-- pos - observer position
-- vec - observer vector
-- target - target position

function angle (pos, vec, target)

	-- Imagine that the observer is wearing spherical helmet of raduis 1.
	-- He looks on the target, and his line of sight crosses the helmet.
	-- We'll calculate this crossing point by normalizing his looking
	-- vector.

	-- Normalization means making length of vector equal to 1, but
	-- still pointing to the same direction.

	local vec_look = vector.normalize(vec)

	-- We also calculate another vector, that is the difference
	-- between observer and target (= position relative to target).

	local vec_diff = vector.subtract(target, pos)

	-- Well, this requires normalization too.

	vec_diff = vector.normalize(vec_diff)

	-- Now both are starting from center and pointing to some point
	-- of surface of helmet. We will calculate the distance of

	-- Calculate the length between two vectors.

	local chord = vector.length(vector.subtract(vec_look, vec_diff))

	-- What we have calculated is a chord on some circle of sphere.
	-- Having this we can calculate the angle.
	-- https://en.wikipedia.org/wiki/Chord_%28geometry%29

	-- c = 2*r*sin(phi / 2)

	-- because r = 1, it degenerates to:

	-- c = 2 * sin(phi / 2)

	-- c/2 = sin(phi / 2)

	-- asin(c/2) = phi / 2

	-- 2 * asin(c/2) = phi

	local angle = 2 * math.asin(chord / 2)

	-- note the result is in radians. Convert it to degrees.

	return angle * 180 / math.pi
end

function yaw2vec(yaw, pitch)
	return {
		x = -math.sin(yaw) * math.cos(pitch),
		y = math.sin(pitch),
		z = math.cos(yaw) * math.cos(pitch)}
end

minetest.register_entity("test:human", {
  hp_max = 1,
  physical = true,
  weight = 5,
  collisionbox = {-0.3, -1.0, -0.3, 0.3, 0.8, 0.3},
  visual = "mesh",
  visual_size = {x=1, y=1},
  mesh = "character.x",
  textures = {"character.png"},
  is_visible = true,
  makes_footstep_sound = false,
  automatic_rotate = true,

  -- When that guy is right-clicked, it will say the angle.
  on_rightclick = function(self, clicker)
    local o = self.object;
    local pos = o:getpos()
    local vec = yaw2vec(o:getyaw(), 0)
    local target = minetest.get_player_by_name('singleplayer'):getpos()

    minetest.chat_send_player(clicker:get_player_name(), angle(pos, vec, target))
  end,
})