local bump = {
    _VERSION     = 'bump v3.1.7',
    _URL         = 'https://github.com/kikito/bump.lua',
    _DESCRIPTION = 'A collision detection library for Lua',
    _LICENSE     = [[
    MIT LICENSE

    Copyright (c) 2014 Enrique García Cota

    Permission is hereby granted, free of charge, to any person obtaining a
    copy of this software and associated documentation files (the
    "Software"), to deal in the Software without restriction, including
    without limitation the rights to use, copy, modify, merge, publish,
    distribute, sublicense, and/or sell copies of the Software, and to
    permit persons to whom the Software is furnished to do so, subject to
    the following conditions:

    The above copyright notice and this permission notice shall be included
    in all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
    OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
    MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
    IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
    CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
    TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
    SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
    ]]
}

------------------------------------------
-- Auxiliary functions
------------------------------------------
local DELTA = 1e-10 -- floating-point margin of error

local abs, floor, ceil, min, max = math.abs, math.floor, math.ceil, math.min, math.max

local function sign(x)
if x > 0 then return 1 end
if x == 0 then return 0 end
return -1
end

local function nearest(x, a, b)
if abs(a - x) < abs(b - x) then return a else return b end
end

local function assertType(desiredType, value, name)
if type(value) ~= desiredType then
  error(name .. ' must be a ' .. desiredType .. ', but was ' .. tostring(value) .. '(a ' .. type(value) .. ')')
end
end

local function assertIsPositiveNumber(value, name)
if type(value) ~= 'number' or value <= 0 then
  error(name .. ' must be a positive integer, but was ' .. tostring(value) .. '(' .. type(value) .. ')')
end
end

local function assertIsRect(x,y,w,h)
assertType('number', x, 'x')
assertType('number', y, 'y')
assertIsPositiveNumber(w, 'w')
assertIsPositiveNumber(h, 'h')
end

local defaultFilter = function()
return 'slide'
end

------------------------------------------
-- Rectangle functions
------------------------------------------

local function rect_getNearestCorner(x,y,w,h, px, py)
return nearest(px, x, x+w), nearest(py, y, y+h)
end

-- This is a generalized implementation of the liang-barsky algorithm, which also returns
-- the normals of the sides where the segment intersects.
-- Returns nil if the segment never touches the rect
-- Notice that normals are only guaranteed to be accurate when initially ti1, ti2 == -math.huge, math.huge
local function rect_getSegmentIntersectionIndices(x,y,w,h, x1,y1,x2,y2, ti1,ti2)
ti1, ti2 = ti1 or 0, ti2 or 1
local dx, dy = x2-x1, y2-y1
local nx, ny
local nx1, ny1, nx2, ny2 = 0,0,0,0
local p, q, r

for side = 1,4 do
  if     side == 1 then nx,ny,p,q = -1,  0, -dx, x1 - x     -- left
  elseif side == 2 then nx,ny,p,q =  1,  0,  dx, x + w - x1 -- right
  elseif side == 3 then nx,ny,p,q =  0, -1, -dy, y1 - y     -- top
  else                  nx,ny,p,q =  0,  1,  dy, y + h - y1 -- bottom
  end

  if p == 0 then
    if q <= 0 then return nil end
  else
    r = q / p
    if p < 0 then
      if     r > ti2 then return nil
      elseif r > ti1 then ti1,nx1,ny1 = r,nx,ny
      end
    else -- p > 0
      if     r < ti1 then return nil
      elseif r < ti2 then ti2,nx2,ny2 = r,nx,ny
      end
    end
  end
end

return ti1,ti2, nx1,ny1, nx2,ny2
end

-- Calculates the minkowsky difference between 2 rects, which is another rect
local function rect_getDiff(x1,y1,w1,h1, x2,y2,w2,h2)
return x2 - x1 - w1,
       y2 - y1 - h1,
       w1 + w2,
       h1 + h2
end

local function rect_containsPoint(x,y,w,h, px,py)
return px - x > DELTA      and py - y > DELTA and
       x + w - px > DELTA  and y + h - py > DELTA
end

local function rect_isIntersecting(x1,y1,w1,h1, x2,y2,w2,h2)
return x1 < x2+w2 and x2 < x1+w1 and
       y1 < y2+h2 and y2 < y1+h1
end

local function rect_getSquareDistance(x1,y1,w1,h1, x2,y2,w2,h2)
local dx = x1 - x2 + (w1 - w2)/2
local dy = y1 - y2 + (h1 - h2)/2
return dx*dx + dy*dy
end

local function rect_detectCollision(x1,y1,w1,h1, x2,y2,w2,h2, goalX, goalY)
goalX = goalX or x1
goalY = goalY or y1

local dx, dy      = goalX - x1, goalY - y1
local x,y,w,h     = rect_getDiff(x1,y1,w1,h1, x2,y2,w2,h2)

local overlaps, ti, nx, ny

if rect_containsPoint(x,y,w,h, 0,0) then -- item was intersecting other
  local px, py    = rect_getNearestCorner(x,y,w,h, 0, 0)
  local wi, hi    = min(w1, abs(px)), min(h1, abs(py)) -- area of intersection
  ti              = -wi * hi -- ti is the negative area of intersection
  overlaps = true
else
  local ti1,ti2,nx1,ny1 = rect_getSegmentIntersectionIndices(x,y,w,h, 0,0,dx,dy, -math.huge, math.huge)

  -- item tunnels into other
  if ti1
  and ti1 < 1
  and (abs(ti1 - ti2) >= DELTA) -- special case for rect going through another rect's corner
  and (0 < ti1 + DELTA
    or 0 == ti1 and ti2 > 0)
  then
    ti, nx, ny = ti1, nx1, ny1
    overlaps   = false
  end
end

if not ti then return end

local tx, ty

if overlaps then
  if dx == 0 and dy == 0 then
    -- intersecting and not moving - use minimum displacement vector
    local px, py = rect_getNearestCorner(x,y,w,h, 0,0)
    if abs(px) < abs(py) then py = 0 else px = 0 end
    nx, ny = sign(px), sign(py)
    tx, ty = x1 + px, y1 + py
  else
    -- intersecting and moving - move in the opposite direction
    local ti1, _
    ti1,_,nx,ny = rect_getSegmentIntersectionIndices(x,y,w,h, 0,0,dx,dy, -math.huge, 1)
    if not ti1 then return end
    tx, ty = x1 + dx * ti1, y1 + dy * ti1
  end
else -- tunnel
  tx, ty = x1 + dx * ti, y1 + dy * ti
end

return {
  overlaps  = overlaps,
  ti        = ti,
  move      = {x = dx, y = dy},
  normal    = {x = nx, y = ny},
  touch     = {x = tx, y = ty},
  itemRect  = {x = x1, y = y1, w = w1, h = h1},
  otherRect = {x = x2, y = y2, w = w2, h = h2}
}
end

------------------------------------------
-- Grid functions
------------------------------------------

local function grid_toWorld(cellSize, cx, cy)
return (cx - 1)*cellSize, (cy-1)*cellSize
end

local function grid_toCell(cellSize, x, y)
return floor(x / cellSize) + 1, floor(y / cellSize) + 1
end

-- grid_traverse* functions are based on "A Fast Voxel Traversal Algorithm for Ray Tracing",
-- by John Amanides and Andrew Woo - http://www.cse.yorku.ca/~amana/research/grid.pdf
-- It has been modified to include both cells when the ray "touches a grid corner",
-- and with a different exit condition

local function grid_traverse_initStep(cellSize, ct, t1, t2)
local v = t2 - t1
if     v > 0 then
  return  1,  cellSize / v, ((ct + v) * cellSize - t1) / v
elseif v < 0 then
  return -1, -cellSize / v, ((ct + v - 1) * cellSize - t1) / v
else
  return 0, math.huge, math.huge
end
end

local function grid_traverse(cellSize, x1,y1,x2,y2, f)
local cx1,cy1        = grid_toCell(cellSize, x1,y1)
local cx2,cy2        = grid_toCell(cellSize, x2,y2)
local stepX, dx, tx  = grid_traverse_initStep(cellSize, cx1, x1, x2)
local stepY, dy, ty  = grid_traverse_initStep(cellSize, cy1, y1, y2)
local cx,cy          = cx1,cy1

f(cx, cy)

-- The default implementation had an infinite loop problem when
-- approaching the last cell in some occassions. We finish iterating
-- when we are *next* to the last cell
while abs(cx - cx2) + abs(cy - cy2) > 1 do
  if tx < ty then
    tx, cx = tx + dx, cx + stepX
    f(cx, cy)
  else
    -- Addition: include both cells when going through corners
    if tx == ty then f(cx + stepX, cy) end
    ty, cy = ty + dy, cy + stepY
    f(cx, cy)
  end
end

-- If we have not arrived to the last cell, use it
if cx ~= cx2 or cy ~= cy2 then f(cx2, cy2) end

end

local function grid_toCellRect(cellSize, x,y,w,h)
local cx,cy = grid_toCell(cellSize, x, y)
local cr,cb = ceil((x+w) / cellSize), ceil((y+h) / cellSize)
return cx, cy, cr - cx + 1, cb - cy + 1
end

------------------------------------------
-- Responses
------------------------------------------

local touch = function(world, col, x,y,w,h, goalX, goalY, filter)
return col.touch.x, col.touch.y, {}, 0
end

local cross = function(world, col, x,y,w,h, goalX, goalY, filter)
local cols, len = world:project(col.item, x,y,w,h, goalX, goalY, filter)
return goalX, goalY, cols, len
end

local slide = function(world, col, x,y,w,h, goalX, goalY, filter)
goalX = goalX or x
goalY = goalY or y

local tch, move  = col.touch, col.move
if move.x ~= 0 or move.y ~= 0 then
  if col.normal.x ~= 0 then
    goalX = tch.x
  else
    goalY = tch.y
  end
end

col.slide = {x = goalX, y = goalY}

x,y = tch.x, tch.y
local cols, len  = world:project(col.item, x,y,w,h, goalX, goalY, filter)
return goalX, goalY, cols, len
end

local bounce = function(world, col, x,y,w,h, goalX, goalY, filter)
goalX = goalX or x
goalY = goalY or y

local tch, move = col.touch, col.move
local tx, ty = tch.x, tch.y

local bx, by = tx, ty

if move.x ~= 0 or move.y ~= 0 then
  local bnx, bny = goalX - tx, goalY - ty
  if col.normal.x == 0 then bny = -bny else bnx = -bnx end
  bx, by = tx + bnx, ty + bny
end

col.bounce   = {x = bx,  y = by}
x,y          = tch.x, tch.y
goalX, goalY = bx, by

local cols, len    = world:project(col.item, x,y,w,h, goalX, goalY, filter)
return goalX, goalY, cols, len
end

------------------------------------------
-- World
------------------------------------------

local World = {}
local World_mt = {__index = World}

-- Private functions and methods

local function sortByWeight(a,b) return a.weight < b.weight end

local function sortByTiAndDistance(a,b)
if a.ti == b.ti then
  local ir, ar, br = a.itemRect, a.otherRect, b.otherRect
  local ad = rect_getSquareDistance(ir.x,ir.y,ir.w,ir.h, ar.x,ar.y,ar.w,ar.h)
  local bd = rect_getSquareDistance(ir.x,ir.y,ir.w,ir.h, br.x,br.y,br.w,br.h)
  return ad < bd
end
return a.ti < b.ti
end

local function addItemToCell(self, item, cx, cy)
self.rows[cy] = self.rows[cy] or setmetatable({}, {__mode = 'v'})
local row = self.rows[cy]
row[cx] = row[cx] or {itemCount = 0, x = cx, y = cy, items = setmetatable({}, {__mode = 'k'})}
local cell = row[cx]
self.nonEmptyCells[cell] = true
if not cell.items[item] then
  cell.items[item] = true
  cell.itemCount = cell.itemCount + 1
end
end

local function removeItemFromCell(self, item, cx, cy)
local row = self.rows[cy]
if not row or not row[cx] or not row[cx].items[item] then return false end

local cell = row[cx]
cell.items[item] = nil
cell.itemCount = cell.itemCount - 1
if cell.itemCount == 0 then
  self.nonEmptyCells[cell] = nil
end
return true
end

local function getDictItemsInCellRect(self, cl,ct,cw,ch)
local items_dict = {}
for cy=ct,ct+ch-1 do
  local row = self.rows[cy]
  if row then
    for cx=cl,cl+cw-1 do
      local cell = row[cx]
      if cell and cell.itemCount > 0 then -- no cell.itemCount > 1 because tunneling
        for item,_ in pairs(cell.items) do
          items_dict[item] = true
        end
      end
    end
  end
end

return items_dict
end

local function getCellsTouchedBySegment(self, x1,y1,x2,y2)

local cells, cellsLen, visited = {}, 0, {}

grid_traverse(self.cellSize, x1,y1,x2,y2, function(cx, cy)
  local row  = self.rows[cy]
  if not row then return end
  local cell = row[cx]
  if not cell or visited[cell] then return end

  visited[cell] = true
  cellsLen = cellsLen + 1
  cells[cellsLen] = cell
end)

return cells, cellsLen
end

local function getInfoAboutItemsTouchedBySegment(self, x1,y1, x2,y2, filter)
local cells, len = getCellsTouchedBySegment(self, x1,y1,x2,y2)
local cell, rect, l,t,w,h, ti1,ti2, tii0,tii1
local visited, itemInfo, itemInfoLen = {},{},0
for i=1,len do
  cell = cells[i]
  for item in pairs(cell.items) do
    if not visited[item] then
      visited[item]  = true
      if (not filter or filter(item)) then
        rect           = self.rects[item]
        l,t,w,h        = rect.x,rect.y,rect.w,rect.h

        ti1,ti2 = rect_getSegmentIntersectionIndices(l,t,w,h, x1,y1, x2,y2, 0, 1)
        if ti1 and ((0 < ti1 and ti1 < 1) or (0 < ti2 and ti2 < 1)) then
          -- the sorting is according to the t of an infinite line, not the segment
          tii0,tii1    = rect_getSegmentIntersectionIndices(l,t,w,h, x1,y1, x2,y2, -math.huge, math.huge)
          itemInfoLen  = itemInfoLen + 1
          itemInfo[itemInfoLen] = {item = item, ti1 = ti1, ti2 = ti2, weight = min(tii0,tii1)}
        end
      end
    end
  end
end
table.sort(itemInfo, sortByWeight)
return itemInfo, itemInfoLen
end

local function getResponseByName(self, name)
local response = self.responses[name]
if not response then
  error(('Unknown collision type: %s (%s)'):format(name, type(name)))
end
return response
end


-- Misc Public Methods

function World:addResponse(name, response)
self.responses[name] = response
end

function World:project(item, x,y,w,h, goalX, goalY, filter)
assertIsRect(x,y,w,h)

goalX = goalX or x
goalY = goalY or y
filter  = filter  or defaultFilter

local collisions, len = {}, 0

local visited = {}
if item ~= nil then visited[item] = true end

-- This could probably be done with less cells using a polygon raster over the cells instead of a
-- bounding rect of the whole movement. Conditional to building a queryPolygon method
local tl, tt = min(goalX, x),       min(goalY, y)
local tr, tb = max(goalX + w, x+w), max(goalY + h, y+h)
local tw, th = tr-tl, tb-tt

local cl,ct,cw,ch = grid_toCellRect(self.cellSize, tl,tt,tw,th)

local dictItemsInCellRect = getDictItemsInCellRect(self, cl,ct,cw,ch)

for other,_ in pairs(dictItemsInCellRect) do
  if not visited[other] then
    visited[other] = true

    local responseName = filter(item, other)
    if responseName then
      local ox,oy,ow,oh   = self:getRect(other)
      local col           = rect_detectCollision(x,y,w,h, ox,oy,ow,oh, goalX, goalY)

      if col then
        col.other    = other
        col.item     = item
        col.type     = responseName

        len = len + 1
        collisions[len] = col
      end
    end
  end
end

table.sort(collisions, sortByTiAndDistance)

return collisions, len
end

function World:countCells()
local count = 0
for _,row in pairs(self.rows) do
  for _,_ in pairs(row) do
    count = count + 1
  end
end
return count
end

function World:hasItem(item)
return not not self.rects[item]
end

function World:getItems()
local items, len = {}, 0
for item,_ in pairs(self.rects) do
  len = len + 1
  items[len] = item
end
return items, len
end

function World:countItems()
local len = 0
for _ in pairs(self.rects) do len = len + 1 end
return len
end

function World:getRect(item)
local rect = self.rects[item]
if not rect then
  error('Item ' .. tostring(item) .. ' must be added to the world before getting its rect. Use world:add(item, x,y,w,h) to add it first.')
end
return rect.x, rect.y, rect.w, rect.h
end

function World:toWorld(cx, cy)
return grid_toWorld(self.cellSize, cx, cy)
end

function World:toCell(x,y)
return grid_toCell(self.cellSize, x, y)
end


--- Query methods

function World:queryRect(x,y,w,h, filter)

assertIsRect(x,y,w,h)

local cl,ct,cw,ch = grid_toCellRect(self.cellSize, x,y,w,h)
local dictItemsInCellRect = getDictItemsInCellRect(self, cl,ct,cw,ch)

local items, len = {}, 0

local rect
for item,_ in pairs(dictItemsInCellRect) do
  rect = self.rects[item]
  if (not filter or filter(item))
  and rect_isIntersecting(x,y,w,h, rect.x, rect.y, rect.w, rect.h)
  then
    len = len + 1
    items[len] = item
  end
end

return items, len
end

function World:queryPoint(x,y, filter)
local cx,cy = self:toCell(x,y)
local dictItemsInCellRect = getDictItemsInCellRect(self, cx,cy,1,1)

local items, len = {}, 0

local rect
for item,_ in pairs(dictItemsInCellRect) do
  rect = self.rects[item]
  if (not filter or filter(item))
  and rect_containsPoint(rect.x, rect.y, rect.w, rect.h, x, y)
  then
    len = len + 1
    items[len] = item
  end
end

return items, len
end

function World:querySegment(x1, y1, x2, y2, filter)
local itemInfo, len = getInfoAboutItemsTouchedBySegment(self, x1, y1, x2, y2, filter)
local items = {}
for i=1, len do
  items[i] = itemInfo[i].item
end
return items, len
end

function World:querySegmentWithCoords(x1, y1, x2, y2, filter)
local itemInfo, len = getInfoAboutItemsTouchedBySegment(self, x1, y1, x2, y2, filter)
local dx, dy        = x2-x1, y2-y1
local info, ti1, ti2
for i=1, len do
  info  = itemInfo[i]
  ti1   = info.ti1
  ti2   = info.ti2

  info.weight  = nil
  info.x1      = x1 + dx * ti1
  info.y1      = y1 + dy * ti1
  info.x2      = x1 + dx * ti2
  info.y2      = y1 + dy * ti2
end
return itemInfo, len
end


--- Main methods

function World:add(item, x,y,w,h)
local rect = self.rects[item]
if rect then
  error('Item ' .. tostring(item) .. ' added to the world twice.')
end
assertIsRect(x,y,w,h)

self.rects[item] = {x=x,y=y,w=w,h=h}

local cl,ct,cw,ch = grid_toCellRect(self.cellSize, x,y,w,h)
for cy = ct, ct+ch-1 do
  for cx = cl, cl+cw-1 do
    addItemToCell(self, item, cx, cy)
  end
end

return item
end

function World:remove(item)
local x,y,w,h = self:getRect(item)

self.rects[item] = nil
local cl,ct,cw,ch = grid_toCellRect(self.cellSize, x,y,w,h)
for cy = ct, ct+ch-1 do
  for cx = cl, cl+cw-1 do
    removeItemFromCell(self, item, cx, cy)
  end
end
end

function World:update(item, x2,y2,w2,h2)
local x1,y1,w1,h1 = self:getRect(item)
w2,h2 = w2 or w1, h2 or h1
assertIsRect(x2,y2,w2,h2)

if x1 ~= x2 or y1 ~= y2 or w1 ~= w2 or h1 ~= h2 then

  local cellSize = self.cellSize
  local cl1,ct1,cw1,ch1 = grid_toCellRect(cellSize, x1,y1,w1,h1)
  local cl2,ct2,cw2,ch2 = grid_toCellRect(cellSize, x2,y2,w2,h2)

  if cl1 ~= cl2 or ct1 ~= ct2 or cw1 ~= cw2 or ch1 ~= ch2 then

    local cr1, cb1 = cl1+cw1-1, ct1+ch1-1
    local cr2, cb2 = cl2+cw2-1, ct2+ch2-1
    local cyOut

    for cy = ct1, cb1 do
      cyOut = cy < ct2 or cy > cb2
      for cx = cl1, cr1 do
        if cyOut or cx < cl2 or cx > cr2 then
          removeItemFromCell(self, item, cx, cy)
        end
      end
    end

    for cy = ct2, cb2 do
      cyOut = cy < ct1 or cy > cb1
      for cx = cl2, cr2 do
        if cyOut or cx < cl1 or cx > cr1 then
          addItemToCell(self, item, cx, cy)
        end
      end
    end

  end

  local rect = self.rects[item]
  rect.x, rect.y, rect.w, rect.h = x2,y2,w2,h2

end
end

function World:move(item, goalX, goalY, filter)
local actualX, actualY, cols, len = self:check(item, goalX, goalY, filter)

self:update(item, actualX, actualY)

return actualX, actualY, cols, len
end

function World:check(item, goalX, goalY, filter)
filter = filter or defaultFilter

local visited = {[item] = true}
local visitedFilter = function(itm, other)
  if visited[other] then return false end
  return filter(itm, other)
end

local cols, len = {}, 0

local x,y,w,h = self:getRect(item)

local projected_cols, projected_len = self:project(item, x,y,w,h, goalX,goalY, visitedFilter)

while projected_len > 0 do
  local col = projected_cols[1]
  len       = len + 1
  cols[len] = col

  visited[col.other] = true

  local response = getResponseByName(self, col.type)

  goalX, goalY, projected_cols, projected_len = response(
    self,
    col,
    x, y, w, h,
    goalX, goalY,
    visitedFilter
  )
end

return goalX, goalY, cols, len
end


-- Public library functions

bump.newWorld = function(cellSize)
cellSize = cellSize or 64
assertIsPositiveNumber(cellSize, 'cellSize')
local world = setmetatable({
  cellSize       = cellSize,
  rects          = {},
  rows           = {},
  nonEmptyCells  = {},
  responses = {}
}, World_mt)

world:addResponse('touch', touch)
world:addResponse('cross', cross)
world:addResponse('slide', slide)
world:addResponse('bounce', bounce)

return world
end

bump.rect = {
getNearestCorner              = rect_getNearestCorner,
getSegmentIntersectionIndices = rect_getSegmentIntersectionIndices,
getDiff                       = rect_getDiff,
containsPoint                 = rect_containsPoint,
isIntersecting                = rect_isIntersecting,
getSquareDistance             = rect_getSquareDistance,
detectCollision               = rect_detectCollision
}

bump.responses = {
touch  = touch,
cross  = cross,
slide  = slide,
bounce = bounce
}

return bump