vector_extras/init.lua

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local load_time_start = os.clock()
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local funcs = {}
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 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
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local function table_contains2(t, v)
for i = #t, 1, -1 do
if t[i] == v then
return true
end
end
return false
end
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local function return_fine_line(pos, dir, range, scale)
local ps1 = return_line(vector.round(vector.multiply(pos, scale)), dir, range*scale)
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local ps2 = {}
local ps2_num = 1
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for _,p1 in ipairs(ps1) do
local p2 = vector.round(vector.divide(p1, scale))
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if not table_contains2(ps2, p2) then
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ps2[ps2_num] = p2
ps2_num = ps2_num+1
end
end
return ps2
end
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function funcs.fine_line(pos, dir, range, scale)
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--assert_vector(pos)
if not range then --dir = pos2
dir = vector.direction(pos, dir)
range = vector.distance(pos, dir)
end
return return_fine_line(pos, dir, range, scale)
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
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 = pos2
dir = vector.round(vector.multiply(dir, range))
else
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
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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
local line = twolines[pstr]
if line then
return line
end
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line = {}
local n = 1
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local dirx = 1
if x < 0 then
dirx = -dirx
end
local ymin, ymax = 0, y
if y < 0 then
ymin, ymax = ymax, ymin
end
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local m = y/x --y/0 works too
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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
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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
local line = threelines[pstr]
if line then
return line
end
if x ~= math.floor(x) then
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minetest.log("error", "[vector_extras] INFO: The position used for vector.threeline isn't round.")
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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
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function funcs.sort(ps, preferred_coords)
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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)
return ps
end
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function funcs.scalar(v1, v2)
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return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z
end
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function funcs.cross(v1, v2)
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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
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--not optimized
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--local areas = {}
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function funcs.plane(ps)
-- sort positions and imagine the first one (A) as vector.zero
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ps = vector.sort(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
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cube_p1 = vector.apply(cube_p1, math.floor)
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)
local nAC = vector.normalize(C)
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local angle_BAC = math.acos(vector.scalar(nAB, nAC))
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local nBA = vector.multiply(nAB, -1)
local nBC = vector.normalize(vector.subtract(C, B))
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local angle_ABC = math.acos(vector.scalar(nBA, nBC))
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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}
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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))
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local nep = vector.normalize(ep)
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local angle_BAep = math.acos(vector.scalar(nAB, nep))
local angle_CAep = math.acos(vector.scalar(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)
nep = vector.normalize(ep)
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local angle_ABep = math.acos(vector.scalar(nBA, nep))
local angle_CBep = math.acos(vector.scalar(nBC, nep))
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local angldif = angle_ABC - (angle_ABep+angle_CBep)
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if math.abs(angldif) < 0.001 then
table.insert(ps, vector.add(pos, p))
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end
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end
end
end
end
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
return s/v
end
return (math.sqrt(v*v+2*a*s)-v)/a
end
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vector.zero = vector.new()
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function funcs.sun_dir(time)
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if not time then
time = minetest.get_timeofday()
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
or t > 0.75 then
return
end
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local tmp = math.cos(math.pi*(2*t-0.5))
return {x=tmp, y=math.sqrt(1-tmp*tmp), z=0}
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end
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function funcs.inside(pos, minp, maxp)
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for _,i in pairs({"x", "y", "z"}) do
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if pos[i] < minp[i]
or pos[i] > maxp[i] then
return false
end
end
return true
end
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function funcs.minmax(p1, p2)
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local p1 = vector.new(p1)
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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
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function funcs.move(p1, p2, s)
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return vector.round(
vector.add(
vector.multiply(
vector.direction(
p1,
p2
),
s
),
p1
)
)
end
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function funcs.from_number(i)
return {x=i, y=i, z=i}
end
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local explosion_tables = {}
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function funcs.explosion_table(r)
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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
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local rc = x*x+y*y+z*z
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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
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minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
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return tab
end
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local default_nparams = {
offset = 0,
scale = 1,
seed = 1337,
octaves = 6,
persist = 0.6
}
function funcs.explosion_perlin(pos, 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 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 maxdist = math.sqrt(bare_maxdist)
local mindist = math.sqrt(bare_mindist)
local dist_diff = 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
local np={x=x, y=y, z=z}
tab[n] = {np, 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 n,i in pairs(tab) do
if i[2] then
local new_pval = (i[2]/pval_diff - pval_min)
if i[3] < math.abs(new_pval) then
tab[n] = {i[1]}
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
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local circle_tables = {}
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function funcs.circle(r)
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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
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minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
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return tab
end
local ring_tables = {}
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function funcs.ring(r)
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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
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minetest.log("info", string.format("[vector_extras] table created after ca. %.2fs", os.clock() - t1))
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return tab2
end
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function funcs.chunkcorner(pos)
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return {x=pos.x-pos.x%16, y=pos.y-pos.y%16, z=pos.z-pos.z%16}
end
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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
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dofile(minetest.get_modpath("vector_extras").."/vector_meta.lua")
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for name,func in pairs(funcs) do
vector[name] = vector[name] or func
end
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minetest.log("info", string.format("[vector_extras] loaded after ca. %.2fs", os.clock() - load_time_start))