from start to finish for some detailed sea/ship parameters.-- timeframe is a massive 200 * 9x9 * {pt,SurfaceParameters}-- note that polar data (ie winds, degrees, speeds) is static here, for simplicity.--    atom t0 = time(),         mintime = 1000.0    integer xmax = length(chart),            ymax = length(chart),            {py,px} = start    sequence todo = {start},             costs = repeat(repeat(-1,xmax),ymax),  -- (lowest durations)             paths = repeat(repeat(0,xmax),ymax),   -- (single backlinks)             minpath = {}    costs[py,px] = 0    while length(todo) do        {py,px} = todo        todo = todo[2..\$]        atom duration = costs[py,px]        integer sdx = remainder(floor(round(duration)/timeinterval),length(timeframe))+1        sequence s = timeframe[sdx]        for nx=px-1 to px+1 do            for ny=py-1 to py+1 do                if (nx!=px or ny!=py)                 and nx>=1 and nx<=xmax                and ny>=1 and ny<=ymax                 and chart[ny,nx]!='x' then                    sequence gp1 = s[py,px],    -- {pt,SurfaceParameters}                             gp2 = s[ny,nx]     --          ""                    atom {lat1, lon1} = gp1,                         {lat2, lon2} = gp2                    SurfaceParameters sp = gp1                    atom nt = duration + sailsegmenttime(sp, lat1, lon1, lat2, lon2)                    if costs[ny,nx]=-1 or nt<costs[ny,nx] then                        -- a larger (than 9x9) simulation might benefit from not                        -- putting any already-too-long routes back on the todo                        -- list and/or processing todo lowest duration first.                        costs[ny,nx] = nt                        paths[ny,nx] = {py,px}                        if not find({ny,nx},todo) then                            todo = append(todo,{ny,nx})                        end if                    elsif nt==costs[ny,nx] then                        -- (Should multiple same-time routes exist, we could store                         --  multiple back-links and whip up a simple [recursive]                        --  routine to rebuild them all. Or just ignore them.)                        ?9/0                     end if                end if            end for        end for        s = {} -- (simplify debugging)    end while    timeframe = {} -- (simplify debugging)    {py,px} = finish    mintime = costs[py,px]    minpath = {finish}    while true do        object pyx = paths[py,px]        if pyx=0 then exit end if        minpath = prepend(minpath,pyx)        paths[py,px] = 0 -- (be safe, why not)        {py,px} = pyx    end while    if minpath!=start then ?9/0 end if    return {minpath,elapsed(mintime*60),elapsed(time()-t0)}end function function surfacebylongitude(atom lon)-- Create regional wind patterns on the map.    sequence p = iff(lon < -155.03 ? { -5.0,  8, 150, 0.5} :                 iff(lon < -155.99 ? {-90.0, 20, 150, 0.4} :                                     {180.0, 25, 150, 0.3}))    SurfaceParameters res = new(p)    return resend function procedure mutatetimeslices(sequence slices)-- Vary wind speeds over time.    for i=1 to length(slices) do        sequence s = slices[i]        for j=1 to length(s) do            sequence sj = s[j]            for k=1 to length(sj) do                SurfaceParameters p = sj[k]                p.windvelocity = p.windvelocity * (1+0.002*i)            end for        end for    end forend procedure sequence slices = repeat(null,200)for s=1 to length(slices) do    sequence gpoints = repeat(null,9)    for i=1 to 9 do        atom lat = 19.78 - 2/60 + i/60        gpoints[i] = repeat(null,9)        for j=1 to 9 do            atom lon = -155.0 - 6/60 + j/60            gpoints[i][j] = {{lat,lon}, surfacebylongitude(lon)}        end for    end for    slices[s] = gpointsend formutatetimeslices(slices)constant fmt = """The route taking the least time found was:    %vwhich has duration %s [route found in %s]"""printf(1,fmt,minimum_time_route(slices,{1,4},{9,4}))`
Output:
```The route taking the least time found was:
{{1,4},{1,5},{2,6},{3,7},{4,7},{5,7},{6,7},{7,7},{8,6},{8,5},{9,4}}
which has duration 4 hours, 43 minutes and 41s [route found in 0.0s]
```

## Wren

Translation of: Julia

A reasonably faithful translation though I haven't bothered to split the code up into modules (which would mean separate files in Wren) and have dispensed altogether with four functions which aren't actually called.

As Wren uses 0-based indexing the points in the minimum path have coordinates one less than those in the Julia results.

As you'd expect, this takes many times longer than Julia to run (about 24.5 minutes versus 3 minutes 20 seconds) but gets there in the end :)

`import "io" for File /*    Class that represents a polar CSV file's data.    Contains a matrix, 'speeds', of sailing speeds indexed by wind velocity and angle of boat to wind.    'winds' is a list of wind speeds.    'degrees' is a list of angles in degrees of direction relative to the wind.    Note 0 degrees is directly into the wind, 180 degrees is directly downwind.*/class SailingPolar {    construct new(winds, degrees, speeds) {        _winds = winds        _degrees = degrees        _speeds = speeds // speeds[wind direction degrees, windspeed knots]    }    winds { _winds }    degrees { _degrees }    speeds {_speeds }} /*    Class that represents wind and surface current direction and velocity for a given position.    Angles in degrees, velocities in knots.*/class SurfaceParameters {    construct new(windDeg, windKts, currentDeg, currentKts) {        _windDeg = windDeg        _windKts = windKts        _currentDeg = currentDeg        _currentKts = currentKts    }    windDeg { _windDeg }    windKts { _windKts }    currentDeg { _currentDeg }    currentKts { _currentKts }} // Reads a sailing polar CSV file and returns a SailingPolar object containing the file data.// A sailing polar file is a CSV file, with ';' used as the comma separator instead of a comma.// The first line of file contains labels for the wind velocities that make up columns, and// the first entry of each row makes up a column of angle of sailing direction from wind in degrees.var getPolarData = Fn.new { |fileName|    var lines = File.read(fileName).split("\n")    var header = lines.trim().split(";")    var winds = header[1..-1].map { |x| Num.fromString(x) }.toList    var degrees = []    var speeds = []    for (line in lines[1..-1]) {        line = line.trim()        if (line == "") break // ignore final blank line if there is one        var cols = line.split(";")        degrees.add(Num.fromString(cols))        speeds.add(cols[1..-1].map{ |x| Num.fromString(x) }.toList)    }    return SailingPolar.new(winds, degrees, speeds)} var R = 6372800  // Earth's approximate radius in meters /*  Class containing various helper methods which work with degrees rather than radians. */class D {    // Converts degrees to radians.    static deg2Rad(deg) { (deg*Num.pi/180 + 2*Num.pi) % (2*Num.pi) }     // Converts radians to degrees.    static rad2Deg(rad) { (rad*180/Num.pi + 360) % 360 }     // Trig functions.    static sin(d) { deg2Rad(d).sin }    static cos(d) { deg2Rad(d).cos }    static asin(d) { rad2Deg(d.asin) }    static atan(x, y) { rad2Deg(x.atan(y)) }} // Calculates the haversine function for two points on the Earth's surface. // Given two latitude, longitude pairs in degrees for a point on the Earth,// get distance in meters and the initial direction of travel in degrees for// movement from point 1 to point 2.var haversine = Fn.new { |lat1, lon1, lat2, lon2|    var dlat = lat2 - lat1    var dlon = lon2 - lon1    var a = D.sin(dlat/2).pow(2) + D.cos(lat1) * D.cos(lat2) * (D.sin(dlon/2).pow(2))    var c = 2 * D.asin(a.sqrt)    var theta = D.atan(D.sin(dlon) * D.cos(lat2),           D.cos(lat1)*D.sin(lat2) - D.sin(lat1) * D.cos(lat2) * D.cos(dlon))    theta = (theta + 360) % 360    return [R * c * 0.5399565, theta]} // Returns the index of the first element of 'a' for which 'pred' returns true or -1 otherwise.var findFirst = Fn.new { |a, pred|    for (i in 0...a.count) if (pred.call(a[i])) return i    return -1} // Returns the index of the last element of 'a' for which 'pred' returns true or -1 otherwise.var findLast = Fn.new { |a, pred|    for (i in a.count-1..0) if (pred.call(a[i])) return i    return -1} // Calculate the expected sailing speed in a specified direction in knots,// given sailing polar data, a desired point of sail in degrees, and wind speed in knots.var boatSpeed = Fn.new { |sp, pointOfSail, windSpeed|    var winds = sp.winds    var degrees = sp.degrees    var speeds = sp.speeds    var udeg = findLast.call(degrees)  { |t| t <= pointOfSail }    var odeg = findFirst.call(degrees) { |t| t >= pointOfSail }    var uvel = findLast.call(winds)    { |t| t <= windSpeed }    var ovel = findFirst.call(winds)   { |t| t >= windSpeed }    if ([udeg, odeg, uvel, ovel].any { |t| t == -1 }) return -1    var frac = (odeg == udeg && uvel == ovel) ? 1 :               (odeg == udeg) ? (windSpeed - winds[uvel])/(winds[ovel] - winds[uvel]) :               (uvel == ovel) ? (pointOfSail - degrees[udeg])/(degrees[odeg] - degrees[udeg]) :               ((pointOfSail - degrees[udeg])/(degrees[odeg] - degrees[udeg]) +               (windSpeed - winds[uvel])/(winds[ovel] - winds[uvel]))/2    return speeds[udeg][uvel] + frac * (speeds[odeg][ovel] - speeds[udeg][uvel])} // Calculates the expected net boat speed in a desired direction versus the wind ('azimuth').// This is generally different from the actual boat speed in its actual direction.// Directions are in degrees ('pointos' is point of sail the ship direction from the wind),// and velocity of wind ('ws') is in knots.var sailingSpeed = Fn.new { |sp, azimuth, pointos, ws|    return boatSpeed.call(sp, pointos, ws) * D.cos((pointos - azimuth).abs)} // Calculates the net direction and velocity of a sailing ship.// Arguments are sailing polar data, direction of travel in degrees from north, wind direction in// degrees from north, wind velocity in knots, surface current direction in degrees, and// current velocity in knots.var bestVectorSpeed = Fn.new { |sp, dirTravel, dirWind, windSpeed, dirCur, velCur|    var azimuth = (dirTravel - dirWind) % 360    azimuth = (azimuth < 0) ? azimuth + 360 : azimuth    azimuth = (azimuth > 180) ? 360 - azimuth : azimuth    var VMG = boatSpeed.call(sp, azimuth, windSpeed)    var other = -1    var idx = -1    for (i in 0...sp.degrees.count) {        var ss = sailingSpeed.call(sp, azimuth, sp.degrees[i], windSpeed)        if (ss > other) {             other = ss             idx = i        }    }    if (other > VMG) {        azimuth = sp.degrees[idx]        VMG = other    }    var dirChosen = D.deg2Rad(dirWind + azimuth)    var wx = VMG * (dirChosen.sin)    var wy = VMG * (dirChosen.cos)    var curX = velCur * (D.deg2Rad(dirCur).sin)    var curY = velCur * (D.deg2Rad(dirCur).cos)    return [D.rad2Deg((wy + curY).atan(wx + curX)), ((wx + curX).pow(2) + (wy + curY).pow(2)).sqrt]} // Calculates the trip time in minutes from (lat1, lon1) to the destination (lat2, lon2).// Uses the data in SurfaceParameters for wind and current velocity and direction.var sailSegmentTime = Fn.new { |sp, p, lat1, lon1, lat2, lon2|    var h = haversine.call(lat1, lon1, lat2, lon2)    var distance = h    var dir = h    var vel = bestVectorSpeed.call(sp, dir, p.windDeg, p.windKts, p.currentDeg, p.currentKts)    // minutes/s * m / (knots * (m/s / knot)) = minutes    return (1 / 60) * distance / (vel * 1.94384)} /* Class that represents a point in 2-D space. Need value type semantics for comparisons etc. */class Point2 {    construct new(x, y) {        _x = x        _y = y    }    x { _x }    y { _y }     + (other) { Point2.new(x + other.x, y + other.y) }     == (other) { x == other.x && y == other.y }    != (other) { !(this == other) }     toString { "[%(_x), %(_y)]" }} /*    Class that consists of a tuple of latitude and longitude in degrees.    NB: This uses latitude (often considered to be y) first then longitude (often considered to be x).    This latitude, then longitude ordering is as per ISO 6709 (en.wikipedia.org/wiki/ISO_6709).*/class Position {    construct new(lat, lon) {        _lat = lat        _lon = lon    }    lat { _lat }    lon { _lon }} /*  Class that represents a Position with the SurfaceParameters of wind and current at the Position. */class GridPoint {    construct new(pt, sp) {        _pt = pt        _sp = sp    }    pt { _pt }    pt=(value) { _pt = value }    sp { _sp }    sp=(value) { _sp = value }} /*    Class that consists of a matrix of GridPoints, each Position point with their SurfaceParameters.    A Vector of TimeSlice can give the surface characteristics for an ocean region over time.*/class TimeSlice {    construct new(gridPoints) {      _gridPoints = gridpoints    }    gridPoints { _gridPoints }} /*    Class that represents a routing problem and requiring the following parameters:    * timeinterval: the minutes duration for each TimeSlice    * timeframe: a vector of sequential timeslices for the ocean region    * obstacleindices: the Cartesian indices in each timeslice for        obstacles, such as land or shoals, where the ship may not go    * startindex: the timeslice position for time of starting    * start: starting location on grid of GridPoints    * finish: destination / finish location on grid of GridPoints    * allowrepeatvisits: whether the vessel may overlap its prior path, usually false.*/class RoutingProblem {    construct new(timeInterval, timeFrame, obstacleIndices, startIndex, start, finish, allowRepeatVisits) {        _timeInterval = timeInterval // minutes between timeFrame slices        _timeFrame = timeFrame        _obstacleIndices = obstacleIndices        _startIndex = startIndex        _start = start        _finish = finish        _allowRepeatVisits = allowRepeatVisits    }     timeInterval { _timeInterval }    timeFrame  { _timeFrame }    obstacleIndices { _obstacleIndices }    startIndex { _startIndex }    start { _start }    finish { _finish }    allowRepeatVisits { _allowRepeatVisits }} /*    Class that represents a timed path and requires the following parameters:    * duration: minutes total to travel the path    * path: vector of Cartesian indices of points in grid for path to travel.*/class TimedPath {    construct new(duration, path) {        _duration = duration        _path = path    }    duration { _duration }    path { _path }     toString { "%(_duration) %(_path)" }     == (other) { this.toString == other.toString }    != (other) { this.toString != other.toString }} var findMin = Fn.new { |a|    var min = a    var idx = 0    for (i in 1...a.count) {        if (a[i] < min) {            min = a[i]            idx = i        }    }    return [min, idx]} var ntuples = [ [-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1] ]var neighbors = List.filled(ntuples.count, null)(0...ntuples.count).each { |i| neighbors[i] = Point2.new(ntuples[i], ntuples[i]) } // Returns a list of points surrounding 'p' which are not otherwise excluded.var surround = Fn.new { |p, mat, excluded|    var xmax = mat.count    var ymax = mat.count    return neighbors.map { |x| x + p }.where { |q|        return (0 <= q.x && q.x < xmax) && (0 <= q.y && q.y < ymax) && !excluded.contains(q)    }.toList} // Get the route (as a TimedPath) that minimizes time from start to finish for a given// RoutingProblem (sea parameters) given sailing polar data (ship parameters).var minimumTimeRoute = Fn.new { |rp, sp, verbose|    var timedPaths = [TimedPath.new(0, [rp.start])]    var completed = false    var minPath = TimedPath.new(1000, [])    for (i in 0...1000) {        var newPaths = []        verbose && System.print("Checking %(timedPaths.count) paths of length %(timedPaths.path.count)")        for (tpath in timedPaths) {            if (tpath.path[-1] == rp.finish) {                completed = true                newPaths.add(tpath)            } else {                var p1 = tpath.path[-1]                var num = tpath.duration.round                var den = rp.timeInterval.round                var slice = rp.timeFrame[(num/den).truncate % rp.timeFrame.count]                for (p2 in surround.call(p1, slice, rp.obstacleIndices)) {                    if (rp.allowRepeatVisits || !tpath.path.contains(p2)) {                        var gp1 = slice[p1.x][p1.y]                        var gp2 = slice[p2.x][p2.y]                        var lat1 = gp1.pt.lat                        var lon1 = gp1.pt.lon                        var lat2 = gp2.pt.lat                        var lon2 = gp2.pt.lon                        var t = sailSegmentTime.call(sp, gp1.sp, lat1, lon1, lat2, lon2)                        var path = tpath.path.toList                        path.add(p2)                        newPaths.add(TimedPath.new(tpath.duration + t, path))                    }                }            }        }        var set = {}        for (np in newPaths) set[np.toString] = np        timedPaths = set.values.toList        if (completed) {            var minDur = findMin.call(timedPaths.map { |x| x.duration }.toList)            var finished = timedPaths.where { |x| x.path[-1] == rp.finish }.toList            var mi = findMin.call(finished.map { |x| x.duration }.toList)            var minFinDur = mi            var idx = mi            if (verbose) {                System.print("Current finished minimum: %(finished[idx]), others %(minDur)")            }            if (minDur == minFinDur) {                minPath = finished[idx]                break            }        }    }    return minPath} /*    The data is selected so the best time path is slightly longer than the    shortest length path. The forbidden regions are x, representing land or reef.    The allowed sailing points are . and start and finish are S and F.     x  .  .  F  .  .  x  .  x    .  .  .  .  .  .  .  x  x    x  .  .  x  x  x  .  .  .    .  .  x  x  x  x  .  x  x    x  .  .  .  x  x  .  x  .    x  .  .  .  x  x  .  x  .    .  .  .  .  x  .  .  x  .    x  .  .  .  .  .  .  x  .    .  .  .  S  .  .  .  .  .*/ // These need to be changed to 0-based for Wren.var ftuples = [    [1, 8], [2, 1], [2, 8], [3, 5], [3, 8], [4, 1], [4, 5], [4, 6], [4, 8], [5, 1],    [5, 5], [5, 6], [5, 8], [6, 3], [6, 4], [6, 5], [6, 6], [6, 8], [6, 9], [7, 1],    [7, 4], [7, 5], [7, 6], [8, 8], [8, 9], [9, 1], [9, 7], [9, 9]] var forbidden = List.filled(ftuples.count, null)(0...ftuples.count).each { |i| forbidden[i] = Point2.new(ftuples[i]-1, ftuples[i]-1) } // Create regional wind patterns on the map.var surfaceByLongitude = Fn.new { |lon|    return (lon < -155.03) ? SurfaceParameters.new(-5, 8, 150, 0.5) :           (lon < -155.99) ? SurfaceParameters.new(-90, 20, 150, 0.4) :                             SurfaceParameters.new(180, 25, 150, 0.3)} // Vary wind speeds over time.var mutateTimeSlices = Fn.new { |slices|    var i = 1    for (slice in slices) {        for (j in 0...slice.count) {            for (k in 0...slice[j].count) {                var x = slice[j][k]                x.sp = SurfaceParameters.new(x.sp.windDeg, x.sp.windKts * (1 + 0.002 * i),                    x.sp.currentDeg, x.sp.currentKts)             }        }        i = i + 1    }} var startPos = Point2.new(0, 3)  // 0-basedvar endPos = Point2.new(8, 3)    // dittovar slices = List.filled(200, null)for (s in 0...200) {    var gpoints = List.filled(9, null)    for (i in 0..8) {        gpoints[i] = List.filled(9, null)        for (j in 0..8) {            var pt = Position.new(19.78 - 1/60 + i/60, -155.0 - 5/60 + j/60)            gpoints[i][j] = GridPoint.new(pt, surfaceByLongitude.call(pt.lon))        }    }    slices[s] = gpoints}mutateTimeSlices.call(slices)var routeProb = RoutingProblem.new(10, slices, forbidden, 0, startPos, endPos, false)var fileName = "polar.csv"var sp = getPolarData.call(fileName)var tp = minimumTimeRoute.call(routeProb, sp, false)System.print("The route taking the least time found was:\n    %(tp.path) \nwhich has duration " +   "%((tp.duration/60).truncate) hours, %((tp.duration%60).round) minutes.")`
Output:
```The route taking the least time found was:
[[0, 3], [0, 4], [1, 5], [2, 6], [3, 6], [4, 6], [5, 6], [6, 6], [7, 5], [7, 4], [8, 3]]
which has duration 4 hours, 44 minutes.
```