feat: 添加游戏数学工具类并重构相关代码

refactor: 将数学工具函数移至GameMath类
feat(音频): 实现地图音频控制器
feat(调试): 添加游戏调试UI组件
feat(地图): 增加移动区域边界获取方法
fix(角色): 修复角色移动区域抑制逻辑
refactor(世界): 重构游戏世界场景初始化
docs(音频): 完善音频数据库注释

Game/include/common/debug/GameDebugActor.h

@@ -0,0 +1,47 @@
+#pragma once
+
+#include <frostbite2D/2d/actor.h>
+
+namespace frostbite2D {
+
+class CharacterObject;
+class GameMap;
+class NineSliceActor;
+class TextSprite;
+
+/**
+ * @brief Reusable singleton debug actor for UI scenes.
+ */
+class GameDebugActor : public Actor {
+public:
+  static GameDebugActor& get();
+  static Ptr<GameDebugActor> getPtr();
+
+  GameDebugActor(const GameDebugActor&) = delete;
+  GameDebugActor& operator=(const GameDebugActor&) = delete;
+
+  bool AttachToScene(Scene* scene);
+  bool AttachToParent(Actor* parent);
+  void DetachFromParent();
+
+  void SetDebugMap(GameMap* map);
+  void SetTrackedCharacter(CharacterObject* character);
+  void ClearDebugContext();
+
+  void OnUpdate(float deltaTime) override;
+
+private:
+  void initOverlay();
+  void updateOverlay();
+  void setOverlayVisible(bool visible);
+
+  GameDebugActor();
+  ~GameDebugActor() override = default;
+
+  GameMap* debugMap_ = nullptr;
+  CharacterObject* trackedCharacter_ = nullptr;
+  RefPtr<NineSliceActor> background_;
+  RefPtr<TextSprite> coordText_;
+};
+
+} // namespace frostbite2D