diff --git a/.gitmodules b/.gitmodules
index d921ba70..87cf933c 100644
--- a/.gitmodules
+++ b/.gitmodules
@@ -16,3 +16,6 @@
 [submodule "game/packages/community-creations"]
 	path = game/packages/community-creations
 	url = https://github.com/Legacy-LuaSTG-Engine/Community-Creations
+[submodule "game/packages/lua-ffi-math"]
+	path = game/packages/lua-ffi-math
+	url = https://github.com/BAKAOLC/Lua-FFI-Math.git
diff --git a/game/config.json b/game/config.json
index 7e3f3973..ff6eabb9 100644
--- a/game/config.json
+++ b/game/config.json
@@ -50,6 +50,11 @@
                 "type": "directory",
                 "path": "packages/thlib-scripts-v2/"
             },
+            {
+                "name": "lua-ffi-math",
+                "type": "directory",
+                "path": "packages/lua-ffi-math/"
+            },
             {
                 "name": "community-creations",
                 "type": "directory",
@@ -69,7 +74,7 @@
     "window": {
         "title": "LuaSTG aex+",
         "cursor_visible": true,
-        "allow_window_corner": true
+        "allow_window_corner": false
     },
     "graphics_system": {
         "preferred_device_name": "",
diff --git a/game/packages/lua-ffi-math b/game/packages/lua-ffi-math
new file mode 160000
index 00000000..adaa76fa
--- /dev/null
+++ b/game/packages/lua-ffi-math
@@ -0,0 +1 @@
+Subproject commit adaa76faedd2946c390f3e33fecf42dfa7f8a485
diff --git a/game/packages/thlib-scripts-v2/foundation/struct/array/BooleanArray.lua b/game/packages/thlib-scripts-v2/foundation/struct/array/BooleanArray.lua
new file mode 100644
index 00000000..ec591b80
--- /dev/null
+++ b/game/packages/thlib-scripts-v2/foundation/struct/array/BooleanArray.lua
@@ -0,0 +1,240 @@
+local ffi = require("ffi")
+
+local type = type
+local error = error
+local tostring = tostring
+local setmetatable = setmetatable
+local table = table
+local math = math
+
+---@class foundation.struct.array.BooleanArray
+---@field size number 数组大小
+---@field offset number 偏移量
+---@field data userdata FFI布尔数组
+local BooleanArray = {}
+
+---创建一个新的布尔数组
+---@param size number 数组大小(必须为正整数)
+---@param offset number 偏移量(默认为1)
+---@return foundation.struct.array.BooleanArray 新创建的布尔数组
+---@overload fun(size:number):foundation.struct.array.BooleanArray
+function BooleanArray.create(size, offset)
+    if type(size) ~= "number" or size <= 0 then
+        error("Invalid size: " .. tostring(size))
+    end
+    if type(offset) == "nil" then
+        offset = 1
+    end
+    if type(offset) ~= "number" or offset ~= math.floor(offset) then
+        error("Invalid offset: " .. tostring(offset))
+    end
+    local self = setmetatable({
+        size = size,
+        offset = offset,
+        data = ffi.new("bool[?]", size)
+    }, BooleanArray)
+    return self
+end
+
+---索引元方法，获取数组元素
+---@param self foundation.struct.array.BooleanArray
+---@param key number|string 索引或方法名
+---@return boolean|function 数组元素值或方法
+function BooleanArray.__index(self, key)
+    if type(key) == "number" then
+        local c_key = key - self.offset
+        if c_key < 0 or c_key >= self.size then
+            error("Index out of bounds: " .. key)
+        end
+        return self.data[c_key]
+    end
+    return BooleanArray[key]
+end
+
+---赋值元方法，设置数组元素
+---@param self foundation.struct.array.BooleanArray
+---@param key number 数组索引
+---@param value boolean 布尔值
+function BooleanArray.__newindex(self, key, value)
+    if type(key) ~= "number" then
+        error("Invalid index type: " .. type(key))
+    end
+    local c_key = key - self.offset
+    if c_key < 0 or c_key >= self.size then
+        error("Index out of bounds: " .. key)
+    end
+    if type(value) ~= "boolean" then
+        error("Invalid value type: " .. type(value))
+    end
+    self.data[c_key] = value
+end
+
+---加法元方法 (逻辑OR操作)
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return foundation.struct.array.BooleanArray 结果数组
+function BooleanArray.__add(a, b)
+    if a.size ~= b.size then
+        error("Cannot add arrays of different sizes")
+    end
+    local result = BooleanArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] or b.data[i]
+    end
+    return result
+end
+
+---减法元方法 (a且非b)
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return foundation.struct.array.BooleanArray 结果数组
+function BooleanArray.__sub(a, b)
+    if a.size ~= b.size then
+        error("Cannot subtract arrays of different sizes")
+    end
+    local result = BooleanArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] and not b.data[i]
+    end
+    return result
+end
+
+---乘法元方法 (逻辑AND操作)
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return foundation.struct.array.BooleanArray 结果数组
+function BooleanArray.__mul(a, b)
+    if a.size ~= b.size then
+        error("Cannot multiply arrays of different sizes")
+    end
+    local result = BooleanArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] and b.data[i]
+    end
+    return result
+end
+
+---除法元方法 (逻辑相等操作)
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return foundation.struct.array.BooleanArray 结果数组
+function BooleanArray.__div(a, b)
+    if a.size ~= b.size then
+        error("Cannot divide arrays of different sizes")
+    end
+    local result = BooleanArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] == b.data[i]
+    end
+    return result
+end
+
+---一元减法元方法 (逻辑NOT操作)
+---@param self foundation.struct.array.BooleanArray
+---@return foundation.struct.array.BooleanArray 取反后的数组
+function BooleanArray.__unm(self)
+    local result = BooleanArray.create(self.size)
+    for i = 0, self.size - 1 do
+        result.data[i] = not self.data[i]
+    end
+    return result
+end
+
+---连接元方法
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return foundation.struct.array.BooleanArray 连接后的数组
+function BooleanArray.__concat(a, b)
+    local result = BooleanArray.create(a.size + b.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i]
+    end
+    for i = 0, b.size - 1 do
+        result.data[a.size + i] = b.data[i]
+    end
+    return result
+end
+
+---相等比较元方法
+---@param a foundation.struct.array.BooleanArray 左操作数
+---@param b foundation.struct.array.BooleanArray 右操作数
+---@return boolean 数组是否相等
+function BooleanArray.__eq(a, b)
+    if a.size ~= b.size then
+        return false
+    end
+    for i = 0, a.size - 1 do
+        if a.data[i] ~= b.data[i] then
+            return false
+        end
+    end
+    return true
+end
+
+---获取数组长度的元方法
+---@param self foundation.struct.array.BooleanArray
+---@return number 数组长度
+function BooleanArray.__len(self)
+    return self.size
+end
+BooleanArray.length = BooleanArray.__len
+
+---转为字符串的元方法
+---@param self foundation.struct.array.BooleanArray
+---@return string 数组的字符串表示
+function BooleanArray.__tostring(self)
+    local result = {}
+    for i = 0, self.size - 1 do
+        result[i + 1] = tostring(self.data[i])
+    end
+    return "BooleanArray: [" .. table.concat(result, ", ") .. "]"
+end
+
+---获取数组索引的偏移量
+---@return number 数组偏移量
+function BooleanArray:getOffset()
+    return self.offset
+end
+
+---设置数组的偏移量
+---@param offset number 新的偏移量
+function BooleanArray:setOffset(offset)
+    if type(offset) ~= "number" then
+        error("Invalid offset type: " .. type(offset))
+    end
+    if offset ~= math.floor(offset) then
+        error("Offset must be an integer")
+    end
+    self.offset = offset
+end
+
+---用指定的值填充整个数组
+---@param value boolean 填充值
+function BooleanArray:fill(value)
+    for i = 0, self.size - 1 do
+        self.data[i] = value
+    end
+end
+
+---获取数组的迭代器
+---@return function,foundation.struct.array.BooleanArray,number 迭代器函数、数组对象和初始索引
+function BooleanArray:ipairs()
+    return function(t, i)
+        i = i + 1
+        if i < t.size then
+            return i, t.data[i]
+        end
+    end, self, -1
+end
+
+---克隆数组
+---@return foundation.struct.array.BooleanArray 数组副本
+function BooleanArray:clone()
+    local clone = BooleanArray.create(self.size)
+    for i = 0, self.size - 1 do
+        clone.data[i] = self.data[i]
+    end
+    return clone
+end
+
+return BooleanArray
\ No newline at end of file
diff --git a/game/packages/thlib-scripts-v2/foundation/struct/array/DoubleArray.lua b/game/packages/thlib-scripts-v2/foundation/struct/array/DoubleArray.lua
new file mode 100644
index 00000000..22e98c5d
--- /dev/null
+++ b/game/packages/thlib-scripts-v2/foundation/struct/array/DoubleArray.lua
@@ -0,0 +1,299 @@
+local ffi = require("ffi")
+
+local type = type
+local error = error
+local tostring = tostring
+local setmetatable = setmetatable
+local table = table
+local math = math
+
+---@class foundation.struct.array.DoubleArray
+---@field size number 数组大小
+---@field offset number 偏移量
+---@field data userdata FFI双精度浮点数数组
+local DoubleArray = {}
+
+---创建一个新的双精度浮点数数组
+---@param size number 数组大小(必须为正整数)
+---@param offset number 偏移量(默认为1)
+---@return foundation.struct.array.DoubleArray 新创建的双精度浮点数数组
+---@overload fun(size:number):foundation.struct.array.DoubleArray
+function DoubleArray.create(size, offset)
+    if type(size) ~= "number" or size <= 0 then
+        error("Invalid size: " .. tostring(size))
+    end
+    if type(offset) == "nil" then
+        offset = 1
+    end
+    if type(offset) ~= "number" or offset ~= math.floor(offset) then
+        error("Invalid offset: " .. tostring(offset))
+    end
+    local self = setmetatable({
+        size = size,
+        offset = offset,
+        data = ffi.new("double[?]", size)
+    }, DoubleArray)
+    return self
+end
+
+---索引元方法，获取数组元素
+---@param self foundation.struct.array.DoubleArray
+---@param key number|string 索引或方法名
+---@return number|function 数组元素值或方法
+function DoubleArray.__index(self, key)
+    if type(key) == "number" then
+        local c_key = key - self.offset
+        if c_key < 0 or c_key >= self.size then
+            error("Index out of bounds: " .. key)
+        end
+        return self.data[c_key]
+    end
+    return DoubleArray[key]
+end
+
+---赋值元方法，设置数组元素
+---@param self foundation.struct.array.DoubleArray
+---@param key number 数组索引
+---@param value number 浮点数值
+function DoubleArray.__newindex(self, key, value)
+    if type(key) ~= "number" then
+        error("Invalid index type: " .. type(key))
+    end
+    local c_key = key - self.offset
+    if c_key < 0 or c_key >= self.size then
+        error("Index out of bounds: " .. key)
+    end
+    if type(value) ~= "number" then
+        error("Invalid value type: " .. type(value))
+    end
+    self.data[c_key] = value
+end
+
+---加法元方法
+---@param a foundation.struct.array.DoubleArray|number 左操作数
+---@param b foundation.struct.array.DoubleArray|number 右操作数
+---@return foundation.struct.array.DoubleArray 结果数组
+function DoubleArray.__add(a, b)
+    if type(a) == "number" then
+        local result = DoubleArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a + b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = DoubleArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] + b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot add arrays of different sizes")
+    end
+    local result = DoubleArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] + b.data[i]
+    end
+    return result
+end
+
+---减法元方法
+---@param a foundation.struct.array.DoubleArray|number 左操作数
+---@param b foundation.struct.array.DoubleArray|number 右操作数
+---@return foundation.struct.array.DoubleArray 结果数组
+function DoubleArray.__sub(a, b)
+    if type(a) == "number" then
+        local result = DoubleArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a - b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = DoubleArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] - b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot subtract arrays of different sizes")
+    end
+    local result = DoubleArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] - b.data[i]
+    end
+    return result
+end
+
+---乘法元方法
+---@param a foundation.struct.array.DoubleArray|number 左操作数
+---@param b foundation.struct.array.DoubleArray|number 右操作数
+---@return foundation.struct.array.DoubleArray 结果数组
+function DoubleArray.__mul(a, b)
+    if type(a) == "number" then
+        local result = DoubleArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a * b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = DoubleArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] * b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot multiply arrays of different sizes")
+    end
+    local result = DoubleArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] * b.data[i]
+    end
+    return result
+end
+
+---除法元方法
+---@param a foundation.struct.array.DoubleArray|number 左操作数
+---@param b foundation.struct.array.DoubleArray|number 右操作数
+---@return foundation.struct.array.DoubleArray 结果数组
+function DoubleArray.__div(a, b)
+    if type(a) == "number" then
+        local result = DoubleArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a / b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = DoubleArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] / b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot divide arrays of different sizes")
+    end
+    local result = DoubleArray.create(a.size)
+    for i = 0, a.size - 1 do
+        if b.data[i] == 0 then
+            error("Division by zero at index: " .. i)
+        end
+        result.data[i] = a.data[i] / b.data[i]
+    end
+    return result
+end
+
+---一元减法元方法
+---@param self foundation.struct.array.DoubleArray
+---@return foundation.struct.array.DoubleArray 取反后的数组
+function DoubleArray.__unm(self)
+    local result = DoubleArray.create(self.size)
+    for i = 0, self.size - 1 do
+        result.data[i] = -self.data[i]
+    end
+    return result
+end
+
+---连接元方法
+---@param a foundation.struct.array.DoubleArray 左操作数
+---@param b foundation.struct.array.DoubleArray 右操作数
+---@return foundation.struct.array.DoubleArray 连接后的数组
+function DoubleArray.__concat(a, b)
+    local result = DoubleArray.create(a.size + b.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i]
+    end
+    for i = 0, b.size - 1 do
+        result.data[a.size + i] = b.data[i]
+    end
+    return result
+end
+
+---相等比较元方法
+---@param a foundation.struct.array.DoubleArray 左操作数
+---@param b foundation.struct.array.DoubleArray 右操作数
+---@return boolean 数组是否相等
+function DoubleArray.__eq(a, b)
+    if a.size ~= b.size then
+        return false
+    end
+    for i = 0, a.size - 1 do
+        if a.data[i] ~= b.data[i] then
+            return false
+        end
+    end
+    return true
+end
+
+---获取数组长度的元方法
+---@param self foundation.struct.array.DoubleArray
+---@return number 数组长度
+function DoubleArray.__len(self)
+    return self.size
+end
+DoubleArray.length = DoubleArray.__len
+
+---转为字符串的元方法
+---@param self foundation.struct.array.DoubleArray
+---@return string 数组的字符串表示
+function DoubleArray.__tostring(self)
+    local result = {}
+    for i = 0, self.size - 1 do
+        result[i + 1] = tostring(self.data[i])
+    end
+    return "DoubleArray: [" .. table.concat(result, ", ") .. "]"
+end
+
+---获取数组索引的偏移量
+---@return number 数组偏移量
+function DoubleArray:getOffset()
+    return self.offset
+end
+
+---设置数组的偏移量
+---@param offset number 新的偏移量
+function DoubleArray:setOffset(offset)
+    if type(offset) ~= "number" then
+        error("Invalid offset type: " .. type(offset))
+    end
+    if offset ~= math.floor(offset) then
+        error("Offset must be an integer")
+    end
+    self.offset = offset
+end
+
+---用指定的值填充整个数组
+---@param value number 填充值
+function DoubleArray:fill(value)
+    for i = 0, self.size - 1 do
+        self.data[i] = value
+    end
+end
+
+---获取数组的迭代器
+---@return function,foundation.struct.array.DoubleArray,number 迭代器函数、数组对象和初始索引
+function DoubleArray:ipairs()
+    return function(t, i)
+        i = i + 1
+        if i < t.size then
+            return i, t.data[i]
+        end
+    end, self, -1
+end
+
+---克隆数组
+---@return foundation.struct.array.DoubleArray 数组副本
+function DoubleArray:clone()
+    local clone = DoubleArray.create(self.size)
+    for i = 0, self.size - 1 do
+        clone.data[i] = self.data[i]
+    end
+    return clone
+end
+
+return DoubleArray
\ No newline at end of file
diff --git a/game/packages/thlib-scripts-v2/foundation/struct/array/IntArray.lua b/game/packages/thlib-scripts-v2/foundation/struct/array/IntArray.lua
new file mode 100644
index 00000000..05dd05b1
--- /dev/null
+++ b/game/packages/thlib-scripts-v2/foundation/struct/array/IntArray.lua
@@ -0,0 +1,299 @@
+local ffi = require("ffi")
+
+local type = type
+local error = error
+local tostring = tostring
+local setmetatable = setmetatable
+local table = table
+local math = math
+
+---@class foundation.struct.array.IntArray
+---@field size number 数组大小
+---@field offset number 偏移量
+---@field data userdata FFI整数数组
+local IntArray = {}
+
+---创建一个新的整型数组
+---@param size number 数组大小(必须为正整数)
+---@param offset number 偏移量(默认为1)
+---@return foundation.struct.array.IntArray 新创建的整型数组
+---@overload fun(size:number):foundation.struct.array.IntArray
+function IntArray.create(size, offset)
+    if type(size) ~= "number" or size <= 0 then
+        error("Invalid size: " .. tostring(size))
+    end
+    if type(offset) == "nil" then
+        offset = 1
+    end
+    if type(offset) ~= "number" or offset ~= math.floor(offset) then
+        error("Invalid offset: " .. tostring(offset))
+    end
+    local self = setmetatable({
+        size = size,
+        offset = offset,
+        data = ffi.new("int[?]", size)
+    }, IntArray)
+    return self
+end
+
+---索引元方法，获取数组元素
+---@param self foundation.struct.array.IntArray
+---@param key number|string 索引或方法名
+---@return number|function 数组元素值或方法
+function IntArray.__index(self, key)
+    if type(key) == "number" then
+        local c_key = key - self.offset
+        if c_key < 0 or c_key >= self.size then
+            error("Index out of bounds: " .. key)
+        end
+        return self.data[c_key]
+    end
+    return IntArray[key]
+end
+
+---赋值元方法，设置数组元素
+---@param self foundation.struct.array.IntArray
+---@param key number 数组索引
+---@param value number 整数值
+function IntArray.__newindex(self, key, value)
+    if type(key) ~= "number" then
+        error("Invalid index type: " .. type(key))
+    end
+    local c_key = key - self.offset
+    if c_key < 0 or c_key >= self.size then
+        error("Index out of bounds: " .. key)
+    end
+    if type(value) ~= "number" then
+        error("Invalid value type: " .. type(value))
+    end
+    self.data[c_key] = value
+end
+
+---加法元方法
+---@param a foundation.struct.array.IntArray|number 左操作数
+---@param b foundation.struct.array.IntArray|number 右操作数
+---@return foundation.struct.array.IntArray 结果数组
+function IntArray.__add(a, b)
+    if type(a) == "number" then
+        local result = IntArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a + b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = IntArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] + b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot add arrays of different sizes")
+    end
+    local result = IntArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] + b.data[i]
+    end
+    return result
+end
+
+---减法元方法
+---@param a foundation.struct.array.IntArray|number 左操作数
+---@param b foundation.struct.array.IntArray|number 右操作数
+---@return foundation.struct.array.IntArray 结果数组
+function IntArray.__sub(a, b)
+    if type(a) == "number" then
+        local result = IntArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a - b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = IntArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] - b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot subtract arrays of different sizes")
+    end
+    local result = IntArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] - b.data[i]
+    end
+    return result
+end
+
+---乘法元方法
+---@param a foundation.struct.array.IntArray|number 左操作数
+---@param b foundation.struct.array.IntArray|number 右操作数
+---@return foundation.struct.array.IntArray 结果数组
+function IntArray.__mul(a, b)
+    if type(a) == "number" then
+        local result = IntArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a * b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = IntArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] * b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot multiply arrays of different sizes")
+    end
+    local result = IntArray.create(a.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i] * b.data[i]
+    end
+    return result
+end
+
+---除法元方法
+---@param a foundation.struct.array.IntArray|number 左操作数
+---@param b foundation.struct.array.IntArray|number 右操作数
+---@return foundation.struct.array.IntArray 结果数组
+function IntArray.__div(a, b)
+    if type(a) == "number" then
+        local result = IntArray.create(b.size)
+        for i = 0, b.size - 1 do
+            result.data[i] = a / b.data[i]
+        end
+        return result
+    end
+    if type(b) == "number" then
+        local result = IntArray.create(a.size)
+        for i = 0, a.size - 1 do
+            result.data[i] = a.data[i] / b
+        end
+        return result
+    end
+    if a.size ~= b.size then
+        error("Cannot divide arrays of different sizes")
+    end
+    local result = IntArray.create(a.size)
+    for i = 0, a.size - 1 do
+        if b.data[i] == 0 then
+            error("Division by zero at index: " .. i)
+        end
+        result.data[i] = a.data[i] / b.data[i]
+    end
+    return result
+end
+
+---一元减法元方法
+---@param self foundation.struct.array.IntArray
+---@return foundation.struct.array.IntArray 取反后的数组
+function IntArray.__unm(self)
+    local result = IntArray.create(self.size)
+    for i = 0, self.size - 1 do
+        result.data[i] = -self.data[i]
+    end
+    return result
+end
+
+---连接元方法
+---@param a foundation.struct.array.IntArray 左操作数
+---@param b foundation.struct.array.IntArray 右操作数
+---@return foundation.struct.array.IntArray 连接后的数组
+function IntArray.__concat(a, b)
+    local result = IntArray.create(a.size + b.size)
+    for i = 0, a.size - 1 do
+        result.data[i] = a.data[i]
+    end
+    for i = 0, b.size - 1 do
+        result.data[a.size + i] = b.data[i]
+    end
+    return result
+end
+
+---相等比较元方法
+---@param a foundation.struct.array.IntArray 左操作数
+---@param b foundation.struct.array.IntArray 右操作数
+---@return boolean 数组是否相等
+function IntArray.__eq(a, b)
+    if a.size ~= b.size then
+        return false
+    end
+    for i = 0, a.size - 1 do
+        if a.data[i] ~= b.data[i] then
+            return false
+        end
+    end
+    return true
+end
+
+---获取数组长度的元方法
+---@param self foundation.struct.array.IntArray
+---@return number 数组长度
+function IntArray.__len(self)
+    return self.size
+end
+IntArray.length = IntArray.__len
+
+---转为字符串的元方法
+---@param self foundation.struct.array.IntArray
+---@return string 数组的字符串表示
+function IntArray.__tostring(self)
+    local result = {}
+    for i = 0, self.size - 1 do
+        result[i + 1] = tostring(self.data[i])
+    end
+    return "IntArray: [" .. table.concat(result, ", ") .. "]"
+end
+
+---获取数组索引的偏移量
+---@return number 数组偏移量
+function IntArray:getOffset()
+    return self.offset
+end
+
+---设置数组的偏移量
+---@param offset number 新的偏移量
+function IntArray:setOffset(offset)
+    if type(offset) ~= "number" then
+        error("Invalid offset type: " .. type(offset))
+    end
+    if offset ~= math.floor(offset) then
+        error("Offset must be an integer")
+    end
+    self.offset = offset
+end
+
+---用指定的值填充整个数组
+---@param value number 填充值
+function IntArray:fill(value)
+    for i = 0, self.size - 1 do
+        self.data[i] = value
+    end
+end
+
+---获取数组的迭代器
+---@return function,foundation.struct.array.IntArray,number 迭代器函数、数组对象和初始索引
+function IntArray:ipairs()
+    return function(t, i)
+        i = i + 1
+        if i < t.size then
+            return i, t.data[i]
+        end
+    end, self, -1
+end
+
+---克隆数组
+---@return foundation.struct.array.IntArray 数组副本
+function IntArray:clone()
+    local clone = IntArray.create(self.size)
+    for i = 0, self.size - 1 do
+        clone.data[i] = self.data[i]
+    end
+    return clone
+end
+
+return IntArray
\ No newline at end of file
diff --git a/laboratory/geometry/.gitignore b/laboratory/geometry/.gitignore
new file mode 100644
index 00000000..084f6144
--- /dev/null
+++ b/laboratory/geometry/.gitignore
@@ -0,0 +1,2 @@
+engine.log
+userdata
\ No newline at end of file
diff --git a/laboratory/geometry/config.json b/laboratory/geometry/config.json
new file mode 100644
index 00000000..ea00826e
--- /dev/null
+++ b/laboratory/geometry/config.json
@@ -0,0 +1,11 @@
+{
+    "log_file_enable": true,
+    "log_file_path": "engine.log",
+    "persistent_log_file_enable": false,
+    "persistent_log_file_directory": "userdata/logs/",
+    "persistent_log_file_max_count": 10,
+    "engine_cache_directory": "",
+    "single_application_instance": true,
+    "application_instance_id": "0689df8f-7886-4d89-a335-5fba6e855d05",
+    "debug_track_window_focus": false
+}
\ No newline at end of file
diff --git a/laboratory/geometry/main.lua b/laboratory/geometry/main.lua
new file mode 100644
index 00000000..643b6c2c
--- /dev/null
+++ b/laboratory/geometry/main.lua
@@ -0,0 +1,1119 @@
+local lstg = require("lstg")
+lstg.FileManager.AddSearchPath("../../game/packages/thlib-scripts/")
+lstg.FileManager.AddSearchPath("../../game/packages/lua-ffi-math/")
+lstg.FileManager.AddSearchPath("../../game/packages/thlib-resources/")
+
+local Keyboard = lstg.Input.Keyboard
+local Mouse = lstg.Input.Mouse
+
+local window = {
+    width = 640,
+    height = 480,
+    view_width = 1280,
+    view_height = 960,
+}
+function window:applyWindowSetting()
+    lstg.ChangeVideoMode(self.view_width, self.view_height, true, false)
+end
+function window:applyCameraSetting()
+    lstg.SetViewport(0, self.view_width, 0, self.view_height)
+    lstg.SetScissorRect(0, self.view_width, 0, self.view_height)
+    lstg.SetOrtho(0, self.width, 0, self.height)
+    lstg.SetFog()
+    lstg.SetImageScale(1.0)
+    lstg.SetZBufferEnable(0)
+end
+
+local function loadSprite(name, path, mipmap)
+    lstg.LoadTexture(name, path, mipmap)
+    local width, height = lstg.GetTextureSize(name)
+    lstg.LoadImage(name, name, 0, 0, width, height)
+end
+loadSprite("white", "white.png", false)
+
+--region Geometry
+local Vector2 = require("foundation.math.Vector2")
+
+local Line = require("foundation.shape.Line")
+local Ray = require("foundation.shape.Ray")
+local Segment = require("foundation.shape.Segment")
+local BezierCurve = require("foundation.shape.BezierCurve")
+
+local Triangle = require("foundation.shape.Triangle")
+local Rectangle = require("foundation.shape.Rectangle")
+local Polygon = require("foundation.shape.Polygon")
+local Circle = require("foundation.shape.Circle")
+local Sector = require("foundation.shape.Sector")
+local Ellipse = require("foundation.shape.Ellipse")
+--endregion
+
+--region Math Method
+local function _A(x1, y1, x2, y2)
+    return math.deg(math.atan2(y2 - y1, x2 - x1))
+end
+local function Angle(a, b, c, d)
+    if a and b and c and d then
+        return _A(a, b, c, d)
+    elseif a and b and c then
+        if type(a) == "table" then
+            return _A(a.x, a.y, b, c)
+        elseif type(c) == "table" then
+            return _A(a, b, c.x, c.y)
+        else
+            error("Error parameters")
+        end
+    elseif a and b then
+        return _A(a.x, a.y, b.x, b.y)
+    else
+        error("Error parameters")
+    end
+end
+
+local function _D(x1, y1, x2, y2)
+    return math.sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2)
+end
+local function Dist(a, b, c, d)
+    if a and b and c and d then
+        return _D(a, b, c, d)
+    elseif a and b and c then
+        if type(a) == "table" then
+            return _D(a.x, a.y, b, c)
+        elseif type(c) == "table" then
+            return _D(a, b, c.x, c.y)
+        else
+            error("Error parameters")
+        end
+    elseif a and b then
+        return _D(a.x, a.y, b.x, b.y)
+    else
+        error("Error parameters")
+    end
+end
+--endregion
+
+--region Render Method
+local function setColor(a, r, g, b)
+    lstg.SetImageState("white", "", lstg.Color(a, r, g, b))
+end
+
+---@param p {x:number, y:number}
+---@param size number
+local function renderPoint(p, size)
+    lstg.Render("white", p.x, p.y, 0, size / 8)
+end
+
+---@param p1 {x:number, y:number}
+---@param p2 {x:number, y:number}
+---@param width number
+local function renderLine(p1, p2, width)
+    local cx = (p1.x + p2.x) / 2
+    local cy = (p1.y + p2.y) / 2
+    local length = Dist(p1, p2)
+    local rot = Angle(p1, p2)
+    local hscale = length / 16
+    local vscale = width / 16
+    lstg.Render("white", cx, cy, rot, hscale, vscale)
+end
+
+---@param p {x:number, y:number}
+---@param radius1 number
+---@param radius2 number
+---@param n number
+local function renderCircle(p, radius1, radius2, n)
+    local angle = 360 / n
+    for i = 1, n do
+        local angle1 = (i - 1) * angle
+        local angle2 = i * angle
+        local x1 = p.x + radius1 * lstg.cos(angle1)
+        local y1 = p.y + radius1 * lstg.sin(angle1)
+        local x2 = p.x + radius1 * lstg.cos(angle2)
+        local y2 = p.y + radius1 * lstg.sin(angle2)
+        local x3 = p.x + radius2 * lstg.cos(angle2)
+        local y3 = p.y + radius2 * lstg.sin(angle2)
+        local x4 = p.x + radius2 * lstg.cos(angle1)
+        local y4 = p.y + radius2 * lstg.sin(angle1)
+        lstg.Render4V("white", x1, y1, 0.5,
+                x2, y2, 0.5,
+                x3, y3, 0.5,
+                x4, y4, 0.5)
+    end
+end
+
+---@param p {x:number, y:number}
+---@param radius1 number
+---@param radius2 number
+---@param angleFrom number
+---@param angleTo number
+---@param n number
+local function renderSector(p, radius1, radius2, angleFrom, angleTo, n)
+    local angle = (angleTo - angleFrom) / n
+    for i = 1, n do
+        local angle1 = angleFrom + (i - 1) * angle
+        local angle2 = angleFrom + i * angle
+        local x1 = p.x + radius1 * lstg.cos(angle1)
+        local y1 = p.y + radius1 * lstg.sin(angle1)
+        local x2 = p.x + radius1 * lstg.cos(angle2)
+        local y2 = p.y + radius1 * lstg.sin(angle2)
+        local x3 = p.x + radius2 * lstg.cos(angle2)
+        local y3 = p.y + radius2 * lstg.sin(angle2)
+        local x4 = p.x + radius2 * lstg.cos(angle1)
+        local y4 = p.y + radius2 * lstg.sin(angle1)
+        lstg.Render4V("white", x1, y1, 0.5,
+                x2, y2, 0.5,
+                x3, y3, 0.5,
+                x4, y4, 0.5)
+    end
+end
+--endregion
+
+--region Player Method
+local player = {}
+function player:pos()
+    local mouseX, mouseY = Mouse.GetPosition()
+    if mouseX ~= mouseX or mouseY ~= mouseY then
+        -- why LuaSTG got NaN?
+        return Vector2.create(0, 0)
+    end
+    mouseX = mouseX / window.view_width * window.width
+    mouseY = mouseY / window.view_height * window.height
+    return Vector2.create(mouseX, mouseY)
+end
+--endregion
+
+--region Object Method
+local object = {
+    pool = {},
+    collision_result = {},
+    render_player_point = true,
+    render_closest_point = true,
+    render_project_point = true,
+    render_bounding_box = true,
+    render_collision_result = true,
+    render_incircle = true,
+    render_circumcircle = true,
+    render_vertex = true,
+    render_direction = true,
+}
+function object:insert(obj)
+    table.insert(self.pool, obj)
+end
+function object:clear()
+    self.pool = {}
+    self.collision_result = {}
+end
+function object:enum()
+    return ipairs(self.pool)
+end
+function object:updateCollisionCheck()
+    local result = {}
+    for i = 1, #self.pool do
+        local obj1 = self.pool[i]
+        for j = i + 1, #self.pool do
+            local obj2 = self.pool[j]
+            local intersection, points = obj1:intersects(obj2)
+            if intersection then
+                for _, point in ipairs(points) do
+                    table.insert(result, point)
+                end
+            end
+        end
+    end
+    self.collision_result = result
+end
+function object:update()
+    self:updateCollisionCheck()
+end
+function object:draw()
+    local player_pos = player:pos()
+    if self.render_player_point then
+        self:renderPlayerPoint(player_pos)
+    end
+    if self.render_bounding_box then
+        for _, obj in self:enum() do
+            self:renderBoundingBox(obj)
+        end
+    end
+    for _, obj in self:enum() do
+        if obj.__type == "foundation.shape.Line" then
+            self:renderLine(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Ray" then
+            self:renderRay(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Segment" then
+            self:renderSegment(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Triangle" then
+            self:renderTriangle(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Circle" then
+            self:renderCircle(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Rectangle" then
+            self:renderRectangle(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Sector" then
+            self:renderSector(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Polygon" then
+            self:renderPolygon(obj, player_pos)
+        elseif obj.__type == "foundation.shape.Ellipse" then
+            self:renderEllipse(obj, player_pos)
+        elseif obj.__type == "foundation.shape.BezierCurve" then
+            self:renderBezierCurve(obj, player_pos)
+        end
+        if self.render_project_point then
+            self:renderProjectPoint(obj, player_pos)
+        end
+        if self.render_closest_point then
+            self:renderClosestPoint(obj, player_pos)
+        end
+    end
+    if self.render_collision_result then
+        self:renderCollisionResult()
+    end
+end
+
+---@param player_pos {x:number, y:number}
+function object:renderPlayerPoint(player_pos)
+    setColor(255, 255, 255, 255)
+    renderPoint(player_pos, 4)
+end
+
+function object:renderCollisionResult()
+    setColor(192, 0, 255, 255)
+    for _, point in ipairs(self.collision_result) do
+        renderPoint(point, 4)
+    end
+end
+
+---@param obj {__type:string, closestPoint:function}
+---@param player_pos {x:number, y:number}
+function object:renderClosestPoint(obj, player_pos)
+    local nearestPoint = obj:closestPoint(player_pos)
+    setColor(127, 127, 127, 127)
+    renderLine(player_pos, nearestPoint, 2)
+    setColor(192, 255, 200, 127)
+    renderPoint(nearestPoint, 4)
+end
+
+---@param obj {__type:string, projectPoint:function}
+---@param player_pos {x:number, y:number}
+function object:renderProjectPoint(obj, player_pos)
+    local projectPoint = obj:projectPoint(player_pos)
+    setColor(127, 127, 127, 127)
+    renderLine(player_pos, projectPoint, 2)
+    setColor(192, 200, 127, 255)
+    renderPoint(projectPoint, 4)
+end
+
+---@param obj {__type:string, getBoundingBoxSize:function, getCenter:function}
+function object:renderBoundingBox(obj)
+    local center = obj:getCenter()
+    local w, h = obj:getBoundingBoxSize()
+    local v1 = Vector2.create(center.x - w / 2, center.y - h / 2)
+    local v2 = Vector2.create(center.x + w / 2, center.y + h / 2)
+    setColor(192, 127, 0, 127)
+    renderLine(v1, Vector2.create(v1.x, v2.y), 2)
+    renderLine(v1, Vector2.create(v2.x, v1.y), 2)
+    renderLine(v2, Vector2.create(v1.x, v2.y), 2)
+    renderLine(v2, Vector2.create(v2.x, v1.y), 2)
+end
+
+---@param line foundation.shape.Line
+---@param player_pos {x:number, y:number}
+function object:renderLine(line, player_pos)
+    if line:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderLine(line:getPoint(-1000), line:getPoint(1000), 2)
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        renderPoint(line.point, 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(line.point, line:getPoint(50), 2)
+    end
+end
+
+---@param ray foundation.shape.Ray
+---@param player_pos {x:number, y:number}
+function object:renderRay(ray, player_pos)
+    if ray:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderLine(ray.point, ray:getPoint(1000), 2)
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        renderPoint(ray.point, 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(ray.point, ray:getPoint(50), 2)
+    end
+end
+
+---@param segment foundation.shape.Segment
+---@param player_pos {x:number, y:number}
+function object:renderSegment(segment, player_pos)
+    if segment:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderLine(segment.point1, segment.point2, 2)
+    if self.render_vertex then
+        setColor(127, 127, 0, 0)
+        renderPoint(segment.point1, 4)
+        renderPoint(segment.point2, 4)
+        setColor(127, 255, 0, 0)
+        renderPoint(segment:midpoint(), 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(segment:midpoint(), segment.point1, 2)
+    end
+end
+
+---@param triangle foundation.shape.Triangle
+---@param player_pos {x:number, y:number}
+function object:renderTriangle(triangle, player_pos)
+    setColor(63, 127, 255, 192)
+    if self.render_incircle then
+        local incenter = triangle:incenter()
+        local inradius = triangle:inradius()
+        setColor(63, 127, 255, 192)
+        renderCircle(incenter, inradius - 1, inradius + 1, 64)
+    end
+    if self.render_circumcircle then
+        local circumcenter = triangle:circumcenter()
+        local circumradius = triangle:circumradius()
+        setColor(63, 127, 192, 255)
+        renderCircle(circumcenter, circumradius - 1, circumradius + 1, 64)
+    end
+    if triangle:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif triangle:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderLine(triangle.point1, triangle.point2, 2)
+    renderLine(triangle.point2, triangle.point3, 2)
+    renderLine(triangle.point3, triangle.point1, 2)
+    if self.render_vertex then
+        setColor(127, 127, 0, 0)
+        renderPoint(triangle.point1, 4)
+        renderPoint(triangle.point2, 4)
+        renderPoint(triangle.point3, 4)
+        setColor(127, 255, 0, 0)
+        renderPoint(triangle:centroid(), 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(triangle:centroid(), triangle.point1, 2)
+    end
+end
+
+---@param rectangle foundation.shape.Rectangle
+---@param player_pos {x:number, y:number}
+function object:renderRectangle(rectangle, player_pos)
+    local p = rectangle.center
+    local w = rectangle.width / 2
+    local h = rectangle.height / 2
+    local a = rectangle.direction:degreeAngle()
+    if self.render_incircle then
+        local inradius = rectangle:inradius()
+        setColor(63, 127, 255, 192)
+        renderCircle(p, inradius - 1, inradius + 1, 64)
+    end
+    if self.render_circumcircle then
+        local circumradius = rectangle:circumradius()
+        setColor(63, 127, 192, 255)
+        renderCircle(p, circumradius - 1, circumradius + 1, 64)
+    end
+    if rectangle:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif rectangle:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderLine(p + Vector2.create(-w, -h):degreeRotated(a), p + Vector2.create(w, -h):degreeRotated(a), 2)
+    renderLine(p + Vector2.create(w, -h):degreeRotated(a), p + Vector2.create(w, h):degreeRotated(a), 2)
+    renderLine(p + Vector2.create(w, h):degreeRotated(a), p + Vector2.create(-w, h):degreeRotated(a), 2)
+    renderLine(p + Vector2.create(-w, h):degreeRotated(a), p + Vector2.create(-w, -h):degreeRotated(a), 2)
+    if self.render_vertex then
+        setColor(127, 127, 0, 0)
+        renderPoint(p + Vector2.create(-w, -h):degreeRotated(a), 4)
+        renderPoint(p + Vector2.create(w, -h):degreeRotated(a), 4)
+        renderPoint(p + Vector2.create(w, h):degreeRotated(a), 4)
+        renderPoint(p + Vector2.create(-w, h):degreeRotated(a), 4)
+        setColor(127, 255, 0, 0)
+        renderPoint(p, 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(p, p + Vector2.create(w, 0):degreeRotated(a), 2)
+    end
+end
+
+---@param polygon foundation.shape.Polygon
+---@param player_pos {x:number, y:number}
+function object:renderPolygon(polygon, player_pos)
+    local vertices = polygon:getVertices()
+    if polygon:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif polygon:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    for i = 1, #vertices do
+        local p1 = vertices[i]
+        local p2 = vertices[i % #vertices + 1]
+        renderLine(p1, p2, 2)
+    end
+    if self.render_vertex then
+        setColor(127, 127, 0, 0)
+        for _, vertex in ipairs(vertices) do
+            renderPoint(vertex, 4)
+        end
+        setColor(127, 255, 0, 0)
+        renderPoint(polygon:centroid(), 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(polygon:centroid(), vertices[1], 2)
+    end
+end
+
+---@param circle foundation.shape.Circle
+---@param player_pos {x:number, y:number}
+function object:renderCircle(circle, player_pos)
+    local p = circle.center
+    local r1 = circle.radius + 1
+    local r2 = circle.radius - 1
+    if circle:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif circle:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    renderCircle(p, r1, r2, 64)
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        renderPoint(p, 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(p, p + Vector2.create(0, r1), 2)
+    end
+end
+
+---@param sector foundation.shape.Sector
+---@param player_pos {x:number, y:number}
+function object:renderSector(sector, player_pos)
+    local p = sector.center
+    local r1 = sector.radius - 1
+    local r2 = sector.radius + 1
+    if sector:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif sector:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+    local a1 = sector.direction:degreeAngle()
+    local a2 = a1 + sector.range * 360
+    renderSector(p, r1, r2, a1, a2, 64)
+    renderLine(p, p + sector.direction * r1, 2)
+    renderLine(p, p + sector.direction:degreeRotated(sector.range * 360) * r1, 2)
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        renderPoint(p, 4)
+    end
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(p, p + sector.direction * r1, 2)
+    end
+end
+
+---@param bezierCurve foundation.shape.BezierCurve
+---@param player_pos {x:number, y:number}
+function object:renderBezierCurve(bezierCurve, player_pos)
+    if bezierCurve:containsPoint(player_pos, 1, 30) then
+        setColor(192, 0, 0, 255)
+    else
+        setColor(192, 255, 255, 255)
+    end
+
+    local vertices = bezierCurve:discretize(30)
+    for i = 1, #vertices - 1 do
+        local p1 = vertices[i]
+        local p2 = vertices[i % #vertices + 1]
+        renderLine(p1, p2, 2)
+    end
+
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        for i = 0, bezierCurve.num_points - 1 do
+            renderPoint(bezierCurve.control_points[i], 4)
+        end
+    end
+
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        for i = 1, math.min(#vertices - 1, 5) do
+            local p1 = vertices[i]
+            local p2 = vertices[i % #vertices + 1]
+            renderLine(p1, p2, 2)
+        end
+        setColor(127, 13, 161, 158)
+        for i = 0, bezierCurve.num_points - 2 do
+            local p1 = bezierCurve.control_points[i]
+            local p2 = bezierCurve.control_points[i + 1]
+            renderLine(p1, p2, 2)
+        end
+    end
+end
+
+---@param ellipse foundation.shape.Ellipse
+---@param player_pos {x:number, y:number}
+function object:renderEllipse(ellipse, player_pos)
+    if ellipse:containsPoint(player_pos, 1) then
+        setColor(192, 0, 0, 255)
+    elseif ellipse:contains(player_pos) then
+        setColor(192, 127, 255, 0)
+    else
+        setColor(192, 255, 255, 255)
+    end
+
+    local vertices = ellipse:discretize(30)
+    for i = 1, #vertices do
+        local p1 = vertices[i]
+        local p2 = vertices[i % #vertices + 1]
+        renderLine(p1, p2, 2)
+    end
+
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        renderPoint(ellipse.center, 4)
+    end
+
+    if self.render_direction then
+        setColor(127, 255, 63, 63)
+        renderLine(ellipse.center, ellipse.center + ellipse.direction * ellipse.rx, 2)
+    end
+end
+--endregion
+
+--region Scene
+local Scene1 = {}
+Scene1.name = "Line"
+function Scene1:create()
+    self.timer = -1
+    object:insert(
+            Line.create(Vector2.create(0, 0), Vector2.createFromAngle(45))
+                :move(Vector2.create(window.width / 4 * 3, window.height / 2))
+    )
+    object:insert(
+            Line.create(Vector2.create(0, 0), Vector2.createFromAngle(45))
+                :move(Vector2.create(window.width / 4, window.height / 2))
+    )
+end
+function Scene1:destroy()
+    object:clear()
+end
+function Scene1:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene1:draw()
+    object:draw()
+end
+
+local Scene2 = {}
+Scene2.name = "Ray"
+function Scene2:create()
+    self.timer = -1
+    object:insert(
+            Ray.create(Vector2.create(0, 0), Vector2.createFromAngle(135))
+               :move(Vector2.create(window.width / 4 * 3, window.height / 2))
+    )
+    object:insert(
+            Ray.create(Vector2.create(0, 0), Vector2.createFromAngle(45))
+               :move(Vector2.create(window.width / 4, window.height / 2))
+    )
+end
+function Scene2:destroy()
+    object:clear()
+end
+function Scene2:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene2:draw()
+    object:draw()
+end
+
+local Scene3 = {}
+Scene3.name = "Segment"
+function Scene3:create()
+    self.timer = -1
+    object:insert(
+            Segment.create(Vector2.create(0, 0), Vector2.create(400, 0))
+                   :move(Vector2.create(0, window.height / 2))
+    )
+    object:insert(
+            Segment.create(Vector2.create(0, 0), Vector2.create(0, 400))
+                   :move(Vector2.create(window.width / 2, window.height / 4))
+    )
+    object:insert(
+            Segment.create(Vector2.create(0, 0), Vector2.create(200, 200))
+                   :move(Vector2.create(window.width / 3, window.height / 2))
+    )
+end
+function Scene3:destroy()
+    object:clear()
+end
+function Scene3:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        local rotate = (-1 + 2 * (i % 2)) * math.floor((i + 1) / 2)
+        local center
+        if i % 3 == 0 then
+            center = obj.point1
+        elseif i % 3 == 1 then
+            center = obj.point2
+        else
+            center = obj:midpoint()
+        end
+        obj:degreeRotate(rotate, center)
+    end
+    object:updateCollisionCheck()
+end
+function Scene3:draw()
+    object:draw()
+end
+
+local Scene4 = {}
+Scene4.name = "Triangle"
+function Scene4:create()
+    self.timer = -1
+    object:insert(
+            Triangle.create(Vector2.create(0, 0), Vector2.create(200, 0), Vector2.create(100, 300))
+                    :move(Vector2.create(window.width / 4, window.height / 2))
+    )
+    object:insert(
+            Triangle.create(Vector2.create(0, 0), Vector2.create(200, 0), Vector2.create(400, -300))
+                    :move(Vector2.create(0, window.height / 2))
+    )
+    object:insert(
+            Triangle.create(Vector2.create(0, 0), Vector2.create(0, 400), Vector2.create(300, 0))
+                    :move(Vector2.create(window.width / 2, 0))
+    )
+end
+function Scene4:destroy()
+    object:clear()
+end
+function Scene4:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene4:draw()
+    object:draw()
+end
+
+local Scene5 = {}
+Scene5.name = "Rectangle"
+function Scene5:create()
+    self.timer = -1
+    object:insert(
+            Rectangle.create(Vector2.create(0, 0), 200, 200)
+                     :move(Vector2.create(window.width / 5 * 2, window.height / 2))
+    )
+    object:insert(
+            Rectangle.create(Vector2.create(0, 0), 400, 100)
+                     :move(Vector2.create(window.width / 5 * 3, window.height / 2))
+    )
+end
+function Scene5:destroy()
+    object:clear()
+end
+function Scene5:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene5:draw()
+    object:draw()
+end
+
+local Scene6 = {}
+Scene6.name = "Sector"
+function Scene6:create()
+    self.timer = -1
+    object:insert(
+            Sector.create(Vector2.create(0, 0), 100, Vector2.createFromAngle(45), 0.25)
+                  :move(Vector2.create(window.width / 2, window.height / 2))
+    )
+end
+function Scene6:destroy()
+    object:clear()
+end
+function Scene6:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+        if obj.__type == "foundation.shape.Sector" then
+            obj.range = 0.75 * math.sin(self.timer / 100)
+        end
+    end
+    object:updateCollisionCheck()
+end
+function Scene6:draw()
+    object:draw()
+end
+
+local Scene7 = {}
+Scene7.name = "Polygon and Sector and Circle"
+function Scene7:create()
+    self.timer = -1
+    object:insert(
+            Polygon.create({
+                Vector2.create(0, -100),
+                Vector2.create(-100, 0),
+                Vector2.create(0, 100),
+                Vector2.create(100, 0),
+                Vector2.create(0, -100),
+                Vector2.create(-100, -100),
+                Vector2.create(-100, 100),
+                Vector2.create(100, 100),
+                Vector2.create(100, -100),
+            })     :move(Vector2.create(window.width / 3, window.height / 7 * 5))
+    )
+    object:insert(
+            Sector.create(Vector2.create(0, 0), 100, Vector2.createFromAngle(45), 0.75)
+                  :move(Vector2.create(window.width / 3, window.height / 7 * 3))
+    )
+    object:insert(
+            Circle.create(Vector2.create(0, 0), 150)
+                  :move(Vector2.create(window.width / 3 * 2, window.height / 2))
+    )
+end
+function Scene7:destroy()
+    object:clear()
+end
+function Scene7:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene7:draw()
+    object:draw()
+end
+
+local Scene8 = {}
+Scene8.name = "Ellipse"
+function Scene8:create()
+    self.timer = -1
+    object:insert(
+            Rectangle.create(Vector2.create(0, 0), 200, 200)
+                     :move(Vector2.create(window.width / 2, window.height / 2))
+    )
+    object:insert(
+            Ellipse.create(Vector2.create(0, 0), 100, 50)
+                   :move(Vector2.create(window.width / 3 * 2, window.height / 2))
+    )
+end
+function Scene8:destroy()
+    object:clear()
+end
+function Scene8:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene8:draw()
+    object:draw()
+end
+
+local Scene9 = {}
+Scene9.name = "BezierCurve"
+function Scene9:create()
+    self.timer = -1
+    object:insert(
+            BezierCurve.create({
+                Vector2.create(0, 0),
+                Vector2.create(100, 200),
+                Vector2.create(200, 100),
+                Vector2.create(300, 200),
+            })         :move(Vector2.create(window.width / 4, window.height / 3))
+    )
+    object:insert(
+            Rectangle.create(Vector2.create(0, 0), 200, 200)
+                     :move(Vector2.create(window.width / 2, window.height / 2))
+    )
+end
+function Scene9:destroy()
+    object:clear()
+end
+function Scene9:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene9:draw()
+    object:draw()
+end
+
+local Scene10 = {}
+Scene10.name = "Crazy"
+function Scene10:create()
+    self.timer = -1
+    local rand = lstg.Rand()
+    rand:Seed(os.time())
+    --每种形状都随机创建一个
+    object:insert(
+            Line.create(Vector2.create(0, 0), Vector2.createFromAngle(rand:Float(0, 360)))
+                :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            Ray.create(Vector2.create(0, 0), Vector2.createFromAngle(rand:Float(0, 360)))
+               :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            Segment.create(Vector2.create(0, 0), Vector2.createFromAngle(rand:Float(0, 360)) * rand:Float(100, 300))
+                   :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            Triangle.create(Vector2.create(0, 0),
+                    Vector2.createFromAngle(rand:Float(0, 360)) * rand:Float(100, 300),
+                    Vector2.createFromAngle(rand:Float(0, 360)) * rand:Float(100, 300))
+                    :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            Rectangle.create(Vector2.create(0, 0), rand:Float(100, 300), rand:Float(100, 300))
+                     :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            object:insert(
+                    Polygon.create({
+                        Vector2.create(0, -100),
+                        Vector2.create(-100, 0),
+                        Vector2.create(0, 100),
+                        Vector2.create(100, 0),
+                        Vector2.create(0, -100),
+                        Vector2.create(-100, -100),
+                        Vector2.create(-100, 100),
+                        Vector2.create(100, 100),
+                        Vector2.create(100, -100),
+                    })     :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+            )
+    )
+    object:insert(
+            Circle.create(Vector2.create(0, 0), rand:Float(100, 300))
+                  :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+    object:insert(
+            Sector.create(Vector2.create(0, 0), rand:Float(100, 300), Vector2.createFromAngle(rand:Float(0, 360)), rand:Float(0.1, 0.9))
+                  :move(Vector2.create(window.width * rand:Float(0.25, 0.75), window.height * rand:Float(0.25, 0.75)))
+    )
+end
+function Scene10:destroy()
+    object:clear()
+end
+function Scene10:update()
+    self.timer = self.timer + 1
+    for i, obj in object:enum() do
+        obj:degreeRotate(-1 + 2 * (i % 2))
+    end
+    object:updateCollisionCheck()
+end
+function Scene10:draw()
+    object:draw()
+end
+
+local Vector3 = require("foundation.math.Vector3")
+local Triangle3D = require("foundation.shape3D.Triangle3D")
+
+local Scene11 = {}
+Scene11.name = "3D Triangle"
+function Scene11:create()
+    self.timer = -1
+
+    self.triangle = Triangle3D.create(
+        Vector3.create(-100, -100, 100),
+        Vector3.create(100, -100, 100),
+        Vector3.create(0, 100, 100)
+    ):move(Vector3.create(window.width / 2, window.height / 2, 0))
+
+    self.rotateAxis = Vector3.create(1, 1, 1):normalize()
+    self.rotateAngle = 1
+    self.rotateCenter = Vector3.create(window.width / 2, window.height / 2, 0)
+end
+
+function Scene11:destroy()
+    object:clear()
+end
+
+function Scene11:update()
+    self.timer = self.timer + 1
+    self.triangleRotated = self.triangle:degreeRotated(self.rotateAxis, self.rotateAngle * self.timer, self.rotateCenter)
+end
+
+function Scene11:draw()
+    local vertices = self.triangleRotated:getVertices()
+
+    setColor(192, 255, 255, 255)
+    for i = 1, #vertices do
+        local p1 = vertices[i]
+        local p2 = vertices[i % #vertices + 1]
+        renderLine(p1, p2, 2)
+    end
+    if self.render_vertex then
+        setColor(127, 255, 0, 0)
+        for _, vertex in ipairs(vertices) do
+            renderPoint(vertex, 4)
+        end
+        setColor(127, 255, 0, 0)
+        renderPoint(self.triangle:centroid(), 4)
+    end
+end
+--endregion
+
+---@generic T
+---@param class T
+---@return T
+local function makeInstance(class)
+    local instance = {}
+    setmetatable(instance, { __index = class })
+    return instance
+end
+
+local scenes = {
+    Scene11,
+    Scene1,
+    Scene2,
+    Scene3,
+    Scene4,
+    Scene5,
+    Scene6,
+    Scene7,
+    Scene8,
+    Scene9,
+    Scene10,
+}
+local current_scene_index = 1
+local current_scene = makeInstance(scenes[current_scene_index])
+local keyState = {}
+local keyStatePre = {}
+local registeredKey = {
+    Keyboard.Left,
+    Keyboard.Right,
+    Keyboard.D1,
+    Keyboard.D2,
+    Keyboard.D3,
+    Keyboard.D4,
+    Keyboard.D5,
+    Keyboard.D6,
+    Keyboard.D7,
+    Keyboard.D8,
+    Keyboard.D9,
+}
+local function UpdateKeyState()
+    for _, key in ipairs(registeredKey) do
+        keyStatePre[key] = keyState[key]
+        keyState[key] = Keyboard.GetKeyState(key)
+    end
+end
+local function KeyIsPressed(key)
+    return keyState[key] and not keyStatePre[key]
+end
+
+function GameInit()
+    window:applyWindowSetting()
+    lstg.LoadTTF("Sans", "assets/font/SourceHanSansCN-Bold.otf", 0, 24)
+    current_scene:create()
+end
+
+function GameExit()
+    current_scene:destroy()
+end
+
+function FrameFunc()
+    UpdateKeyState()
+    local change = 0
+    if KeyIsPressed(Keyboard.Left) then
+        if current_scene_index > 1 then
+            change = -1
+        end
+    end
+    if KeyIsPressed(Keyboard.Right) then
+        if current_scene_index < #scenes then
+            change = 1
+        end
+    end
+    if KeyIsPressed(Keyboard.D1) then
+        object.render_player_point = not object.render_player_point
+    end
+    if KeyIsPressed(Keyboard.D2) then
+        object.render_closest_point = not object.render_closest_point
+    end
+    if KeyIsPressed(Keyboard.D3) then
+        object.render_project_point = not object.render_project_point
+    end
+    if KeyIsPressed(Keyboard.D4) then
+        object.render_bounding_box = not object.render_bounding_box
+    end
+    if KeyIsPressed(Keyboard.D5) then
+        object.render_collision_result = not object.render_collision_result
+    end
+    if KeyIsPressed(Keyboard.D6) then
+        object.render_incircle = not object.render_incircle
+    end
+    if KeyIsPressed(Keyboard.D7) then
+        object.render_circumcircle = not object.render_circumcircle
+    end
+    if KeyIsPressed(Keyboard.D8) then
+        object.render_vertex = not object.render_vertex
+    end
+    if KeyIsPressed(Keyboard.D9) then
+        object.render_direction = not object.render_direction
+    end
+    if change ~= 0 then
+        current_scene:destroy()
+        current_scene_index = current_scene_index + change
+        current_scene = makeInstance(scenes[current_scene_index])
+        current_scene:create()
+    end
+    current_scene:update()
+    return false
+end
+
+function RenderFunc()
+    lstg.BeginScene()
+    window:applyCameraSetting()
+    lstg.RenderClear(lstg.Color(255, 0, 0, 0))
+    current_scene:draw()
+    local edge = 4
+    lstg.RenderTTF("Sans", string.format("%s\n< %d/%d >", current_scene.name, current_scene_index, #scenes), edge, window.width - edge, edge, window.height - edge, 1 + 8, lstg.Color(255, 255, 255, 64), 2)
+    lstg.EndScene()
+end
\ No newline at end of file
diff --git a/laboratory/geometry/start.bat b/laboratory/geometry/start.bat
new file mode 100644
index 00000000..74d655e6
--- /dev/null
+++ b/laboratory/geometry/start.bat
@@ -0,0 +1,4 @@
+@setlocal
+    @cd %~dp0
+    @start ..\..\game\LuaSTGSub.exe
+@endlocal
diff --git a/laboratory/geometry/white.png b/laboratory/geometry/white.png
new file mode 100644
index 00000000..4ae1d8e5
Binary files /dev/null and b/laboratory/geometry/white.png differ