diff --git a/mods/CORE/mcl_mapgen/init.lua b/mods/CORE/mcl_mapgen/init.lua index f24d76880f..3d5d1a8176 100644 --- a/mods/CORE/mcl_mapgen/init.lua +++ b/mods/CORE/mcl_mapgen/init.lua @@ -11,6 +11,39 @@ local order = { -- mcl_mapgen.order... LARGE_BUILDINGS = 2000000, } +-- Begin of Compatibility stuff + +local function unsigned(v) + if v < 0 then + v = 0x100000000 - (math.abs(v) % 0x100000000) + end + return v % 0x100000000 +end + +if not bit then + bit = {} + function bit.bxor(a, b) + local a = unsigned(a) + local b = unsigned(b) + local c = 0 + for n = 31, 0, -1 do + local mask = math.floor(2^n) + if (a >= mask) ~= (b >= mask) then + c = c + mask + end + a = a % mask + b = b % mask + end + return c + end +end + +if not vector.metatable then + dofile(minetest.get_modpath(minetest.get_current_modname() .. "/vector.lua")) +end + +-- End of compatibility stuff + local math_floor = math.floor local math_max = math.max local minetest_get_node = minetest.get_node diff --git a/mods/CORE/mcl_mapgen/vector.lua b/mods/CORE/mcl_mapgen/vector.lua new file mode 100644 index 0000000000..581d014e06 --- /dev/null +++ b/mods/CORE/mcl_mapgen/vector.lua @@ -0,0 +1,362 @@ +--[[ +Vector helpers +Note: The vector.*-functions must be able to accept old vectors that had no metatables +]] + +-- localize functions +local setmetatable = setmetatable + +vector = {} + +local metatable = {} +vector.metatable = metatable + +local xyz = {"x", "y", "z"} + +-- only called when rawget(v, key) returns nil +function metatable.__index(v, key) + return rawget(v, xyz[key]) or vector[key] +end + +-- only called when rawget(v, key) returns nil +function metatable.__newindex(v, key, value) + rawset(v, xyz[key] or key, value) +end + +-- constructors + +local function fast_new(x, y, z) + return setmetatable({x = x, y = y, z = z}, metatable) +end + +function vector.new(a, b, c) + if a and b and c then + return fast_new(a, b, c) + end + + -- deprecated, use vector.copy and vector.zero directly + if type(a) == "table" then + return vector.copy(a) + else + assert(not a, "Invalid arguments for vector.new()") + return vector.zero() + end +end + +function vector.zero() + return fast_new(0, 0, 0) +end + +function vector.copy(v) + assert(v.x and v.y and v.z, "Invalid vector passed to vector.copy()") + return fast_new(v.x, v.y, v.z) +end + +function vector.from_string(s, init) + local x, y, z, np = string.match(s, "^%s*%(%s*([^%s,]+)%s*[,%s]%s*([^%s,]+)%s*[,%s]" .. + "%s*([^%s,]+)%s*[,%s]?%s*%)()", init) + x = tonumber(x) + y = tonumber(y) + z = tonumber(z) + if not (x and y and z) then + return nil + end + return fast_new(x, y, z), np +end + +function vector.to_string(v) + return string.format("(%g, %g, %g)", v.x, v.y, v.z) +end +metatable.__tostring = vector.to_string + +function vector.equals(a, b) + return a.x == b.x and + a.y == b.y and + a.z == b.z +end +metatable.__eq = vector.equals + +-- unary operations + +function vector.length(v) + return math.sqrt(v.x * v.x + v.y * v.y + v.z * v.z) +end +-- Note: we can not use __len because it is already used for primitive table length + +function vector.normalize(v) + local len = vector.length(v) + if len == 0 then + return fast_new(0, 0, 0) + else + return vector.divide(v, len) + end +end + +function vector.floor(v) + return vector.apply(v, math.floor) +end + +function vector.round(v) + return fast_new( + math.round(v.x), + math.round(v.y), + math.round(v.z) + ) +end + +function vector.apply(v, func) + return fast_new( + func(v.x), + func(v.y), + func(v.z) + ) +end + +function vector.distance(a, b) + local x = a.x - b.x + local y = a.y - b.y + local z = a.z - b.z + return math.sqrt(x * x + y * y + z * z) +end + +function vector.direction(pos1, pos2) + return vector.subtract(pos2, pos1):normalize() +end + +function vector.angle(a, b) + local dotp = vector.dot(a, b) + local cp = vector.cross(a, b) + local crossplen = vector.length(cp) + return math.atan2(crossplen, dotp) +end + +function vector.dot(a, b) + return a.x * b.x + a.y * b.y + a.z * b.z +end + +function vector.cross(a, b) + return fast_new( + a.y * b.z - a.z * b.y, + a.z * b.x - a.x * b.z, + a.x * b.y - a.y * b.x + ) +end + +function metatable.__unm(v) + return fast_new(-v.x, -v.y, -v.z) +end + +-- add, sub, mul, div operations + +function vector.add(a, b) + if type(b) == "table" then + return fast_new( + a.x + b.x, + a.y + b.y, + a.z + b.z + ) + else + return fast_new( + a.x + b, + a.y + b, + a.z + b + ) + end +end +function metatable.__add(a, b) + return fast_new( + a.x + b.x, + a.y + b.y, + a.z + b.z + ) +end + +function vector.subtract(a, b) + if type(b) == "table" then + return fast_new( + a.x - b.x, + a.y - b.y, + a.z - b.z + ) + else + return fast_new( + a.x - b, + a.y - b, + a.z - b + ) + end +end +function metatable.__sub(a, b) + return fast_new( + a.x - b.x, + a.y - b.y, + a.z - b.z + ) +end + +function vector.multiply(a, b) + if type(b) == "table" then + return fast_new( + a.x * b.x, + a.y * b.y, + a.z * b.z + ) + else + return fast_new( + a.x * b, + a.y * b, + a.z * b + ) + end +end +function metatable.__mul(a, b) + if type(a) == "table" then + return fast_new( + a.x * b, + a.y * b, + a.z * b + ) + else + return fast_new( + a * b.x, + a * b.y, + a * b.z + ) + end +end + +function vector.divide(a, b) + if type(b) == "table" then + return fast_new( + a.x / b.x, + a.y / b.y, + a.z / b.z + ) + else + return fast_new( + a.x / b, + a.y / b, + a.z / b + ) + end +end +function metatable.__div(a, b) + -- scalar/vector makes no sense + return fast_new( + a.x / b, + a.y / b, + a.z / b + ) +end + +-- misc stuff + +function vector.offset(v, x, y, z) + return fast_new( + v.x + x, + v.y + y, + v.z + z + ) +end + +function vector.sort(a, b) + return fast_new(math.min(a.x, b.x), math.min(a.y, b.y), math.min(a.z, b.z)), + fast_new(math.max(a.x, b.x), math.max(a.y, b.y), math.max(a.z, b.z)) +end + +function vector.check(v) + return getmetatable(v) == metatable +end + +local function sin(x) + if x % math.pi == 0 then + return 0 + else + return math.sin(x) + end +end + +local function cos(x) + if x % math.pi == math.pi / 2 then + return 0 + else + return math.cos(x) + end +end + +function vector.rotate_around_axis(v, axis, angle) + local cosangle = cos(angle) + local sinangle = sin(angle) + axis = vector.normalize(axis) + -- https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula + local dot_axis = vector.multiply(axis, vector.dot(axis, v)) + local cross = vector.cross(v, axis) + return vector.new( + cross.x * sinangle + (v.x - dot_axis.x) * cosangle + dot_axis.x, + cross.y * sinangle + (v.y - dot_axis.y) * cosangle + dot_axis.y, + cross.z * sinangle + (v.z - dot_axis.z) * cosangle + dot_axis.z + ) +end + +function vector.rotate(v, rot) + local sinpitch = sin(-rot.x) + local sinyaw = sin(-rot.y) + local sinroll = sin(-rot.z) + local cospitch = cos(rot.x) + local cosyaw = cos(rot.y) + local cosroll = math.cos(rot.z) + -- Rotation matrix that applies yaw, pitch and roll + local matrix = { + { + sinyaw * sinpitch * sinroll + cosyaw * cosroll, + sinyaw * sinpitch * cosroll - cosyaw * sinroll, + sinyaw * cospitch, + }, + { + cospitch * sinroll, + cospitch * cosroll, + -sinpitch, + }, + { + cosyaw * sinpitch * sinroll - sinyaw * cosroll, + cosyaw * sinpitch * cosroll + sinyaw * sinroll, + cosyaw * cospitch, + }, + } + -- Compute matrix multiplication: `matrix` * `v` + return vector.new( + matrix[1][1] * v.x + matrix[1][2] * v.y + matrix[1][3] * v.z, + matrix[2][1] * v.x + matrix[2][2] * v.y + matrix[2][3] * v.z, + matrix[3][1] * v.x + matrix[3][2] * v.y + matrix[3][3] * v.z + ) +end + +function vector.dir_to_rotation(forward, up) + forward = vector.normalize(forward) + local rot = vector.new(math.asin(forward.y), -math.atan2(forward.x, forward.z), 0) + if not up then + return rot + end + assert(vector.dot(forward, up) < 0.000001, + "Invalid vectors passed to vector.dir_to_rotation().") + up = vector.normalize(up) + -- Calculate vector pointing up with roll = 0, just based on forward vector. + local forwup = vector.rotate(vector.new(0, 1, 0), rot) + -- 'forwup' and 'up' are now in a plane with 'forward' as normal. + -- The angle between them is the absolute of the roll value we're looking for. + rot.z = vector.angle(forwup, up) + + -- Since vector.angle never returns a negative value or a value greater + -- than math.pi, rot.z has to be inverted sometimes. + -- To determine wether this is the case, we rotate the up vector back around + -- the forward vector and check if it worked out. + local back = vector.rotate_around_axis(up, forward, -rot.z) + + -- We don't use vector.equals for this because of floating point imprecision. + if (back.x - forwup.x) * (back.x - forwup.x) + + (back.y - forwup.y) * (back.y - forwup.y) + + (back.z - forwup.z) * (back.z - forwup.z) > 0.0000001 then + rot.z = -rot.z + end + return rot +end