How to generate coordinates in between two known points

Question

Background:

I'm working with transport routes and Google provides Route points far apart enough to create 'shapes'. These are the bus/train routes you see in Google Maps.

My Requirement:

Google's points are far enough to create straight lines. However I want a point every, say, 5 metres.

Problem:

So, say I have two points [lat,long]:

[-33.8824219918503,151.206686052582] and [-33.8815434600467,151.206556440037]

Given those two points I can calculate the distance between them. Say it's 1km for the sake of argument.

So we can imagine an imaginary straight line in between those two points.

How do I generate coordinates for that imaginary line for every, say, 5 metres?

Answer 1

Destination point given distance and bearing from start point applied to your problem:

class Numeric
  def to_rad
    self * Math::PI / 180
  end
  def to_deg
    self * 180 / Math::PI
  end
end

include Math

R = 6371.0

def waypoint(φ1, λ1, θ, d)
  φ2 = asin( sin(φ1) * cos(d/R) + cos(φ1) * sin(d/R) * cos(θ) )
  λ2 = λ1 + atan2( sin(θ) * sin(d/R) * cos(φ1), cos(d/R) - sin(φ1) * sin(φ2) )
  λ2 = (λ2 + 3 * Math::PI) % (2 * Math::PI) - Math::PI # normalise to -180..+180°
  [φ2, λ2]
end

φ1, λ1 = -33.to_rad, -71.6.to_rad   # Valparaíso
φ2, λ2 = 31.4.to_rad, 121.8.to_rad  # Shanghai

d = R * acos( sin(φ1) * sin(φ2) + cos(φ1) * cos(φ2) * cos(λ2 - λ1) )
θ = atan2( sin(λ2 - λ1) * cos(φ2), cos(φ1) * sin(φ2) - sin(φ1) * cos(φ2) * cos(λ2 - λ1) )

waypoints = (0..d).step(2000).map { |d| waypoint(φ1, λ1, θ, d) }

markers = waypoints.map { |φ, λ| "#{φ.to_deg},#{λ.to_deg}" }.join("|")

puts "http://maps.googleapis.com/maps/api/staticmap?size=640x320&sensor=false&markers=#{markers}"

Generates a Google Static Maps link with the waypoints from Valparaíso to Shanghai every 2,000 km:

http://maps.googleapis.com/maps/api/staticmap?size=640x320&sensor=false&markers=-33.0,-71.60000000000002|-32.54414813683714,-93.02142653011552|-28.59922979115139,-113.43958859125276|-21.877555679819015,-131.91586675556778|-13.305784544363858,-148.5297601858932|-3.7370081151180683,-163.94988578467394|6.094273692291354,-179.03345538133888|15.493534924596633,165.33401731030006|23.70233917422386,148.3186618914762|29.83806632244171,129.34766276764626

Answer 2

Step 1 - Get the overall distance

Comprehensive answer can be found here: http://www.movable-type.co.uk/scripts/latlong.html

TL;DR:

This uses the ‘haversine’ formula to calculate the great-circle distance between two points – that is, the shortest distance over the earth’s surface – giving an ‘as-the-crow-flies’ distance between the points (ignoring any hills, of course!).

var R = 6371; // km
var dLat = (lat2-lat1).toRad();
var dLon = (lon2-lon1).toRad();
var lat1 = lat1.toRad();
var lat2 = lat2.toRad();

var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
        Math.sin(dLon/2) * Math.sin(dLon/2) * Math.cos(lat1) * Math.cos(lat2); 
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
var distance = R * c;

Step 2 - Get the percentage travelled.

Now you have the distance for this straight line, you can then work out a percentage of the overall distance for each 5 meters.

Step 3 - Apply the percentage travelled to the difference between the Latitude and Longitude

Find out the difference between the starting latitude and the final latitude. With this number, multiply it by the percentage traveled (as a decimal). This can then be added back to the starting latitude to find the current latitude of this point. Repeat for longitude.

Answer 3

The following solution isn't exactly what you've requested, but may suffice for your purposes...

Check the official docs (https://developers.google.com/maps/documentation/javascript/reference) for the interpolate method. From the docs: 'Returns the LatLng which lies the given fraction of the way between the origin LatLng and the destination LatLng.'

So if you know that your original points are, say, 100m apart, and you specify 0.05 as the fraction, the method will return the lat/lng along that line for every 5m.