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