Module: GeoCalc::Intersection

Defined in:
lib/geo_calc/calc/intersection.rb

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.intersection(p1, brng1, p2, brng2) ⇒ Array

Returns the point of intersection of two paths defined by point and bearing

see http:#williams.best.vwh.net/avform.htm#Intersection

Parameters:

  • p1: (GeoPoint) —

    First point

  • brng1: (Number) —

    Initial bearing from first point

  • p2: (GeoPoint) —

    Second point

  • brng2: (Number) —

    Initial bearing from second point

Returns:

  • (Array) —

    Destination point (null if no unique intersection defined)



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# File 'lib/geo_calc/calc/intersection.rb', line 17

def self.intersection p1, brng1, p2, brng2
  lat1 = p1.lat.to_rad
  lon1 = p1.lon.to_rad

  lat2 = p2.lat.to_rad
  lon2 = p2.lon.to_rad

  brng13 = brng1.to_rad
  brng23 = brng2.to_rad

  dlat = lat2-lat1
  dlon = lon2-lon1;

  dist12 = 2*Math.asin( Math.sqrt( Math.sin(dlat/2)*Math.sin(dlat/2) + Math.cos(lat1)*Math.cos(lat2)*Math.sin(dlon/2)*Math.sin(dlon/2) ) )
  return nil if dist12 == 0

  # initial/final bearings between points
  brng_a = begin
    Math.acos( ( Math.sin(lat2) - Math.sin(lat1)*Math.cos(dist12) ) / ( Math.sin(dist12)*Math.cos(lat1) ) )
  rescue # protect against rounding
    0
  end

  brng_b = Math.acos( ( Math.sin(lat1) - Math.sin(lat2)*Math.cos(dist12) ) / ( Math.sin(dist12)*Math.cos(lat2) ) )

  brng12, brng21 = if Math.sin(lon2-lon1) > 0
    [brng_a, 2*Math::PI - brng_b] 
  else
    [2*Math::PI - brng_a, brng_b]
  end

  alpha1 = (brng13 - brng12 + Math::PI) % (2*Math::PI) - Math::PI  # angle 2-1-3
  alpha2 = (brng21 - brng23 + Math::PI) % (2*Math::PI) - Math::PI  # angle 1-2-3

  return nil if (Math.sin(alpha1)==0 && Math.sin(alpha2)==0) # infinite intersections
  return nil if (Math.sin(alpha1)*Math.sin(alpha2) < 0)    # ambiguous intersection

  # alpha1 = Math.abs(alpha1);
  # alpha2 = Math.abs(alpha2);
  # ... Ed Williams takes abs of alpha1/alpha2, but seems to break calculation?

  alpha3 = Math.acos( -Math.cos(alpha1)*Math.cos(alpha2) + Math.sin(alpha1)*Math.sin(alpha2)*Math.cos(dist12) )

  dist13 = Math.atan2( Math.sin(dist12)*Math.sin(alpha1)*Math.sin(alpha2), Math.cos(alpha2)+Math.cos(alpha1)*Math.cos(alpha3) )

  lat3 = Math.asin( Math.sin(lat1)*Math.cos(dist13) + Math.cos(lat1)*Math.sin(dist13)*Math.cos(brng13) )

  dlon13 = Math.atan2( Math.sin(brng13)*Math.sin(dist13)*Math.cos(lat1), Math.cos(dist13)-Math.sin(lat1)*Math.sin(lat3) )

  lon3 = lon1 + dlon13;
  lon3 = (lon3 + Math::PI) % (2*Math::PI) - Math::PI  # normalise to -180..180ยบ

  [lat3.to_deg, lon3.to_deg]
end

Instance Method Details

#intersection(brng1, p2, brng2) ⇒ Object 



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# File 'lib/geo_calc/calc/intersection.rb', line 3

def intersection brng1, p2, brng2
  GeoCalc::Intersection.intersection self, brng1, p2, brng2
end