--- Heuristic functions for search algorithms.
-- A <a href="http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html">distance heuristic</a> 
-- provides an *estimate of the optimal distance cost* from a given location to a target. 
-- As such, it guides the pathfinder to the goal, helping it to decide which route is the best.
--
-- This script holds the definition of some built-in heuristics available through jumper.
--
-- Distance functions are internally used by the `pathfinder` to evaluate the optimal path
-- from the start location to the goal. These functions share the same prototype:
--     local function myHeuristic(nodeA, nodeB)
--       -- function body
--     end
-- Jumper features some built-in distance heuristics, namely `MANHATTAN`, `EUCLIDIAN`, `DIAGONAL`, `CARDINTCARD`.
-- You can also supply your own heuristic function, following the same template as above.


local abs = math.abs
local sqrt = math.sqrt
local sqrt2 = sqrt(2)
local max, min = math.max, math.min

local Heuristics = {}
  --- Manhattan distance.
  -- <br/>This heuristic is the default one being used by the `pathfinder` object.
  -- <br/>Evaluates as <code>distance = |dx|+|dy|</code>
  -- @class function
  -- @tparam node nodeA a node
  -- @tparam node nodeB another node
  -- @treturn number the distance from __nodeA__ to __nodeB__
	-- @usage
  -- -- First method
  -- pathfinder:setHeuristic('MANHATTAN')
  -- -- Second method
  -- local Distance = require ('jumper.core.heuristics')
  -- pathfinder:setHeuristic(Distance.MANHATTAN)
  function Heuristics.MANHATTAN(nodeA, nodeB) 
		local dx = abs(nodeA._x - nodeB._x)
    local dy = abs(nodeA._y - nodeB._y)
    local dz = abs(nodeA._z - nodeB._z)
		return (dx + dy + dz) 
	end
  
  --- Euclidian distance.
  -- <br/>Evaluates as <code>distance = squareRoot(dx*dx+dy*dy)</code>
  -- @class function
  -- @tparam node nodeA a node
  -- @tparam node nodeB another node
  -- @treturn number the distance from __nodeA__ to __nodeB__
	-- @usage
  -- -- First method
  -- pathfinder:setHeuristic('EUCLIDIAN')
  -- -- Second method
  -- local Distance = require ('jumper.core.heuristics')
  -- pathfinder:setHeuristic(Distance.EUCLIDIAN) 
  function Heuristics.EUCLIDIAN(nodeA, nodeB)
		local dx = nodeA._x - nodeB._x
    local dy = nodeA._y - nodeB._y
    local dz = nodeA._z - nodeB._z
		return sqrt(dx*dx+dy*dy+dz*dz)
	end
  
  --- Diagonal distance.
  -- <br/>Evaluates as <code>distance = max(|dx|, abs|dy|)</code>
  -- @class function
  -- @tparam node nodeA a node
  -- @tparam node nodeB another node
  -- @treturn number the distance from __nodeA__ to __nodeB__
	-- @usage
  -- -- First method
  -- pathfinder:setHeuristic('DIAGONAL')
  -- -- Second method
  -- local Distance = require ('jumper.core.heuristics')
  -- pathfinder:setHeuristic(Distance.DIAGONAL)
  function Heuristics.DIAGONAL(nodeA, nodeB)
		local dx = abs(nodeA._x - nodeB._x)
		local dy = abs(nodeA._y - nodeB._y)	
		return max(dx,dy) 
	end
  
  --- Cardinal/Intercardinal distance.
  -- <br/>Evaluates as <code>distance = min(dx, dy)*squareRoot(2) + max(dx, dy) - min(dx, dy)</code>
  -- @class function
  -- @tparam node nodeA a node
  -- @tparam node nodeB another node
  -- @treturn number the distance from __nodeA__ to __nodeB__
	-- @usage
  -- -- First method
  -- pathfinder:setHeuristic('CARDINTCARD')
  -- -- Second method
  -- local Distance = require ('jumper.core.heuristics')
  -- pathfinder:setHeuristic(Distance.CARDINTCARD)
  function Heuristics.CARDINTCARD(nodeA, nodeB)
		local dx = abs(nodeA._x - nodeB._x)
		local dy = abs(nodeA._y - nodeB._y)	
    return min(dx,dy) * sqrt2 + max(dx,dy) - min(dx,dy)
  end

return Heuristics