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 route

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