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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
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