平面に適当に置いた n 個の質点の重心が原点に来るよう各質点の座標を設定し直す

-- 平面に適当に置いた n 個の質点の重心が原点に来るよう、各質点の座標を設定し直す。
function shift2center(mList)
   local n      = #mList
   local denom  = 0
   local numerX = 0
   local numerY = 0
   for i = 1, n do
      denom  = denom  + mList[i].m
      numerX = numerX + mList[i].m * mList[i].x
      numerY = numerY + mList[i].m * mList[i].y
   end
   local cx = numerX / denom
   local cy = numerY / denom
   for i = 1, n do
      mList[i].x = mList[i].x - cx
      mList[i].y = mList[i].y - cy
   end
   return mList
end


-- 確かめる。
mList = {{m = 3, x =  1 + 10, y =  3 - 20},
         {m = 4, x = -2 + 10, y = -1 - 20},
         {m = 5, x =  1 + 10, y = -1 - 20},}
mList = shift2center(mList)
for i = 1, #mList do
   print(string.format("mList[%d], x = %f, y = %f", i, mList[i].x, mList[i].y))
end