mirror of
https://github.com/minetest/minetest_game.git
synced 2024-11-16 15:00:18 +01:00
1041 lines
24 KiB
Lua
1041 lines
24 KiB
Lua
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local path = minetest.get_modpath"vector_extras"
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local funcs = {}
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function funcs.pos_to_string(pos)
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return "("..pos.x.."|"..pos.y.."|"..pos.z..")"
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end
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local r_corr = 0.25 --remove a bit more nodes (if shooting diagonal) to let it
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-- look like a hole (sth like antialiasing)
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-- this doesn't need to be calculated every time
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local f_1 = 0.5-r_corr
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local f_2 = 0.5+r_corr
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--returns information about the direction
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local function get_used_dir(dir)
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local abs_dir = {x=math.abs(dir.x), y=math.abs(dir.y), z=math.abs(dir.z)}
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local dir_max = math.max(abs_dir.x, abs_dir.y, abs_dir.z)
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if dir_max == abs_dir.x then
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local tab = {"x", {x=1, y=dir.y/dir.x, z=dir.z/dir.x}}
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if dir.x >= 0 then
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tab[3] = "+"
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end
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return tab
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end
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if dir_max == abs_dir.y then
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local tab = {"y", {x=dir.x/dir.y, y=1, z=dir.z/dir.y}}
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if dir.y >= 0 then
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tab[3] = "+"
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end
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return tab
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end
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local tab = {"z", {x=dir.x/dir.z, y=dir.y/dir.z, z=1}}
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if dir.z >= 0 then
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tab[3] = "+"
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end
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return tab
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end
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local function node_tab(z, d)
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local n1 = math.floor(z*d+f_1)
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local n2 = math.floor(z*d+f_2)
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if n1 == n2 then
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return {n1}
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end
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return {n1, n2}
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end
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local function return_line(pos, dir, range) --range ~= length
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local tab = {}
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local num = 1
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local t_dir = get_used_dir(dir)
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local dir_typ = t_dir[1]
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local f_tab
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if t_dir[3] == "+" then
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f_tab = {0, range, 1}
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else
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f_tab = {0, -range, -1}
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end
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local d_ch = t_dir[2]
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if dir_typ == "x" then
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for d = f_tab[1],f_tab[2],f_tab[3] do
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local x = d
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local ytab = node_tab(d_ch.y, d)
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local ztab = node_tab(d_ch.z, d)
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for _,y in ipairs(ytab) do
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for _,z in ipairs(ztab) do
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tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
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num = num+1
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end
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end
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end
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elseif dir_typ == "y" then
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for d = f_tab[1],f_tab[2],f_tab[3] do
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local xtab = node_tab(d_ch.x, d)
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local y = d
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local ztab = node_tab(d_ch.z, d)
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for _,x in ipairs(xtab) do
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for _,z in ipairs(ztab) do
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tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
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num = num+1
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end
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end
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end
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else
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for d = f_tab[1],f_tab[2],f_tab[3] do
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local xtab = node_tab(d_ch.x, d)
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local ytab = node_tab(d_ch.y, d)
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local z = d
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for _,x in ipairs(xtab) do
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for _,y in ipairs(ytab) do
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tab[num] = {x=pos.x+x, y=pos.y+y, z=pos.z+z}
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num = num+1
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end
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end
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end
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end
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return tab
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end
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function funcs.rayIter(pos, dir)
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-- make a table of possible movements
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local step = {}
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for i in pairs(pos) do
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local v = math.sign(dir[i])
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if v ~= 0 then
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step[i] = v
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end
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end
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local p
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return function()
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if not p then
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-- avoid skipping the first position
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p = vector.round(pos)
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return vector.new(p)
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end
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-- find the position which has the smallest distance to the line
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local choose = {}
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local choosefit = vector.new()
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for i in pairs(step) do
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choose[i] = vector.new(p)
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choose[i][i] = choose[i][i] + step[i]
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choosefit[i] = vector.dot(vector.normalize(vector.subtract(choose[i], pos)), dir)
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end
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p = choose[vector.get_max_coord(choosefit)]
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return vector.new(p)
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end
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end
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function funcs.fine_line(pos, dir, range)
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if not range then --dir = pos2
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dir, range = vector.direction(pos, dir), vector.distance(pos, dir)
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end
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local result,n = {},1
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for p in vector.rayIter(pos, dir) do
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if vector.distance(p, pos) > range then
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break
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end
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result[n] = p
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n = n+1
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end
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return result
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end
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function funcs.line(pos, dir, range, alt)
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--assert_vector(pos)
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if alt then
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if not range then --dir = pos2
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dir, range = vector.direction(pos, dir), vector.distance(pos, dir)
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end
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return return_line(pos, dir, range)
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end
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if range then
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dir = vector.round(vector.multiply(dir, range))
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else --dir = pos2
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dir = vector.subtract(dir, pos)
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end
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local line,n = {},1
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for _,i in ipairs(vector.threeline(dir.x, dir.y, dir.z)) do
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line[n] = {x=pos.x+i[1], y=pos.y+i[2], z=pos.z+i[3]}
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n = n+1
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end
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return line
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end
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local twolines = {}
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function funcs.twoline(x, y)
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local pstr = x.." "..y
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local line = twolines[pstr]
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if line then
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return line
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end
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line = {}
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local n = 1
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local dirx = 1
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if x < 0 then
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dirx = -dirx
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end
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local ymin, ymax = 0, y
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if y < 0 then
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ymin, ymax = ymax, ymin
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end
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local m = y/x --y/0 works too
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local dir = 1
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if m < 0 then
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dir = -dir
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end
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for i = 0,x,dirx do
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local p1 = math.max(math.min(math.floor((i-0.5)*m+0.5), ymax), ymin)
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local p2 = math.max(math.min(math.floor((i+0.5)*m+0.5), ymax), ymin)
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for j = p1,p2,dir do
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line[n] = {i, j}
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n = n+1
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end
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end
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twolines[pstr] = line
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return line
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end
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local threelines = {}
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function funcs.threeline(x, y, z)
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local pstr = x.." "..y.." "..z
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local line = threelines[pstr]
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if line then
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return line
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end
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if x ~= math.floor(x) then
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minetest.log("error", "[vector_extras] INFO: The position used for " ..
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"vector.threeline isn't round.")
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end
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local two_line = vector.twoline(x, y)
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line = {}
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local n = 1
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local zmin, zmax = 0, z
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if z < 0 then
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zmin, zmax = zmax, zmin
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end
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local m = z/math.hypot(x, y)
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local dir = 1
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if m < 0 then
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dir = -dir
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end
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for _,i in ipairs(two_line) do
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local px, py = unpack(i)
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local ph = math.hypot(px, py)
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local z1 = math.max(math.min(math.floor((ph-0.5)*m+0.5), zmax), zmin)
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local z2 = math.max(math.min(math.floor((ph+0.5)*m+0.5), zmax), zmin)
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for pz = z1,z2,dir do
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line[n] = {px, py, pz}
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n = n+1
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end
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end
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threelines[pstr] = line
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return line
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end
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function funcs.sort_positions(ps, preferred_coords)
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preferred_coords = preferred_coords or {"z", "y", "x"}
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local a,b,c = unpack(preferred_coords)
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local function ps_sorting(p1, p2)
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if p1[a] == p2[a] then
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if p1[b] == p2[a] then
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if p1[c] < p2[c] then
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return true
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end
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elseif p1[b] < p2[b] then
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return true
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end
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elseif p1[a] < p2[a] then
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return true
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end
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end
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table.sort(ps, ps_sorting)
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end
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-- Tschebyschew norm
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function funcs.maxnorm(v)
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return math.max(math.max(math.abs(v.x), math.abs(v.y)), math.abs(v.z))
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end
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function funcs.sumnorm(v)
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return math.abs(v.x) + math.abs(v.y) + math.abs(v.z)
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end
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function funcs.pnorm(v, p)
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return (math.abs(v.x)^p + math.abs(v.y)^p + math.abs(v.z)^p)^(1 / p)
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end
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--not optimized
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--local areas = {}
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function funcs.plane(ps)
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-- sort positions and imagine the first one (A) as vector.zero
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vector.sort_positions(ps)
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local pos = ps[1]
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local B = vector.subtract(ps[2], pos)
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local C = vector.subtract(ps[3], pos)
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-- get the positions for the fors
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local cube_p1 = {x=0, y=0, z=0}
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local cube_p2 = {x=0, y=0, z=0}
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for i in pairs(cube_p1) do
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cube_p1[i] = math.min(B[i], C[i], 0)
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cube_p2[i] = math.max(B[i], C[i], 0)
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end
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cube_p1 = vector.apply(cube_p1, math.floor)
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cube_p2 = vector.apply(cube_p2, math.ceil)
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local vn = vector.normalize(vector.cross(B, C))
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local nAB = vector.normalize(B)
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local nAC = vector.normalize(C)
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local angle_BAC = math.acos(vector.dot(nAB, nAC))
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local nBA = vector.multiply(nAB, -1)
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local nBC = vector.normalize(vector.subtract(C, B))
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local angle_ABC = math.acos(vector.dot(nBA, nBC))
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for z = cube_p1.z, cube_p2.z do
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for y = cube_p1.y, cube_p2.y do
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for x = cube_p1.x, cube_p2.x do
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local p = {x=x, y=y, z=z}
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local n = -vector.dot(p, vn)/vector.dot(vn, vn)
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if math.abs(n) <= 0.5 then
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local ep = vector.add(p, vector.multiply(vn, n))
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local nep = vector.normalize(ep)
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local angle_BAep = math.acos(vector.dot(nAB, nep))
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local angle_CAep = math.acos(vector.dot(nAC, nep))
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local angldif = angle_BAC - (angle_BAep+angle_CAep)
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if math.abs(angldif) < 0.001 then
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ep = vector.subtract(ep, B)
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nep = vector.normalize(ep)
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local angle_ABep = math.acos(vector.dot(nBA, nep))
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local angle_CBep = math.acos(vector.dot(nBC, nep))
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angldif = angle_ABC - (angle_ABep+angle_CBep)
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if math.abs(angldif) < 0.001 then
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table.insert(ps, vector.add(pos, p))
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end
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end
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end
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end
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end
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end
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return ps
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end
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function funcs.straightdelay(s, v, a)
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if not a then
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return s/v
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end
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return (math.sqrt(v*v+2*a*s)-v)/a
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end
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-- override vector.zero
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-- builtin used not to have the vector.zero function. to keep compatibility,
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-- vector.zero has to be a 0-vector and vector.zero() has to return a 0-vector
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-- => we make a callable 0-vector table
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if not vector.zero then
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vector.zero = {x = 0, y = 0, z = 0}
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else
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local old_zero = vector.zero
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vector.zero = setmetatable({x = 0, y = 0, z = 0}, {__call = old_zero})
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end
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function funcs.sun_dir(time)
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if not time then
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time = minetest.get_timeofday()
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end
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local t = (time-0.5)*5/6+0.5 --the sun rises at 5 o'clock, not at 6
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if t < 0.25
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or t > 0.75 then
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return
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end
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local tmp = math.cos(math.pi*(2*t-0.5))
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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(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]
|
||
|
|
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 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]
|
||
|
|
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*z
|
||
|
|
for y=-r,r do
|
||
|
|
local bare_dist_yz = bare_dist_z + y*y
|
||
|
|
for x=-r,r do
|
||
|
|
local bare_dist = bare_dist_yz + 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
|
||
|
|
|
||
|
|
-- change strange values
|
||
|
|
local pval_diff = pval_max - pval_min
|
||
|
|
pval_min = pval_min/pval_diff
|
||
|
|
|
||
|
|
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[k] = {i[1]}
|
||
|
|
elseif i[3] < new_pval then
|
||
|
|
tab[k] = {i[1], true}
|
||
|
|
else
|
||
|
|
tab[k] = 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
|
||
|
|
|
||
|
|
local function get_parabola_points(pos, vel, gravity, waypoints, max_pointcount,
|
||
|
|
time)
|
||
|
|
local pointcount = 0
|
||
|
|
|
||
|
|
-- the height of the 45° angle point
|
||
|
|
local yswitch = -0.5 * (vel.x^2 + vel.z^2 - vel.y^2)
|
||
|
|
/ gravity + pos.y
|
||
|
|
|
||
|
|
-- the times of the 45° angle point
|
||
|
|
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
|
||
|
|
-- 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^2 + 2 * gravity * (pos.y - y))) / gravity
|
||
|
|
if t > time then
|
||
|
|
return
|
||
|
|
end
|
||
|
|
local p = {
|
||
|
|
x = math.floor(vel.x * t + pos.x +.5),
|
||
|
|
y = y,
|
||
|
|
z = math.floor(vel.z * t + pos.z +.5),
|
||
|
|
}
|
||
|
|
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]
|
||
|
|
if t > time then
|
||
|
|
return
|
||
|
|
end
|
||
|
|
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),
|
||
|
|
}
|
||
|
|
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 = yswitch
|
||
|
|
if vel.y < 0
|
||
|
|
and pos.y < yswitch then
|
||
|
|
y = pos.y
|
||
|
|
end
|
||
|
|
y = math.floor(y +.5)
|
||
|
|
while pointcount < max_pointcount do
|
||
|
|
local t = (vel.y +
|
||
|
|
math.sqrt(vel.y^2 + 2 * gravity * (pos.y - y))) / gravity
|
||
|
|
if t > time then
|
||
|
|
return
|
||
|
|
end
|
||
|
|
local p = {
|
||
|
|
x = math.floor(vel.x * t + pos.x +.5),
|
||
|
|
y = y,
|
||
|
|
z = math.floor(vel.z * t + pos.z +.5),
|
||
|
|
}
|
||
|
|
pointcount = pointcount+1
|
||
|
|
waypoints[pointcount] = {p, t}
|
||
|
|
y = y-1
|
||
|
|
end
|
||
|
|
end
|
||
|
|
--[[
|
||
|
|
minetest.override_item("default:axe_wood", {
|
||
|
|
on_use = function(_, player)
|
||
|
|
local dir = player:get_look_dir()
|
||
|
|
local pos = player:getpos()
|
||
|
|
local grav = 0.03
|
||
|
|
local ps = vector.throw_parabola(pos, dir, grav, 80)
|
||
|
|
for i = 1,#ps do
|
||
|
|
minetest.set_node(ps[i], {name="default:stone"})
|
||
|
|
end
|
||
|
|
--~ for t = 0,50,3 do
|
||
|
|
--~ local p = {
|
||
|
|
--~ x = dir.x * t + pos.x,
|
||
|
|
--~ y = -0.5*grav*t*t + dir.y*t + pos.y,
|
||
|
|
--~ z = dir.z * t + pos.z
|
||
|
|
--~ }
|
||
|
|
--~ minetest.set_node(p, {name="default:sandstone"})
|
||
|
|
--~ end
|
||
|
|
end,
|
||
|
|
})--]]
|
||
|
|
|
||
|
|
function funcs.throw_parabola(pos, vel, gravity, point_count, time)
|
||
|
|
local waypoints = {}
|
||
|
|
get_parabola_points(pos, vel, gravity, waypoints, point_count,
|
||
|
|
time or math.huge)
|
||
|
|
local ps = {}
|
||
|
|
local ptscnt = #waypoints
|
||
|
|
local i = 1
|
||
|
|
while i < ptscnt do
|
||
|
|
local p,t = unpack(waypoints[i])
|
||
|
|
i = i+1
|
||
|
|
local p2,t2 = unpack(waypoints[i])
|
||
|
|
ps[#ps+1] = p
|
||
|
|
local dist = vector.distance(p, p2)
|
||
|
|
if dist < 1.1 then
|
||
|
|
if dist < 0.9 then
|
||
|
|
-- same position
|
||
|
|
i = i+1
|
||
|
|
end
|
||
|
|
-- touching
|
||
|
|
elseif dist < 1.7 then
|
||
|
|
-- common edge
|
||
|
|
-- get a list of possible positions between
|
||
|
|
local diff = vector.subtract(p2, p)
|
||
|
|
local possible_positions = {}
|
||
|
|
for c,v in pairs(diff) do
|
||
|
|
if v ~= 0 then
|
||
|
|
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
|
||
|
|
t = 0.5 * (t + t2)
|
||
|
|
local near_p = {
|
||
|
|
x = vel.x * t + pos.x,
|
||
|
|
y = -0.5 * gravity * t * t + vel.y * t + pos.y,
|
||
|
|
z = vel.z * t + pos.z,
|
||
|
|
}
|
||
|
|
local d = math.huge
|
||
|
|
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
|
||
|
|
ps[#ps+1] = p
|
||
|
|
elseif dist < 1.8 then
|
||
|
|
-- common vertex
|
||
|
|
for k = 1,2 do
|
||
|
|
-- get a list of possible positions between
|
||
|
|
local diff = vector.subtract(p2, p)
|
||
|
|
local possible_positions = {}
|
||
|
|
for c,v in pairs(diff) do
|
||
|
|
if v ~= 0 then
|
||
|
|
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
|
||
|
|
t = k / 3 * (t + t2)
|
||
|
|
local near_p = {
|
||
|
|
x = vel.x * t + pos.x,
|
||
|
|
y = -0.5 * gravity * t * t + vel.y * t + pos.y,
|
||
|
|
z = vel.z * t + pos.z,
|
||
|
|
}
|
||
|
|
local d = math.huge
|
||
|
|
assert(#possible_positions == 4-k, "how, number positions?")
|
||
|
|
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
|
||
|
|
ps[#ps+1] = p
|
||
|
|
end
|
||
|
|
else
|
||
|
|
minetest.log("warning", "[vector_extras] A gap: " .. dist)
|
||
|
|
--~ error("A gap, it's a gap!: " .. dist)
|
||
|
|
end
|
||
|
|
end
|
||
|
|
if i == ptscnt then
|
||
|
|
ps[#ps+1] = waypoints[i]
|
||
|
|
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(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])
|
||
|
|
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 = minetest.line_of_sight(p1, p2)
|
||
|
|
if clear then
|
||
|
|
return false
|
||
|
|
end
|
||
|
|
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
|
||
|
|
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
|
||
|
|
end
|
||
|
|
return true, collision_pos, node_pos
|
||
|
|
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
|
||
|
|
|
||
|
|
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
|
||
|
|
|
||
|
|
dofile(path .. "/legacy.lua")
|
||
|
|
--dofile(minetest.get_modpath("vector_extras").."/vector_meta.lua")
|
||
|
|
|
||
|
|
vector_extras_functions = nil
|
||
|
|
|
||
|
|
|
||
|
|
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
|