vector_extras/init.lua

local load_time_start = os.clock()

local funcs = {}

function funcs.pos_to_string(pos)
	return "("..pos.x.."|"..pos.y.."|"..pos.z..")"
end

local r_corr = 0.25 --remove a bit more nodes (if shooting diagonal) to let it look like a hole (sth like antialiasing)

-- this doesn't need to be calculated every time
local f_1 = 0.5-r_corr
local f_2 = 0.5+r_corr

--returns information about the direction
local function get_used_dir(dir)
	local abs_dir = {x=math.abs(dir.x), y=math.abs(dir.y), z=math.abs(dir.z)}
	local dir_max = math.max(abs_dir.x, abs_dir.y, abs_dir.z)
	if dir_max == abs_dir.x then
		local tab = {"x", {x=1, y=dir.y/dir.x, z=dir.z/dir.x}}
		if dir.x >= 0 then
			tab[3] = "+"
		end
		return tab
	end
	if dir_max == abs_dir.y then
		local tab = {"y", {x=dir.x/dir.y, y=1, z=dir.z/dir.y}}
		if dir.y >= 0 then
			tab[3] = "+"
		end
		return tab
	end
	local tab = {"z", {x=dir.x/dir.z, y=dir.y/dir.z, z=1}}
	if dir.z >= 0 then
		tab[3] = "+"
	end
	return tab
end

local function node_tab(z, d)
	local n1 = math.floor(z*d+f_1)
	local n2 = math.floor(z*d+f_2)
	if n1 == n2 then
		return {n1}
	end
	return {n1, n2}
end

local function return_line(pos, dir, range) --range ~= length
	local tab = {}
	local num = 1
	local t_dir = get_used_dir(dir)
	local dir_typ = t_dir[1]
	if t_dir[3] == "+" then
		f_tab = {0, range, 1}
	else
		f_tab = {0, -range, -1}
	end
	local d_ch = t_dir[2]
	if dir_typ == "x" then
		for d = f_tab[1],f_tab[2],f_tab[3] do
			local x = d
			local ytab = node_tab(d_ch.y, d)
			local ztab = node_tab(d_ch.z, d)
			for _,y in ipairs(ytab) do
				for _,z in ipairs(ztab) do
					tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
					num = num+1
				end
			end
		end
	elseif dir_typ == "y" then
		for d = f_tab[1],f_tab[2],f_tab[3] do
			local xtab = node_tab(d_ch.x, d)
			local y = d
			local ztab = node_tab(d_ch.z, d)
			for _,x in ipairs(xtab) do
				for _,z in ipairs(ztab) do
					tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
					num = num+1
				end
			end
		end
	else
		for d = f_tab[1],f_tab[2],f_tab[3] do
			local xtab = node_tab(d_ch.x, d)
			local ytab = node_tab(d_ch.y, d)
			local z = d
			for _,x in ipairs(xtab) do
				for _,y in ipairs(ytab) do
					tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
					num = num+1
				end
			end
		end
	end
	return tab
end

function funcs.rayIter(pos, dir)
	-- make a table of possible movements
	local step = {}
	for i in pairs(pos) do
		local v = math.sign(dir[i])
		if v ~= 0 then
			step[i] = v
		end
	end

	local p
	return function()
		if not p then
			-- avoid skipping the first position
			p = vector.round(pos)
			return vector.new(p)
		end

		-- find the position which has the smallest distance to the line
		local choose = {}
		local choosefit = vector.new()
		for i in pairs(step) do
			choose[i] = vector.new(p)
			choose[i][i] = choose[i][i] + step[i]
			choosefit[i] = vector.scalar(vector.normalize(vector.subtract(choose[i], pos)), dir)
		end
		p = choose[vector.get_max_coord(choosefit)]

		return vector.new(p)
	end
end

function funcs.fine_line(pos, dir, range)
	if not range then --dir = pos2
		dir, range = vector.direction(pos, dir), vector.distance(pos, dir)
	end
	local result,n = {},1
	for p in vector.rayIter(pos, dir) do
		if vector.distance(p, pos) > range then
			break
		end
		result[n] = p
		n = n+1
	end
	return result
end

function funcs.line(pos, dir, range, alt)
	--assert_vector(pos)
	if alt then
		if not range then --dir = pos2
			dir, range = vector.direction(pos, dir), vector.distance(pos, dir)
		end
		return return_line(pos, dir, range)
	end
	if range then
		dir = vector.round(vector.multiply(dir, range))
	else --dir = pos2
		dir = vector.subtract(dir, pos)
	end
	local line,n = {},1
	for _,i in ipairs(vector.threeline(dir.x, dir.y, dir.z)) do
		line[n] = {x=pos.x+i[1], y=pos.y+i[2], z=pos.z+i[3]}
		n = n+1
	end
	return line
end

local twolines = {}
function funcs.twoline(x, y)
	local pstr = x.." "..y
	local line = twolines[pstr]
	if line then
		return line
	end
	line = {}
	local n = 1
	local dirx = 1
	if x < 0 then
		dirx = -dirx
	end
	local ymin, ymax = 0, y
	if y < 0 then
		ymin, ymax = ymax, ymin
	end
	local m = y/x --y/0 works too
	local dir = 1
	if m < 0 then
		dir = -dir
	end
	for i = 0,x,dirx do
		local p1 = math.max(math.min(math.floor((i-0.5)*m+0.5), ymax), ymin)
		local p2 = math.max(math.min(math.floor((i+0.5)*m+0.5), ymax), ymin)
		for j = p1,p2,dir do
			line[n] = {i, j}
			n = n+1
		end
	end
	twolines[pstr] = line
	return line
end

local threelines = {}
function funcs.threeline(x, y, z)
	local pstr = x.." "..y.." "..z
	local line = threelines[pstr]
	if line then
		return line
	end
	if x ~= math.floor(x) then
		minetest.log("error", "[vector_extras] INFO: The position used for vector.threeline isn't round.")
	end
	local two_line = vector.twoline(x, y)
	line = {}
	local n = 1
	local zmin, zmax = 0, z
	if z < 0 then
		zmin, zmax = zmax, zmin
	end
	local m = z/math.hypot(x, y)
	local dir = 1
	if m < 0 then
		dir = -dir
	end
	for _,i in ipairs(two_line) do
		local px, py = unpack(i)
		local ph = math.hypot(px, py)
		local z1 = math.max(math.min(math.floor((ph-0.5)*m+0.5), zmax), zmin)
		local z2 = math.max(math.min(math.floor((ph+0.5)*m+0.5), zmax), zmin)
		for pz = z1,z2,dir do
			line[n] = {px, py, pz}
			n = n+1
		end
	end
	threelines[pstr] = line
	return line
end

function funcs.sort_positions(ps, preferred_coords)
	preferred_coords = preferred_coords or {"z", "y", "x"}
	local a,b,c = unpack(preferred_coords)
	local function ps_sorting(p1, p2)
		if p1[a] == p2[a] then
			if p1[b] == p2[a] then
				if p1[c] < p2[c] then
					return true
				end
			elseif p1[b] < p2[b] then
				return true
			end
		elseif p1[a] < p2[a] then
			return true
		end
	end
	table.sort(ps, ps_sorting)
end

function funcs.scalar(v1, v2)
	return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z
end

function funcs.cross(v1, v2)
	return {
		x = v1.y*v2.z - v1.z*v2.y,
		y = v1.z*v2.x - v1.x*v2.z,
		z = v1.x*v2.y - v1.y*v2.x
	}
end

--not optimized
--local areas = {}
function funcs.plane(ps)
	-- sort positions and imagine the first one (A) as vector.zero
	ps = vector.sort_positions(ps)
	local pos = ps[1]
	local B = vector.subtract(ps[2], pos)
	local C = vector.subtract(ps[3], pos)

	-- get the positions for the fors
	local cube_p1 = {x=0, y=0, z=0}
	local cube_p2 = {x=0, y=0, z=0}
	for i in pairs(cube_p1) do
		cube_p1[i] = math.min(B[i], C[i], 0)
		cube_p2[i] = math.max(B[i], C[i], 0)
	end
	cube_p1 = vector.apply(cube_p1, math.floor)
	cube_p2 = vector.apply(cube_p2, math.ceil)

	local vn = vector.normalize(vector.cross(B, C))

	local nAB = vector.normalize(B)
	local nAC = vector.normalize(C)
	local angle_BAC = math.acos(vector.scalar(nAB, nAC))

	local nBA = vector.multiply(nAB, -1)
	local nBC = vector.normalize(vector.subtract(C, B))
	local angle_ABC = math.acos(vector.scalar(nBA, nBC))

	for z = cube_p1.z, cube_p2.z do
		for y = cube_p1.y, cube_p2.y do
			for x = cube_p1.x, cube_p2.x do
				local p = {x=x, y=y, z=z}
				local n = -vector.scalar(p, vn)/vector.scalar(vn, vn)
				if math.abs(n) <= 0.5 then
					local ep = vector.add(p, vector.multiply(vn, n))
					local nep = vector.normalize(ep)
					local angle_BAep = math.acos(vector.scalar(nAB, nep))
					local angle_CAep = math.acos(vector.scalar(nAC, nep))
					local angldif = angle_BAC - (angle_BAep+angle_CAep)
					if math.abs(angldif) < 0.001 then
						ep = vector.subtract(ep, B)
						nep = vector.normalize(ep)
						local angle_ABep = math.acos(vector.scalar(nBA, nep))
						local angle_CBep = math.acos(vector.scalar(nBC, nep))
						local angldif = angle_ABC - (angle_ABep+angle_CBep)
						if math.abs(angldif) < 0.001 then
							table.insert(ps, vector.add(pos, p))
						end
					end
				end
			end
		end
	end
	return ps
end

function funcs.straightdelay(s, v, a)
	if not a then
		return s/v
	end
	return (math.sqrt(v*v+2*a*s)-v)/a
end

vector.zero = vector.new()

function funcs.sun_dir(time)
	if not time then
		time = minetest.get_timeofday()
	end
	local t = (time-0.5)*5/6+0.5 --the sun rises at 5 o'clock, not at 6
	if t < 0.25
	or t > 0.75 then
		return
	end
	local tmp = math.cos(math.pi*(2*t-0.5))
	return {x=tmp, y=math.sqrt(1-tmp*tmp), z=0}
end

function funcs.inside(pos, minp, maxp)
	for _,i in pairs({"x", "y", "z"}) do
		if pos[i] < minp[i]
		or pos[i] > maxp[i] then
			return false
		end
	end
	return true
end

function funcs.minmax(p1, p2)
	local p1 = vector.new(p1)
	local p2 = vector.new(p2)
	for _,i in ipairs({"x", "y", "z"}) do
		if p1[i] > p2[i] then
			p1[i], p2[i] = p2[i], p1[i]
		end
	end
	return p1, p2
end

function funcs.move(p1, p2, s)
	return vector.round(
		vector.add(
			vector.multiply(
				vector.direction(
					p1,
					p2
				),
				s
			),
			p1
		)
	)
end

function funcs.from_number(i)
	return {x=i, y=i, z=i}
end

local explosion_tables = {}
function funcs.explosion_table(r)
	local table = explosion_tables[r]
	if table then
		return table
	end

	local t1 = os.clock()
	local tab, n = {}, 1

	local tmp = r*r + r
	for x=-r,r do
		for y=-r,r do
			for z=-r,r do
				local rc = x*x+y*y+z*z
				if rc <= tmp then
					local np={x=x, y=y, z=z}
					if math.floor(math.sqrt(rc) +0.5) > r-1 then
						tab[n] = {np, true}
					else
						tab[n] = {np}
					end
					n = n+1
				end
			end
		end
	end
	explosion_tables[r] = tab
	minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
	return tab
end

local default_nparams = {
   offset = 0,
   scale = 1,
   seed = 1337,
   octaves = 6,
   persist = 0.6
}
function funcs.explosion_perlin(rmin, rmax, nparams)
	local t1 = os.clock()

	local r = math.ceil(rmax)
	nparams = nparams or {}
	for i,v in pairs(default_nparams) do
		nparams[i] = nparams[i] or v
	end
	nparams.spread = nparams.spread or vector.from_number(r*5)

	local pos = {x=math.random(-30000, 30000), y=math.random(-30000, 30000), z=math.random(-30000, 30000)}
	local map = minetest.get_perlin_map(nparams, vector.from_number(r+r+1)):get3dMap_flat(pos)

	local id = 1

	local bare_maxdist = rmax*rmax
	local bare_mindist = rmin*rmin

	local mindist = math.sqrt(bare_mindist)
	local dist_diff = math.sqrt(bare_maxdist)-mindist
	mindist = mindist/dist_diff

	local pval_min, pval_max

	local tab, n = {}, 1
	for z=-r,r do
		local bare_dist = z*z
		for y=-r,r do
			local bare_dist = bare_dist+y*y
			for x=-r,r do
				local bare_dist = bare_dist+x*x
				local add = bare_dist < bare_mindist
				local pval, distdiv
				if not add
				and bare_dist <= bare_maxdist then
					distdiv = math.sqrt(bare_dist)/dist_diff-mindist
					pval = math.abs(map[id]) -- strange perlin values…
					if not pval_min then
						pval_min = pval
						pval_max = pval
					else
						pval_min = math.min(pval, pval_min)
						pval_max = math.max(pval, pval_max)
					end
					add = true--distdiv < 1-math.abs(map[id])
				end

				if add then
					tab[n] = {{x=x, y=y, z=z}, pval, distdiv}
					n = n+1
				end
				id = id+1
			end
		end
	end

	map = nil
	collectgarbage()

	-- change strange values
	local pval_diff = pval_max - pval_min
	pval_min = pval_min/pval_diff

	for n,i in pairs(tab) do
		if i[2] then
			local new_pval = math.abs(i[2]/pval_diff - pval_min)
			if i[3]+0.33 < new_pval then
				tab[n] = {i[1]}
			elseif i[3] < new_pval then
				tab[n] = {i[1], true}
			else
				tab[n] = nil
			end
		end
	end

	minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
	return tab
end

local circle_tables = {}
function funcs.circle(r)
	local table = circle_tables[r]
	if table then
		return table
	end

	local t1 = os.clock()
	local tab, n = {}, 1

	for i = -r, r do
		for j = -r, r do
			if math.floor(math.sqrt(i*i+j*j)+0.5) == r then
				tab[n] = {x=i, y=0, z=j}
				n = n+1
			end
		end
	end
	circle_tables[r] = tab
	minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
	return tab
end

local ring_tables = {}
function funcs.ring(r)
	local table = ring_tables[r]
	if table then
		return table
	end

	local t1 = os.clock()
	local tab, n = {}, 1

	local tmp = r*r
	local p = {x=math.floor(r+0.5), z=0}
	while p.x > 0 do
		tab[n] = p
		n = n+1
		local p1, p2 = {x=p.x-1, z=p.z}, {x=p.x, z=p.z+1}
		local dif1 = math.abs(tmp-p1.x*p1.x-p1.z*p1.z)
		local dif2 = math.abs(tmp-p2.x*p2.x-p2.z*p2.z)
		if dif1 <= dif2 then
			p = p1
		else
			p = p2
		end
	end

	local tab2, n = {}, 1
	for _,i in ipairs(tab) do
		for _,j in ipairs({
			{i.x, i.z},
			{-i.z, i.x},
			{-i.x, -i.z},
			{i.z, -i.x},
		}) do
			tab2[n] = {x=j[1], y=0, z=j[2]}
			n = n+1
		end
	end
	ring_tables[r] = tab2
	minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
	return tab2
end

	--~ posy(t) = att + bt + c
	--~ vely(t) = 2at + b
	--~ accy(t) = 2a

	--~ a = -0.5gravity
	--~ vely(0) = b = vel.y
	--~ posy(0) = c = pos.y

	--~ posy(t) = -0.5gravity*tt + vel.y*t + pos.y
	--~ vely(t) = -gravity*t + vel.y

	--~ Scheitel:
	--~ vely(t) = 0 = -gravity*t + vel.y
	--~ t = vel.y / gravity

	--~ 45°
	--~ vely(t) = +/-1 = -gravity*t + vel.y
	--~ t = (vel.y - 1) / gravity //links
	--~ t = (vel.y + 1) / gravity //rechts

	--~ yswitch = posy(t) //links und rechts gleich
	--~ yswitch = -0.5gravity*((vel.y + 1) / gravity)^2 + vel.y*(vel.y + 1) / gravity + pos.y
	--~ yswitch = -0.5(vel.y + 1)^2 / gravity + (vel.y^2 + vel.y) / gravity + pos.y
	--~ yswitch = -0.5(vel.y^2 + 2vel.y + 1) / gravity + (vel.y^2 + vel.y) / gravity + pos.y
	--~ yswitch = (-0.5vel.y^2 - vel.y - 0.5 + vel.y^2 + vel.y) / gravity + pos.y
	--~ yswitch = (0.5vel.y^2 - 0.5) / gravity + pos.y

	--~ yswitch = -0.5gravity*((vel.y - 1) / gravity)^2 + vel.y*(vel.y - 1) / gravity + pos.y
	--~ yswitch = -0.5(vel.y - 1)^2 / gravity + (vel.y^2 - vel.y) / gravity + pos.y
	--~ yswitch = (-0.5(vel.y - 1)^2  + vel.y^2 - vel.y) / gravity + pos.y
	--~ yswitch = (-0.5(vel.y^2 - 2vel.y + 1)  + vel.y^2 - vel.y) / gravity + pos.y
	--~ yswitch = (-0.5vel.y^2  + vel.y - 0.5  + vel.y^2 - vel.y) / gravity + pos.y
	--~ yswitch = (0.5vel.y^2  - 0.5) / gravity + pos.y

	--~ posy nach t umstellen, kleineres beim Aufstieg, größeres beim Fall
	--~ posy = -0.5gravity*tt + vel.y*t + pos.y
	--~ 0 = -0.5gravity*tt + vel.y*t + pos.y - posy //→Mitternachtsformel
	--~ t = -vel.y +-rt(vel.y^2 -4(-0.5gravity)(pos.y - posy)) / 2(-0.5gravity)
	--~ t = -vel.y +-rt(vel.y^2 +2gravity(pos.y - posy)) / gravity
	--~ t_rise = -vel.y - rt(vel.y^2 +2gravity(pos.y - posy)) / gravity
	--~ t_fall = -vel.y + rt(vel.y^2 +2gravity(pos.y - posy)) / gravity

	--~ posx(t) = vel.x * t + pos.x
	--~ posz(t) = vel.z * t + pos.z

	--~ posx nach t umstellen
	--~ posx - pos.x = vel.x * t
	--~ t = (posx - pos.x) / vel.x


local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount)
	local pointcount = 0

	-- the height of the 45° angle point
	local yswitch = 0.5 * (vel.y * vel.y  - 1) / gravity + pos.y

	local t_fall_start = (vel.y + 1) / gravity
	local t_raise_end = (vel.y - 1) / gravity
	if t_fall_start > 0 then
		-- the right 45° angle point wasn't passed yet
		if t_raise_end > 0 then
			-- put points from before the 45° angle
			for y = math.ceil(pos.y), math.floor(yswitch +.5) do
				local t = -vel.y
					- math.sqrt(vel.y * vel.y - 2 * gravity * (y - pos.y)) / gravity
				local p = {
					x = math.floor(vel.x * t + pos.x +.5),
					y = y,
					z = math.floor(vel.z * t + pos.z +.5),
					name = "default:stone"
				}
				pointcount = pointcount+1
				waypoints[pointcount] = {p, t}
				if pointcount == max_pointcount then
					return
				end
			end
		end
		-- smaller and bigger horizonzal pivot
		local shp, bhp
		if math.abs(vel.x) > math.abs(vel.z) then
			shp = "z"
			bhp = "x"
		else
			shp = "x"
			bhp = "z"
		end
		-- put points between the 45° angles
		local cstart, cdir
		local cend = math.floor(vel[bhp] * t_fall_start + pos[bhp] +.5)
		if vel[bhp] > 0 then
			cstart = math.floor(math.max(pos[bhp],
				vel[bhp] * t_raise_end + pos[bhp]) +.5)
			cdir = 1
		else
			cstart = math.floor(math.min(pos[bhp],
				vel[bhp] * t_raise_end + pos[bhp]) +.5)
			cdir = -1
		end
		for i = cstart, cend, cdir do
			local t = (i - pos[bhp]) / vel[bhp]
			local p = {
				[bhp] = i,
				y = math.floor(-0.5 * gravity * t * t + vel.y * t + pos.y +.5),
				[shp] = math.floor(vel[shp] * t + pos[shp] +.5),
				name = "default:wood"
			}
			pointcount = pointcount+1
			waypoints[pointcount] = {p, t}
			if pointcount == max_pointcount then
				return
			end
		end
	end
	-- put points from after the 45° angle
	local y = math.floor(math.min(yswitch, pos.y) +.5)
	while pointcount < max_pointcount do
		local t = -vel.y
			+ math.sqrt(vel.y * vel.y + 2 * gravity * (pos.y - y)) / gravity
		local p = {
			x = math.floor(vel.x * t + pos.x +.5),
			y = y,
			z = math.floor(vel.z * t + pos.z +.5),
			name = "default:mese"
		}
		pointcount = pointcount+1
		waypoints[pointcount] = {p, t}
		y = y-1
	end
end
		--~ local ps = vector.throw_parabola(player:getpos(), player:get_look_dir(),
			--~ 0.03, 80, true)
		--~ for i = 1,#ps do
			--~ minetest.set_node(ps[i], ps[i])
		--~ end

function funcs.throw_parabola(pos, vel, gravity, point_count, thicken)
	local waypoints = {}
	get_parabola_points(pos, vel, gravity, waypoints, point_count)
	local ps = {}
	for i = 1,#waypoints do
		ps[i] = waypoints[i][1]
	end
	return ps
end

function funcs.chunkcorner(pos)
	return {x=pos.x-pos.x%16, y=pos.y-pos.y%16, z=pos.z-pos.z%16}
end

function funcs.point_distance_minmax(p1, p2)
	local p1 = vector.new(p1)
	local p2 = vector.new(p2)
	local min, max, vmin, vmax, num
	for _,i in ipairs({"x", "y", "z"}) do
		num = math.abs(p1[i] - p2[i])
		if not vmin or num < vmin then
			vmin = num
			min = i
		end
		if not vmax or num > vmax then
			vmax = num
			max = i
		end
	end
	return min, max
end

function funcs.collision(p1, p2)
	local clear, node_pos, collision_pos, max, min, dmax, dcmax, pt
	clear, node_pos = minetest.line_of_sight(p1, p2)
	if clear then
		return false
	end
	collision_pos = {}
	min, max = funcs.point_distance_minmax(node_pos, p2)
	if node_pos[max] > p2[max] then
		collision_pos[max] = node_pos[max] - 0.5
	else
		collision_pos[max] = node_pos[max] + 0.5
	end
	dmax = p2[max] - node_pos[max]
	dcmax = p2[max] - collision_pos[max]
	pt = dcmax/dmax

	for _,i in ipairs({"x", "y", "z"}) do
		collision_pos[i] = p2[i] - (p2[i] - node_pos[i]) * pt
	end
	return true, collision_pos, node_pos
end

function funcs.get_data_from_pos(tab, z,y,x)
	local data = tab[z]
	if data then
		data = data[y]
		if data then
			return data[x]
		end
	end
end

function funcs.set_data_to_pos(tab, z,y,x, data)
	if tab[z] then
		if tab[z][y] then
			tab[z][y][x] = data
			return
		end
		tab[z][y] = {[x] = data}
		return
	end
	tab[z] = {[y] = {[x] = data}}
end

function funcs.set_data_to_pos_optional(tab, z,y,x, data)
	if vector.get_data_from_pos(tab, z,y,x) ~= nil then
		return
	end
	funcs.set_data_to_pos(tab, z,y,x, data)
end

function funcs.remove_data_from_pos(tab, z,y,x)
	if vector.get_data_from_pos(tab, z,y,x) == nil then
		return
	end
	tab[z][y][x] = nil
	if not next(tab[z][y]) then
		tab[z][y] = nil
	end
	if not next(tab[z]) then
		tab[z] = nil
	end
end

function funcs.get_data_pos_table(tab)
	local t,n = {},1
	local minz, miny, minx, maxz, maxy, maxx
	for z,yxs in pairs(tab) do
		if not minz then
			minz = z
			maxz = z
		else
			minz = math.min(minz, z)
			maxz = math.max(maxz, z)
		end
		for y,xs in pairs(yxs) do
			if not miny then
				miny = y
				maxy = y
			else
				miny = math.min(miny, y)
				maxy = math.max(maxy, y)
			end
			for x,v in pairs(xs) do
				if not minx then
					minx = x
					maxx = x
				else
					minx = math.min(minx, x)
					maxx = math.max(maxx, x)
				end
				t[n] = {z,y,x, v}
				n = n+1
			end
		end
	end
	return t, {x=minx, y=miny, z=minz}, {x=maxx, y=maxy, z=maxz}, n-1
end

function funcs.update_minp_maxp(minp, maxp, pos)
	for _,i in pairs({"z", "y", "x"}) do
		minp[i] = math.min(minp[i], pos[i])
		maxp[i] = math.max(maxp[i], pos[i])
	end
end

function funcs.quickadd(pos, z,y,x)
	if z then
		pos.z = pos.z+z
	end
	if y then
		pos.y = pos.y+y
	end
	if x then
		pos.x = pos.x+x
	end
end

function funcs.unpack(pos)
	return pos.z, pos.y, pos.x
end

function funcs.get_max_coord(vec)
	if vec.x < vec.y then
		if vec.y < vec.z then
			return "z"
		end
		return "y"
	end
	if vec.x < vec.z then
		return "z"
	end
	return "x"
end

function funcs.get_max_coords(pos)
	if pos.x < pos.y then
		if pos.y < pos.z then
			return "z", "y", "x"
		end
		if pos.x < pos.z then
			return "y", "z", "x"
		end
		return "y", "x", "z"
	end
	if pos.x < pos.z then
		return "z", "x", "y"
	end
	if pos.y < pos.z then
		return "x", "z", "y"
	end
	return "x", "y", "z"
end

function funcs.serialize(vec)
	return "{x=" .. vec.x .. ",y=" .. vec.y .. ",z=" .. vec.z .. "}"
end


--dofile(minetest.get_modpath("vector_extras").."/vector_meta.lua")

for name,func in pairs(funcs) do
	if vector[name] then
		minetest.log("error", "[vector_extras] vector."..name.." already exists.")
	else
		vector[name] = func
	end
end

minetest.log("info", string.format("[vector_extras] loaded after ca. %.2fs", os.clock() - load_time_start))