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Jun 24th, 2015
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Lua 1.49 KB | None | 0 0
  1. -- pos - observer position
  2. -- vec - observer vector
  3. -- target - target position
  4.  
  5. function angle (pos, vec, target)
  6.  
  7.     -- Imagine that the observer is wearing spherical helmet of raduis 1.
  8.     -- He looks on the target, and his line of sight crosses the helmet.
  9.     -- We'll calculate this crossing point by normalizing his looking
  10.     -- vector.
  11.    
  12.     -- Normalization means making length of vector equal to 1, but
  13.     -- still pointing to the same direction.
  14.    
  15.     local vec_look = vector.normalize(vec)
  16.    
  17.     -- We also calculate another vector, that is the difference
  18.     -- between observer and target (= position relative to target).
  19.    
  20.     local vec_diff = vector.subtract(target, pos)
  21.    
  22.     -- Well, this requires normalization too.
  23.    
  24.     vec_diff = vector.normalize(vec_diff)
  25.    
  26.     -- Now both are starting from center and pointing to some point
  27.     -- of surface of helmet. We will calculate the distance of
  28.    
  29.     -- Calculate the length between two vectors.
  30.    
  31.     local chord = vector.length(vector.subtract(vec_look, vec_diff))
  32.    
  33.     -- What we have calculated is a chord on some circle of sphere.
  34.     -- Having this we can calculate the angle.
  35.     -- https://en.wikipedia.org/wiki/Chord_%28geometry%29
  36.    
  37.     -- c = 2*r*sin(phi / 2)
  38.    
  39.     -- because r = 1, it degenerates to:
  40.    
  41.     -- c = 2 * sin(phi / 2)
  42.    
  43.     -- c/2 = sin(phi / 2)
  44.    
  45.     -- asin(c/2) = phi / 2
  46.    
  47.     -- 2 * asin(c/2) = phi
  48.    
  49.     local angle = 2 * math.asin(chord / 2)
  50.    
  51.     -- note the result is in radians. Convert it to degrees.
  52.    
  53.     return angle * 180 / math.pi
  54. end
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