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

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.