Merge remote-tracking branch 'upstream/master'

This is needed to keep compatibility with new minetest builtin code

.luacheckrc

@@ -0,0 +1,5 @@
+read_globals = {
+	-- Defined by Minetest
+	"minetest", "PseudoRandom", "VoxelArea", "string", "dump", "math"
+}
+globals = {"vector", "vector_extras_functions"}

LICENSE.txt

@@ -1 +1 @@
-WTFPL
+CC0, except for code copied from e.g. minetest's builtin

README.txt

@@ -1,2 +1,6 @@
 TODO:
-— maybe make the explosion table function return a perlin explosion table
+* maybe make the explosion table function return a perlin explosion table
+* Figure out and implement 3D scanline search
+* Add vector.hollowsphere, less positions than WorldEdit hollowsphere
+* Add unit tests
+* Use %a string format for vector.serialize so that it is reversible

adammil_flood_fill.lua

@@ -0,0 +1,116 @@
+-- http://www.adammil.net/blog/v126_A_More_Efficient_Flood_Fill.html
+
+local can_go
+local marked_places
+local function calc_2d_index(x, y)
+	return (y + 32768) * 65536 + x + 32768
+end
+local function mark(x, y)
+	marked_places[calc_2d_index(x, y)] = true
+end
+
+local _fill
+local function fill(x, y)
+	if can_go(x, y) then
+		_fill(x, y)
+	end
+end
+
+local corefill
+function _fill(x, y)
+	while true do
+		local ox = x
+		local oy = y
+		while can_go(x, y-1) do
+			y = y-1
+		end
+		while can_go(x-1, y) do
+			x = x-1
+		end
+		if x == ox
+		and y == oy then
+			break
+		end
+	end
+	corefill(x, y)
+end
+
+function corefill(x, y)
+	local lastcnt = 0
+	repeat
+		local cnt = 0
+		local sx = x
+		if lastcnt ~= 0
+		and not can_go(y, x) then
+			-- go right to find the x start
+			repeat
+				lastcnt = lastcnt-1
+				if lastcnt == 0 then
+					return
+				end
+				x = x+1
+			until can_go(x, y)
+			sx = x
+		else
+			-- go left if possible, and mark and _fill above
+			while can_go(x-1, y) do
+				x = x-1
+				mark(x, y)
+				if can_go(x, y-1) then
+					_fill(x, y-1)
+				end
+				cnt = cnt+1
+				lastcnt = lastcnt+1
+			end
+		end
+
+		-- go right if possible, and mark
+		while can_go(sx, y) do
+			mark(sx, y)
+			cnt = cnt+1
+			sx = sx+1
+		end
+
+		if cnt < lastcnt then
+			local e = x + lastcnt
+			sx = sx+1
+			while sx < e do
+				if can_go(sx, y) then
+					corefill(sx, y)
+				end
+				sx = sx+1
+			end
+		elseif cnt > lastcnt then
+			local ux = x + lastcnt + 1
+			while ux < sx do
+				if can_go(ux, y-1) then
+					_fill(ux, y-1)
+				end
+				ux = ux+1
+			end
+		end
+		lastcnt = cnt
+		y = y+1
+	until lastcnt == 0
+end
+
+local function apply_fill(go_test, x0, y0, allow_revisit)
+	if allow_revisit then
+		can_go = go_test
+	else
+		local visited = {}
+		can_go = function(x, y)
+			local vi = calc_2d_index(x, y)
+			if visited[vi] then
+				return false
+			end
+			visited[vi] = true
+			return go_test(x, y)
+		end
+	end
+	marked_places = {}
+	fill(x0, y0)
+	return marked_places
+end
+
+return apply_fill

doc.md

@@ -0,0 +1,154 @@
+
+# Vector helpers added by this mod
+
+## Helpers which return many positions for a shape, e.g. a line
+
+### Line functions
+
+These may be deprecated since raycasting has been added to minetest.
+See e.g. `minetest.line_of_sight`.
+
+* `vector.line([pos, dir[, range][, alt]])`: returns a table of vectors
+    * `dir` is either a direction (when range is a number) or
+      the start position (when range is the end position).
+    * If alt is true, an old path calculation is used.
+* `vector.twoline(x, y)`: can return e.g. `{{0,0}, {0,1}}`
+    * This is a lower-level function than `vector.line`; it can be used for
+      a 2D line.
+* `vector.threeline(x, y, z)`: can return e.g. `{{0,0,0}, {0,1,0}}`
+    * Similar to `vector.twoline`; this one is for the 3D case.
+    * The parameters should be integers.
+* `vector.rayIter(pos, dir)`: returns an iterator for a for loop
+    * `pos` can have non-integer values
+* `vector.fine_line([pos, dir[, range], scale])`: returns a table of vectors
+    * Like `vector.line` but allows non-integer positions
+    * It uses `vector.rayIter`.
+
+
+### Flood Fill
+
+* `vector.search_2d(go_test, x0, y0, allow_revisit, give_map)`: returns e.g.
+  `{{0,0}, {0,1}}`
+    * This function uses a Flood Fill algorithm, so it can be used to detect
+      positions connected to each other in 2D.
+    * `go_test(x, y)` should be a function which returns true iff the algorithm
+      can "fill" at the position `(x, y)`.
+    * `(x0, y0)` defines the start position.
+    * If `allow_revisit` is false (the default), the function
+      invokes `go_test` only once at every potential position.
+    * If `give_map` is true (default is false), the function returns the
+      marked table, whose indices are 2D vector indices, instead of a list of
+      2D positions.
+* `vector.search_3d(can_go, startpos, apply_move, moves)`: returns FIXME
+    * FIXME
+
+
+### Other Shapes
+
+* `vector.explosion_table(r)`: returns e.g. `{{pos1}, {pos2, true}}`
+    * The returned list of positions and boolean represents a sphere;
+      if the boolean is true, the position is on the outer side of the sphere.
+    * It might be used for explosion calculations; but `vector.explosion_perlin`
+      should make more realistic holes.
+* `vector.explosion_perlin(rmin, rmax[, nparams])`: returns e.g.
+  `{{pos1}, {pos2, true}}`
+    * This function is similar to `vector.explosion_table`; the positions
+      do not represent a sphere but a more complex hole which is calculated
+      with the help of perlin noise.
+    * `rmin` and `rmax` represent the minimum and maximum radius,
+      and `nparams` (which has a default value) are parameters for the perlin
+      noise.
+* `vector.circle(r)`: returns a table of vectors
+    * The returned positions represent a circle of radius `r` along the x and z
+      directions; the y coordinates are all zero.
+* `vector.ring(r)`: returns a table of vectors
+    * This function is similar to `vector.circle`; the positions are all
+      touching each other (i.e. they are connected on whole surfaces and not
+      only infinitely thin edges), so it is called `ring` instead of `circle`
+    * `r` can be a non-integer number.
+* `vector.throw_parabola(pos, vel, gravity, point_count, time)`
+    * FIXME: should return positions along a parabola so that moving objects
+      collisions can be calculated
+* `vector.triangle(pos1, pos2, pos3)`: returns a table of positions, a number
+  and a table with barycentric coordinates
+    * This function calculates integer positions for a triangle defined by
+      `pos1`, `pos2` and `pos3`, so it can be used to place polygons in
+      minetest.
+    * The returned number is the number of positions.
+    * The barycentric coordinates are specified in a table with three elements;
+      the first one corresponds to `pos1`, etc.
+
+
+## Helpers for various vector calculations
+
+* `vector.sort_positions(ps[, preferred_coords])`
+    * Sorts a table of vectors `ps` along the coordinates specified in the
+      table `preferred_coords` in-place.
+    * If `preferred_coords` is omitted, it sorts along z, y and x in this order,
+      where z has the highest priority.
+* `vector.maxnorm(v)`: returns the Tschebyshew norm of `v`
+* `vector.sumnorm(v)`: returns the Manhattan norm of `v`
+* `vector.pnorm(v, p)`: returns the `p` norm of `v`
+* `vector.inside(pos, minp, maxp)`: returns a boolean
+    * Returns true iff `pos` is within the closed AABB defined by `minp`
+      and `maxp`.
+* `vector.minmax(pos1, pos2)`: returns two vectors
+    * This does the same as `worldedit.sort_pos`.
+    * The components of the second returned vector are all bigger or equal to
+      those of the first one.
+* `vector.move(pos1, pos2, length)`: returns a vector
+    * Go from `pos1` `length` metres to `pos2` and then round to the nearest
+      integer position.
+    * Made for rubenwardy
+* `vector.from_number(i)`: returns `{x=i, y=i, z=i}`
+* `vector.chunkcorner(pos)`: returns a vector
+    * Returns the mapblock position of the mapblock which contains
+      the integer position `pos`
+* `vector.point_distance_minmax(p1, p2)`: returns two numbers
+    * Returns the minimum and maximum of the absolute component-wise distances
+* `vector.collision(p1, p2)` FIXME
+* `vector.update_minp_maxp(minp, maxp, pos)`
+    * Can change `minp` and `maxp` so that `pos` is within the AABB defined by
+      `minp` and `maxp`
+* `vector.unpack(v)`: returns three numbers
+    * Returns `v.z, v.y, v.x`
+* `vector.get_max_coord(v)`: returns a string
+    * Returns `"x"`, `"y"` or `"z"`, depending on which component has the
+      biggest value
+* `vector.get_max_coords(v)`: returns three strings
+    * Similar to `vector.get_max_coord`; it returns the coordinates in the order
+      of their component values
+    * Example: `vector.get_max_coords{x=1, y=5, z=3}` returns `"y", "z", "x"`
+* `vector.serialize(v)`: returns a string
+    * In comparison to `minetest.serialize`, this function uses a more compact
+      string for the serialization.
+
+
+## Minetest-specific helper functions
+
+* `vector.straightdelay([length, vel[, acc]])`: returns a number
+    * Returns the time an object takes to move `length` if it has velocity `vel`
+      and acceleration `acc`
+* `vector.sun_dir([time])`: returns a vector or nil
+    * Returns the vector which points to the sun
+    * If `time` is omitted, it uses the current time.
+    * This function does not yet support the moon;
+      at night it simply returns `nil`.
+
+
+## Helpers which I don't recommend to use now
+
+* `vector.pos_to_string(pos)`: returns a string
+    * It is similar to `minetest.pos_to_string`; it uses a different format:
+      `"("..pos.x.."|"..pos.y.."|"..pos.z..")"`
+* `vector.zero`
+    * The zero vector `{x=0, y=0, z=0}`
+* `vector.quickadd(pos, [z],[y],[x])`
+    * Adds values to the vector components in-place
+
+
+## Deprecated helpers
+
+* `vector.plane`
+    * should be removed soon; it should have done the same as vector.triangle
+

fill_3d.lua

@@ -0,0 +1,53 @@
+-- Algorithm created by sofar and changed by others:
+-- https://github.com/minetest/minetest/commit/d7908ee49480caaab63d05c8a53d93103579d7a9
+
+local function search(go, p, apply_move, moves)
+	local num_moves = #moves
+
+	-- We make a stack, and manually maintain size for performance.
+	-- Stored in the stack, we will maintain tables with pos, and
+	-- last neighbor visited. This way, when we get back to each
+	-- node, we know which directions we have already walked, and
+	-- which direction is the next to walk.
+	local s = {}
+	local n = 0
+	-- The neighbor order we will visit from our table.
+	local v = 1
+
+	while true do
+		-- Push current pos onto the stack.
+		n = n + 1
+		s[n] = {p = p, v = v}
+		-- Select next node from neighbor list.
+		p = apply_move(p, moves[v])
+		-- Now we check out the node. If it is in need of an update,
+		-- it will let us know in the return value (true = updated).
+		if not go(p) then
+			-- If we don't need to "recurse" (walk) to it then pop
+			-- our previous pos off the stack and continue from there,
+			-- with the v value we were at when we last were at that
+			-- node
+			repeat
+				local pop = s[n]
+				p = pop.p
+				v = pop.v
+				s[n] = nil
+				n = n - 1
+				-- If there's nothing left on the stack, and no
+				-- more sides to walk to, we're done and can exit
+				if n == 0 and v == num_moves then
+					return
+				end
+			until v < num_moves
+			-- The next round walk the next neighbor in list.
+			v = v + 1
+		else
+			-- If we did need to walk the neighbor, then
+			-- start walking it from the walk order start (1),
+			-- and not the order we just pushed up the stack.
+			v = 1
+		end
+	end
+end
+
+return search

init.lua

@@ -1,4 +1,4 @@
-local load_time_start = minetest.get_us_time()
+local path = minetest.get_modpath"vector_extras"
 
 local funcs = {}
 
@@ -6,7 +6,8 @@ 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)
+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
@@ -51,6 +52,7 @@ local function return_line(pos, dir, range) --range ~= length
 	local num = 1
 	local t_dir = get_used_dir(dir)
 	local dir_typ = t_dir[1]
+	local f_tab
 	if t_dir[3] == "+" then
 		f_tab = {0, range, 1}
 	else
@@ -121,7 +123,7 @@ function funcs.rayIter(pos, dir)
 		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)
+			choosefit[i] = vector.dot(vector.normalize(vector.subtract(choose[i], pos)), dir)
 		end
 		p = choose[vector.get_max_coord(choosefit)]
 
@@ -255,18 +257,6 @@ function funcs.sort_positions(ps, preferred_coords)
 	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
-
 -- Tschebyschew norm
 function funcs.maxnorm(v)
 	return math.max(math.max(math.abs(v.x), math.abs(v.y)), math.abs(v.z))
@@ -284,7 +274,7 @@ end
 --local areas = {}
 function funcs.plane(ps)
 	-- sort positions and imagine the first one (A) as vector.zero
-	ps = vector.sort_positions(ps)
+	vector.sort_positions(ps)
 	local pos = ps[1]
 	local B = vector.subtract(ps[2], pos)
 	local C = vector.subtract(ps[3], pos)
@@ -303,29 +293,29 @@ function funcs.plane(ps)
 
 	local nAB = vector.normalize(B)
 	local nAC = vector.normalize(C)
-	local angle_BAC = math.acos(vector.scalar(nAB, nAC))
+	local angle_BAC = math.acos(vector.dot(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))
+	local angle_ABC = math.acos(vector.dot(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)
+				local n = -vector.dot(p, vn)/vector.dot(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 angle_BAep = math.acos(vector.dot(nAB, nep))
+					local angle_CAep = math.acos(vector.dot(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)
+						local angle_ABep = math.acos(vector.dot(nBA, nep))
+						local angle_CBep = math.acos(vector.dot(nBC, nep))
+						angldif = angle_ABC - (angle_ABep+angle_CBep)
 						if math.abs(angldif) < 0.001 then
 							table.insert(ps, vector.add(pos, p))
 						end
@@ -344,7 +334,16 @@ function funcs.straightdelay(s, v, a)
 	return (math.sqrt(v*v+2*a*s)-v)/a
 end
 
-vector.zero = vector.new()
+-- override vector.zero
+-- builtin used not to have the vector.zero function. to keep compatibility,
+-- vector.zero has to be a 0-vector and vector.zero() has to return a 0-vector
+-- => we make a callable 0-vector table
+if not vector.zero then
+	vector.zero = {x = 0, y = 0, z = 0}
+else
+	local old_zero = vector.zero
+	vector.zero = setmetatable({x = 0, y = 0, z = 0}, {__call = old_zero})
+end
 
 function funcs.sun_dir(time)
 	if not time then
@@ -369,9 +368,9 @@ function funcs.inside(pos, minp, maxp)
 	return true
 end
 
-function funcs.minmax(p1, p2)
-	local p1 = vector.new(p1)
-	local p2 = vector.new(p2)
+function funcs.minmax(pos1, pos2)
+	local p1 = vector.new(pos1)
+	local p2 = vector.new(pos2)
 	for _,i in ipairs({"x", "y", "z"}) do
 		if p1[i] > p2[i] then
 			p1[i], p2[i] = p2[i], p1[i]
@@ -399,6 +398,66 @@ function funcs.from_number(i)
 	return {x=i, y=i, z=i}
 end
 
+local adammil_fill = dofile(path .. "/adammil_flood_fill.lua")
+function funcs.search_2d(go_test, x0, y0, allow_revisit, give_map)
+	local marked_places = adammil_fill(go_test, x0, y0, allow_revisit)
+	if give_map then
+		return marked_places
+	end
+	local l = {}
+	for vi in pairs(marked_places) do
+		local x = (vi % 65536) - 32768
+		local y = (math.floor(x / 65536) % 65536) - 32768
+		l[#l+1] = {x, y}
+	end
+	return l
+end
+
+local fallings_search = dofile(path .. "/fill_3d.lua")
+local moves_touch = {
+	{x = -1, y = 0, z = 0},
+	{x = 0, y = 0, z = 0},  -- FIXME should this be here?
+	{x = 1, y = 0, z = 0},
+	{x = 0, y = -1, z = 0},
+	{x = 0, y = 1, z = 0},
+	{x = 0, y = 0, z = -1},
+	{x = 0, y = 0, z = 1},
+}
+local moves_near = {}
+for z = -1,1 do
+	for y = -1,1 do
+		for x = -1,1 do
+			moves_near[#moves_near+1] = {x = x, y = y, z = z}
+		end
+	end
+end
+
+function funcs.search_3d(can_go, startpos, apply_move, moves)
+	local visited = {}
+	local found = {}
+	local function on_visit(pos)
+		local vi = minetest.hash_node_position(pos)
+		if visited[vi] then
+			return false
+		end
+		visited[vi] = true
+		local valid_pos = can_go(pos)
+		if valid_pos then
+			found[#found+1] = pos
+		end
+		return valid_pos
+	end
+	if apply_move == "touch" then
+		apply_move = vector.add
+		moves = moves_touch
+	elseif apply_move == "near" then
+		apply_move = vector.add
+		moves = moves_near
+	end
+	fallings_search(on_visit, startpos, apply_move, moves)
+end
+
+
 local explosion_tables = {}
 function funcs.explosion_table(r)
 	local table = explosion_tables[r]
@@ -449,7 +508,8 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
 	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 map = minetest.get_perlin_map(nparams, vector.from_number(r+r+1)
+		):get3dMap_flat(pos)
 
 	local id = 1
 
@@ -464,11 +524,11 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
 
 	local tab, n = {}, 1
 	for z=-r,r do
-		local bare_dist = z*z
+		local bare_dist_z = z*z
 		for y=-r,r do
-			local bare_dist = bare_dist+y*y
+			local bare_dist_yz = bare_dist_z + y*y
 			for x=-r,r do
-				local bare_dist = bare_dist+x*x
+				local bare_dist = bare_dist_yz + x*x
 				local add = bare_dist < bare_mindist
 				local pval, distdiv
 				if not add
@@ -494,22 +554,19 @@ function funcs.explosion_perlin(rmin, rmax, nparams)
 		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
+	for k,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]}
+				tab[k] = {i[1]}
 			elseif i[3] < new_pval then
-				tab[n] = {i[1], true}
+				tab[k] = {i[1], true}
 			else
-				tab[n] = nil
+				tab[k] = nil
 			end
 		end
 	end
@@ -584,67 +641,6 @@ function funcs.ring(r)
 	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) = -0.5 * gravity * t * t + 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)^2 = velx(t)^2 + velz(t)^2
-	--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
-	--~ gravity^2 * t^2 + vel.y^2 - -2*gravity*t*vel.y = vel.x * vel.x + vel.z * vel.z
-	--~ gravity^2 * t^2 - 2*gravity*vel.y * t + (vel.y^2 - vel.x^2 - vel.z^2) = 0
-	--~ t = (2*gravity*vel.y .. rt((2*gravity*vel.y)^2 - 4*gravity^2*(vel.y^2 - vel.x^2 - vel.z^2))) / (2*gravity^2)
-	--~ t = (2*gravity*vel.y .. rt(4*gravity^2*vel.y^2 - 4*gravity^2*(vel.y^2) + 4*gravity^2*(vel.x^2 + vel.z^2))) / (2*gravity^2)
-	--~ t = (2*gravity*vel.y .. 2*gravity*rt(vel.x^2 + vel.z^2)) / (2*gravity^2)
-	--~ t = (vel.y .. rt(vel.x^2 + vel.z^2)) / gravity
-	--~ t1 = (vel.y - math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
-	--~ t2 = (vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity
-
-	--~ yswitch = posy(t1) (= posy(t2)) //links und rechts gleich
-	--~ yswitch = -0.5 * gravity * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity)^2 + vel.y * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
-	--~ yswitch = -0.5 * gravity * (vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z))^2 / gravity^2 + vel.y * ((vel.y + math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
-	--~ yswitch = -0.5 * (vel.y^2 + 2*vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.x^2 + vel.z^2) / gravity + ((vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity) + pos.y
-	--~ yswitch = (-0.5 * (vel.y^2 + 2*vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.x^2 + vel.z^2) + ((vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)))) / gravity + pos.y
-	--~ yswitch = (-0.5 * vel.y^2 - vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z) - 0.5 * vel.x^2 - 0.5 * vel.z^2 + vel.y^2 + vel.y*math.sqrt(vel.x * vel.x + vel.z * vel.z)) / gravity + pos.y
-	--~ yswitch = (-0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2 + vel.y^2) / gravity + pos.y
-	--~ yswitch = (0.5 * vel.y^2 - 0.5 * vel.x^2 - 0.5 * vel.z^2) / gravity + pos.y
-	--~ yswitch = -0.5 * (vel.x * vel.x + vel.z * vel.z - vel.y * vel.y) / gravity + pos.y
-
-
-	--~ 45° Zeitpunkte kleineres beim Aufstieg, größeres beim Fall
-	--~ (-gravity*t + vel.y)^2 = vel.x * vel.x + vel.z * vel.z
-	--~ -gravity*t + vel.y = ..math.sqrt(vel.x * vel.x + vel.z * vel.z)
-	--~ t = (..math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
-	--~ t_raise = (-math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
-	--~ t_fall = (math.sqrt(vel.x * vel.x + vel.z * vel.z) + vel.y) / gravity
-
-	--~ posy nach t umstellen
-	--~ y = -0.5 * gravity * t * t + vel.y * t + pos.y
-	--~ 0 = -0.5 * gravity * t * t + vel.y * t + pos.y - y
-	--~ t = (-vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / (-gravity)
-	--~ t = (vel.y .. math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
-	--~ t_up = (vel.y - math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
-	--~ t_down = (vel.y + math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / 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,
 		time)
 	local pointcount = 0
@@ -654,9 +650,9 @@ local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount,
 		/ gravity + pos.y
 
 	-- the times of the 45° angle point
-	local i = math.sqrt(vel.x^2 + vel.z^2)
-	local t_raise_end = (-i + vel.y) / gravity
-	local t_fall_start = (i + vel.y) / gravity
+	local vel_len = math.sqrt(vel.x^2 + vel.z^2)
+	local t_raise_end = (-vel_len + vel.y) / gravity
+	local t_fall_start = (vel_len + vel.y) / gravity
 	if t_fall_start > 0 then
 		-- the right 45° angle point wasn't passed yet
 		if t_raise_end > 0 then
@@ -785,11 +781,11 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
 			-- get a list of possible positions between
 			local diff = vector.subtract(p2, p)
 			local possible_positions = {}
-			for i,v in pairs(diff) do
+			for c,v in pairs(diff) do
 				if v ~= 0 then
-					local p = vector.new(p)
-					p[i] = p[i] + v
-					possible_positions[#possible_positions+1] = p
+					local pos_moved = vector.new(p)
+					pos_moved[c] = pos_moved[c] + v
+					possible_positions[#possible_positions+1] = pos_moved
 				end
 			end
 			-- test which one fits best
@@ -800,12 +796,12 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
 				z = vel.z * t + pos.z,
 			}
 			local d = math.huge
-			for i = 1,2 do
-				local pos = possible_positions[i]
-				local dist = vector.distance(pos, near_p)
-				if dist < d then
-					p = pos
-					d = dist
+			for k = 1,2 do
+				local pos_moved = possible_positions[k]
+				local dist_current = vector.distance(pos_moved, near_p)
+				if dist_current < d then
+					p = pos_moved
+					d = dist_current
 				end
 			end
 			-- add it
@@ -816,11 +812,11 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
 				-- get a list of possible positions between
 				local diff = vector.subtract(p2, p)
 				local possible_positions = {}
-				for i,v in pairs(diff) do
+				for c,v in pairs(diff) do
 					if v ~= 0 then
-						local p = vector.new(p)
-						p[i] = p[i] + v
-						possible_positions[#possible_positions+1] = p
+						local pos_moved = vector.new(p)
+						pos_moved[c] = pos_moved[c] + v
+						possible_positions[#possible_positions+1] = pos_moved
 					end
 				end
 				-- test which one fits best
@@ -832,12 +828,12 @@ function funcs.throw_parabola(pos, vel, gravity, point_count, time)
 				}
 				local d = math.huge
 				assert(#possible_positions == 4-k, "how, number positions?")
-				for i = 1,4-k do
-					local pos = possible_positions[i]
-					local dist = vector.distance(pos, near_p)
-					if dist < d then
-						p = pos
-						d = dist
+				for j = 1,4-k do
+					local pos_moved = possible_positions[j]
+					local dist_current = vector.distance(pos_moved, near_p)
+					if dist_current < d then
+						p = pos_moved
+						d = dist_current
 					end
 				end
 				-- add it
@@ -858,9 +854,9 @@ 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)
+function funcs.point_distance_minmax(pos1, pos2)
+	local p1 = vector.new(pos1)
+	local p2 = vector.new(pos2)
 	local min, max, vmin, vmax, num
 	for _,i in ipairs({"x", "y", "z"}) do
 		num = math.abs(p1[i] - p2[i])
@@ -877,21 +873,20 @@ function funcs.point_distance_minmax(p1, p2)
 end
 
 function funcs.collision(p1, p2)
-	local clear, node_pos, collision_pos, max, dmax, dcmax, pt
-	clear, node_pos = minetest.line_of_sight(p1, p2)
+	local 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)
+	local collision_pos = {}
+	local _, 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
+	local dmax = p2[max] - node_pos[max]
+	local dcmax = p2[max] - collision_pos[max]
+	local pt = dcmax / dmax
 
 	for _,i in ipairs({"x", "y", "z"}) do
 		collision_pos[i] = p2[i] - (p2[i] - node_pos[i]) * pt
@@ -958,10 +953,77 @@ function funcs.serialize(vec)
 	return "{x=" .. vec.x .. ",y=" .. vec.y .. ",z=" .. vec.z .. "}"
 end
 
+function funcs.triangle(pos1, pos2, pos3)
+	local normal = vector.cross(vector.subtract(pos2, pos1),
+		vector.subtract(pos3, pos1))
+	-- Find the biggest absolute component of the normal vector
+	local dir = vector.get_max_coord({
+		x = math.abs(normal.x),
+		y = math.abs(normal.y),
+		z = math.abs(normal.z),
+	})
+	-- Find the other directions for the for loops
+	local all_other_dirs = {
+		x = {"z", "y"},
+		y = {"z", "x"},
+		z = {"y", "x"},
+	}
+	local other_dirs = all_other_dirs[dir]
+	local odir1, odir2 = other_dirs[1], other_dirs[2]
+
+	local pos1_2d = {pos1[odir1], pos1[odir2]}
+	local pos2_2d = {pos2[odir1], pos2[odir2]}
+	local pos3_2d = {pos3[odir1], pos3[odir2]}
+	-- The boundaries of the 2D AABB along other_dirs
+	local p1 = {}
+	local p2 = {}
+	for i = 1,2 do
+		p1[i] = math.floor(math.min(pos1_2d[i], pos2_2d[i], pos3_2d[i]))
+		p2[i] = math.ceil(math.max(pos1_2d[i], pos2_2d[i], pos3_2d[i]))
+	end
+
+	-- https://www.scratchapixel.com/lessons/3d-basic-rendering/rasterization-practical-implementation/rasterization-stage
+	local function edgefunc(vert1, vert2, pos)
+		return (pos[1] - vert1[1]) * (vert2[2] - vert1[2])
+			- (pos[2] - vert1[2]) * (vert2[1] - vert1[1])
+	end
+	-- eps is used to prevend holes in neighbouring triangles
+	-- It should be smaller than the smallest possible barycentric value
+	-- FIXME: I'm not sure if it really does what it should.
+	local eps = 0.5 / math.max(p2[1] - p1[1], p2[2] - p1[2])
+	local a_all_inv = 1.0 / edgefunc(pos1_2d, pos2_2d, pos3_2d)
+	local step_k3 = - (pos2_2d[1] - pos1_2d[1]) * a_all_inv
+	local step_k1 = - (pos3_2d[1] - pos2_2d[1]) * a_all_inv
+	-- Calculate the triangle points
+	local points = {}
+	local barycentric_coords = {}
+	local n = 0
+	-- It is possible to further optimize this
+	for v1 = p1[1], p2[1] do
+		local p = {v1, p1[2]}
+		local k3 = edgefunc(pos1_2d, pos2_2d, p) * a_all_inv
+		local k1 = edgefunc(pos2_2d, pos3_2d, p) * a_all_inv
+		for _ = p1[2], p2[2] do
+			local k2 = 1 - k1 - k3
+			if k1 >= -eps and k2 >= -eps and k3 >= -eps then
+				-- On triangle
+				local h = math.floor(k1 * pos1[dir] + k2 * pos2[dir] +
+					k3 * pos3[dir] + 0.5)
+				n = n+1
+				points[n] = {[odir1] = v1, [odir2] = p[2], [dir] = h}
+				barycentric_coords[n] = {k1, k2, k3}
+			end
+			p[2] = p[2]+1
+			k3 = k3 + step_k3
+			k1 = k1 + step_k1
+		end
+	end
+	return points, n, barycentric_coords
+end
+
 
 vector_extras_functions = funcs
 
-local path = minetest.get_modpath"vector_extras"
 dofile(path .. "/legacy.lua")
 --dofile(minetest.get_modpath("vector_extras").."/vector_meta.lua")
 
@@ -977,11 +1039,4 @@ for name,func in pairs(funcs) do
 	end
 end
 
-
-local time = (minetest.get_us_time() - load_time_start) / 1000000
-local msg = "[vector_extras] loaded after ca. " .. time .. " seconds."
-if time > 0.01 then
-	print(msg)
-else
-	minetest.log("action", msg)
-end
+minetest.log("action", "[vector_extras] loaded.")

legacy.lua

@@ -1,5 +1,11 @@
 local funcs = vector_extras_functions
 
+function funcs.scalar(v1, v2)
+	minetest.log("deprecated", "[vector_extras] vector.scalar is " ..
+		"deprecated, use vector.dot instead.")
+	return vector.dot(v1, v2)
+end
+
 function funcs.get_data_from_pos(tab, z,y,x)
 	minetest.log("deprecated", "[vector_extras] get_data_from_pos is " ..
 		"deprecated, use the minetest pos hash function instead.")

vector_meta.lua

@@ -94,15 +94,15 @@ function vector.meta.complete_node_table(pos, name) --neccesary because tab[1] w
 	if not tmp then
 		vector.meta.nodes[pos.x] = {}
 	end
-	local tmp = vector.meta.nodes[pos.x][pos.y]
+	tmp = vector.meta.nodes[pos.x][pos.y]
 	if not tmp then
 		vector.meta.nodes[pos.x][pos.y] = {}
 	end
-	local tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
+	tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
 	if not tmp then
 		vector.meta.nodes[pos.x][pos.y][pos.z] = {}
 	end
-	local tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
+	tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
 	if not tmp then
 		vector.meta.nodes[pos.x][pos.y][pos.z][name] = {}
 	end
@@ -117,12 +117,12 @@ function vector.meta.get_node(pos, name)
 	or table_empty(tmp) then
 		return false
 	end
-	local tmp = vector.meta.nodes[pos.x][pos.y]
+	tmp = vector.meta.nodes[pos.x][pos.y]
 	if not tmp
 	or table_empty(tmp) then
 		return false
 	end
-	local tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
+	tmp = vector.meta.nodes[pos.x][pos.y][pos.z]
 	if not tmp
 	or table_empty(tmp) then
 		return false
@@ -133,7 +133,7 @@ function vector.meta.get_node(pos, name)
 		return true
 	end
 
-	local tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
+	tmp = vector.meta.nodes[pos.x][pos.y][pos.z][name]
 	if not tmp
 	or table_empty(tmp) then
 		return false