feat: add fixed-point math and network sync, fix docs links (#440)

- feat(math): add Fixed32, FixedMath, FixedVector2 for deterministic calculations - feat(network): add FixedSnapshotBuffer and FixedClientPrediction for lockstep sync - docs: fix relative links in behavior-tree, blueprint, guide docs - docs: add missing sidebar items (cocos-editor, distributed) - docs: add scene-manager and persistent-entity Chinese translations
2026-01-05 22:17:30 +08:00
parent 12da6bd609
commit 30173f0764
49 changed files with 6073 additions and 103 deletions
@@ -0,0 +1,11 @@
+---
+"@esengine/ecs-framework-math": minor
+---
+
+feat(math): 添加定点数数学库 | Add fixed-point math library
+
+**@esengine/ecs-framework-math** - 新增定点数支持 | Add fixed-point number support
+- 新增 `Fixed32` 类：Q16.16 定点数实现 | Add `Fixed32` class: Q16.16 fixed-point implementation
+- 新增 `FixedMath` 工具类：定点数数学运算 | Add `FixedMath` utility: fixed-point math operations
+- 新增 `FixedVector2` 类：定点数二维向量 | Add `FixedVector2` class: fixed-point 2D vector
+- 支持基本算术运算、三角函数、向量运算 | Support basic arithmetic, trigonometry, vector operations
@@ -0,0 +1,10 @@
+---
+"@esengine/network": minor
+---
+
+feat(network): 添加定点数网络同步支持 | Add fixed-point network sync support
+
+**@esengine/network** - 新增定点数同步模块 | Add fixed-point sync module
+- 新增 `FixedSnapshotBuffer`：定点数快照缓冲区 | Add `FixedSnapshotBuffer`: fixed-point snapshot buffer
+- 新增 `FixedClientPrediction`：定点数客户端预测 | Add `FixedClientPrediction`: fixed-point client prediction
+- 支持确定性帧同步和状态回滚 | Support deterministic lockstep and state rollback
@@ -100,6 +100,8 @@ export default defineConfig({
                { label: '最佳实践', slug: 'guide/scene/best-practices', translations: { en: 'Best Practices' } },
              ],
            },
+            { label: '场景管理器', slug: 'guide/scene-manager', translations: { en: 'SceneManager' } },
+            { label: '持久实体', slug: 'guide/persistent-entity', translations: { en: 'Persistent Entity' } },
            {
              label: '序列化',
              translations: { en: 'Serialization' },
@@ -237,6 +239,7 @@ export default defineConfig({
              items: [
                { label: '概述', slug: 'modules/blueprint', translations: { en: 'Overview' } },
                { label: '编辑器使用指南', slug: 'modules/blueprint/editor-guide', translations: { en: 'Editor Guide' } },
+                { label: 'Cocos Creator 编辑器', slug: 'modules/blueprint/cocos-editor', translations: { en: 'Cocos Creator Editor' } },
                { label: '虚拟机 API', slug: 'modules/blueprint/vm', translations: { en: 'VM API' } },
                { label: '自定义节点', slug: 'modules/blueprint/custom-nodes', translations: { en: 'Custom Nodes' } },
                { label: '内置节点', slug: 'modules/blueprint/nodes', translations: { en: 'Built-in Nodes' } },
@@ -275,7 +278,9 @@ export default defineConfig({
                { label: 'HTTP 路由', slug: 'modules/network/http', translations: { en: 'HTTP Routing' } },
                { label: '认证系统', slug: 'modules/network/auth', translations: { en: 'Authentication' } },
                { label: '速率限制', slug: 'modules/network/rate-limit', translations: { en: 'Rate Limiting' } },
+                { label: '分布式房间', slug: 'modules/network/distributed', translations: { en: 'Distributed Rooms' } },
                { label: '状态同步', slug: 'modules/network/sync', translations: { en: 'State Sync' } },
+                { label: '定点数同步', slug: 'modules/network/fixed-point', translations: { en: 'Fixed-Point Sync' } },
                { label: '客户端预测', slug: 'modules/network/prediction', translations: { en: 'Prediction' } },
                { label: 'AOI 兴趣区域', slug: 'modules/network/aoi', translations: { en: 'AOI' } },
                { label: '增量压缩', slug: 'modules/network/delta', translations: { en: 'Delta Compression' } },
@@ -359,6 +359,5 @@ class GoodScene extends Scene {

 ## Related Documentation

- [Scene](./scene) - Learn the basics of scenes
- [SceneManager](./scene-manager) - Learn about scene transitions
- [WorldManager](./world-manager) - Learn about multi-world management
+- [Scene](/en/guide/scene/) - Learn the basics of scenes
+- [SceneManager](/en/guide/scene-manager/) - Learn about scene transitions
@@ -16,7 +16,7 @@ The ECS framework provides a platform adapter interface that allows users to imp

 ## Supported Platforms

-### [Browser Adapter](./platform-adapter/browser/)
+### [Browser Adapter](/en/guide/platform-adapter/browser/)

 Supports all modern browser environments, including Chrome, Firefox, Safari, Edge, etc.

@@ -30,7 +30,7 @@ Supports all modern browser environments, including Chrome, Firefox, Safari, Edg

 ---

-### [WeChat Mini Game Adapter](./platform-adapter/wechat-minigame/)
+### [WeChat Mini Game Adapter](/en/guide/platform-adapter/wechat-minigame/)

 Designed specifically for the WeChat Mini Game environment, handling special restrictions and APIs.

@@ -44,7 +44,7 @@ Designed specifically for the WeChat Mini Game environment, handling special res

 ---

-### [Node.js Adapter](./platform-adapter/nodejs/)
+### [Node.js Adapter](/en/guide/platform-adapter/nodejs/)

 Provides support for Node.js server environments, suitable for game servers and compute servers.

@@ -23,7 +23,7 @@ SceneManager is suitable for:
 - Automatic ECS fluent API management
 - Automatic scene lifecycle handling
 - Integrated with Core, auto-updated
- Supports [Persistent Entity](./persistent-entity) migration across scenes (v2.3.0+)
+- Supports [Persistent Entity](/en/guide/persistent-entity/) migration across scenes (v2.3.0+)

 ## Basic Usage

@@ -434,7 +434,6 @@ Core (Global Services)

 ## Related Documentation

- [Persistent Entity](./persistent-entity) - Learn how to keep entities across scene transitions
- [WorldManager](./world-manager) - Learn about advanced multi-world isolation features
+- [Persistent Entity](/en/guide/persistent-entity/) - Learn how to keep entities across scene transitions

 SceneManager provides simple yet powerful scene management capabilities for most games. Through Core's static methods, you can easily manage scene transitions.
@@ -100,6 +100,6 @@ console.log('Current state:', runtime.state);

 ## Next Steps

- [Core Concepts](./core-concepts/) - Understand nodes and execution
- [Custom Actions](./custom-actions/) - Create your own nodes
- [Editor Guide](./editor-guide/) - Visual tree creation
+- [Core Concepts](/en/modules/behavior-tree/core-concepts/) - Understand nodes and execution
+- [Custom Actions](/en/modules/behavior-tree/custom-actions/) - Create your own nodes
+- [Editor Guide](/en/modules/behavior-tree/editor-guide/) - Visual tree creation
@@ -0,0 +1,383 @@
+---
+title: "Cocos Creator Blueprint Editor"
+description: "Using the blueprint visual scripting system in Cocos Creator"
+---
+
+This document explains how to install and use the blueprint visual scripting editor extension in Cocos Creator projects.
+
+## Installation
+
+### 1. Copy Extension to Project
+
+Copy the `cocos-node-editor` extension to your Cocos Creator project's `extensions` directory:
+
+```
+your-project/
+├── assets/
+├── extensions/
+│   └── cocos-node-editor/    # Blueprint editor extension
+└── ...
+```
+
+### 2. Install Dependencies
+
+Install dependencies in the extension directory:
+
+```bash
+cd extensions/cocos-node-editor
+npm install
+```
+
+### 3. Enable Extension
+
+1. Open Cocos Creator
+2. Go to **Extensions → Extension Manager**
+3. Find `cocos-node-editor` and enable it
+
+## Opening the Blueprint Editor
+
+Open the blueprint editor panel via menu **Panel → Node Editor**.
+
+## Editor Interface
+
+### Toolbar
+
+| Button | Shortcut | Function |
+|--------|----------|----------|
+| New | - | Create empty blueprint |
+| Load | - | Load blueprint from file |
+| Save | `Ctrl+S` | Save blueprint to file |
+| Undo | `Ctrl+Z` | Undo last operation |
+| Redo | `Ctrl+Shift+Z` | Redo operation |
+| Cut | `Ctrl+X` | Cut selected nodes |
+| Copy | `Ctrl+C` | Copy selected nodes |
+| Paste | `Ctrl+V` | Paste nodes |
+| Delete | `Delete` | Delete selected items |
+| Rescan | - | Rescan project for blueprint nodes |
+
+### Canvas Operations
+
+- **Right-click on canvas**: Open node addition menu
+- **Drag nodes**: Move node position
+- **Click node**: Select node
+- **Ctrl+Click**: Multi-select nodes
+- **Drag pin to pin**: Create connection
+- **Scroll wheel**: Zoom canvas
+- **Middle-click drag**: Pan canvas
+
+### Node Menu
+
+Right-clicking on canvas shows the node menu:
+
+- Search box at top for quick node search
+- Nodes grouped by category
+- Press `Enter` to quickly add first search result
+- Press `Esc` to close menu
+
+## Blueprint File Format
+
+Blueprints are saved as `.blueprint.json` files, fully compatible with runtime:
+
+```json
+{
+  "version": 1,
+  "type": "blueprint",
+  "metadata": {
+    "name": "My Blueprint",
+    "createdAt": 1704307200000,
+    "modifiedAt": 1704307200000
+  },
+  "variables": [],
+  "nodes": [
+    {
+      "id": "node-1",
+      "type": "PrintString",
+      "position": { "x": 100, "y": 200 },
+      "data": {}
+    }
+  ],
+  "connections": [
+    {
+      "id": "conn-1",
+      "fromNodeId": "node-1",
+      "fromPin": "exec",
+      "toNodeId": "node-2",
+      "toPin": "exec"
+    }
+  ]
+}
+```
+
+## Running Blueprints in Game
+
+Use ECS system to manage and execute blueprints.
+
+### 1. Define Blueprint Component
+
+```typescript
+import { Component, ECSComponent, Property, Serialize } from '@esengine/ecs-framework';
+import type { BlueprintAsset } from '@esengine/blueprint';
+
+@ECSComponent('Blueprint')
+export class BlueprintComponent extends Component {
+    @Serialize()
+    @Property({ type: 'asset', label: 'Blueprint Asset' })
+    blueprintPath: string = '';
+
+    @Serialize()
+    @Property({ type: 'boolean', label: 'Auto Start' })
+    autoStart: boolean = true;
+
+    // Runtime data (not serialized)
+    blueprintAsset: BlueprintAsset | null = null;
+    vm: BlueprintVM | null = null;
+    isStarted: boolean = false;
+}
+```
+
+### 2. Create Blueprint Execution System
+
+```typescript
+import { EntitySystem, Matcher, Entity } from '@esengine/ecs-framework';
+import {
+    BlueprintVM,
+    validateBlueprintAsset
+} from '@esengine/blueprint';
+import { BlueprintComponent } from './BlueprintComponent';
+
+export class BlueprintExecutionSystem extends EntitySystem {
+    constructor() {
+        super(Matcher.empty().all(BlueprintComponent));
+    }
+
+    protected override process(entities: readonly Entity[]): void {
+        const dt = Time.deltaTime;
+
+        for (const entity of entities) {
+            const bp = entity.getComponent(BlueprintComponent)!;
+
+            // Skip entities without blueprint asset
+            if (!bp.blueprintAsset) continue;
+
+            // Initialize VM
+            if (!bp.vm) {
+                bp.vm = new BlueprintVM(bp.blueprintAsset, entity, this.scene!);
+            }
+
+            // Auto start
+            if (bp.autoStart && !bp.isStarted) {
+                bp.vm.start();
+                bp.isStarted = true;
+            }
+
+            // Update blueprint
+            if (bp.isStarted) {
+                bp.vm.tick(dt);
+            }
+        }
+    }
+
+    protected override onRemoved(entity: Entity): void {
+        const bp = entity.getComponent(BlueprintComponent);
+        if (bp?.vm && bp.isStarted) {
+            bp.vm.stop();
+            bp.vm = null;
+            bp.isStarted = false;
+        }
+    }
+}
+```
+
+### 3. Load Blueprint and Add to Entity
+
+```typescript
+import { resources, JsonAsset } from 'cc';
+import { validateBlueprintAsset } from '@esengine/blueprint';
+
+// Load blueprint asset
+async function loadBlueprint(path: string): Promise<BlueprintAsset | null> {
+    return new Promise((resolve) => {
+        resources.load(path, JsonAsset, (err, asset) => {
+            if (err || !asset) {
+                console.error('Failed to load blueprint:', err);
+                resolve(null);
+                return;
+            }
+
+            const data = asset.json;
+            if (validateBlueprintAsset(data)) {
+                resolve(data as BlueprintAsset);
+            } else {
+                console.error('Invalid blueprint format');
+                resolve(null);
+            }
+        });
+    });
+}
+
+// Create entity with blueprint
+async function createBlueprintEntity(scene: IScene, blueprintPath: string): Promise<Entity> {
+    const entity = scene.createEntity('BlueprintEntity');
+
+    const bpComponent = entity.addComponent(BlueprintComponent);
+    bpComponent.blueprintPath = blueprintPath;
+    bpComponent.blueprintAsset = await loadBlueprint(blueprintPath);
+
+    return entity;
+}
+```
+
+### 4. Register System to Scene
+
+```typescript
+// During scene initialization
+scene.addSystem(new BlueprintExecutionSystem());
+```
+
+## Creating Custom Nodes
+
+### Using Decorators for Components
+
+Use decorators to automatically generate blueprint nodes from components:
+
+```typescript
+import { Component, ECSComponent } from '@esengine/ecs-framework';
+import { BlueprintExpose, BlueprintProperty, BlueprintMethod } from '@esengine/blueprint';
+
+@ECSComponent('Health')
+@BlueprintExpose({ displayName: 'Health Component' })
+export class HealthComponent extends Component {
+    @BlueprintProperty({ displayName: 'Current Health', category: 'number' })
+    current: number = 100;
+
+    @BlueprintProperty({ displayName: 'Max Health', category: 'number' })
+    max: number = 100;
+
+    @BlueprintMethod({ displayName: 'Heal', isExec: true })
+    heal(amount: number): void {
+        this.current = Math.min(this.current + amount, this.max);
+    }
+
+    @BlueprintMethod({ displayName: 'Take Damage', isExec: true })
+    takeDamage(amount: number): void {
+        this.current = Math.max(this.current - amount, 0);
+    }
+
+    @BlueprintMethod({ displayName: 'Is Dead' })
+    isDead(): boolean {
+        return this.current <= 0;
+    }
+}
+```
+
+### Register Component Nodes
+
+```typescript
+import { registerAllComponentNodes } from '@esengine/blueprint';
+
+// Register all decorated components at application startup
+registerAllComponentNodes();
+```
+
+### Manual Node Definition (Advanced)
+
+For fully custom node logic:
+
+```typescript
+import {
+    BlueprintNodeTemplate,
+    INodeExecutor,
+    RegisterNode,
+    ExecutionContext,
+    ExecutionResult
+} from '@esengine/blueprint';
+
+const MyNodeTemplate: BlueprintNodeTemplate = {
+    type: 'MyCustomNode',
+    title: 'My Custom Node',
+    category: 'custom',
+    description: 'Custom node example',
+    inputs: [
+        { name: 'exec', type: 'exec', direction: 'input', isExec: true },
+        { name: 'value', type: 'number', direction: 'input', defaultValue: 0 }
+    ],
+    outputs: [
+        { name: 'exec', type: 'exec', direction: 'output', isExec: true },
+        { name: 'result', type: 'number', direction: 'output' }
+    ]
+};
+
+@RegisterNode(MyNodeTemplate)
+class MyNodeExecutor implements INodeExecutor {
+    execute(node: BlueprintNode, context: ExecutionContext): ExecutionResult {
+        const value = context.getInput<number>(node.id, 'value');
+        return {
+            outputs: { result: value * 2 },
+            nextExec: 'exec'
+        };
+    }
+}
+```
+
+## Node Categories
+
+| Category | Description | Color |
+|----------|-------------|-------|
+| `event` | Event nodes | Red |
+| `flow` | Flow control | Gray |
+| `entity` | Entity operations | Blue |
+| `component` | Component access | Cyan |
+| `math` | Math operations | Green |
+| `logic` | Logic operations | Red |
+| `variable` | Variable access | Purple |
+| `time` | Time utilities | Cyan |
+| `debug` | Debug utilities | Gray |
+| `custom` | Custom nodes | Blue-gray |
+
+## Best Practices
+
+1. **File Organization**
+   - Place blueprint files in `assets/blueprints/` directory
+   - Use meaningful file names like `player-controller.blueprint.json`
+
+2. **Component Design**
+   - Use `@BlueprintExpose` to mark components that should be exposed to blueprints
+   - Provide clear `displayName` for properties and methods
+   - Mark execution methods with `isExec: true`
+
+3. **Performance Considerations**
+   - Avoid heavy computation in Tick events
+   - Use variables to cache intermediate results
+   - Pure function nodes automatically cache outputs
+
+4. **Debugging Tips**
+   - Use Print nodes to output intermediate values
+   - Enable `vm.debug = true` to view execution logs
+
+## FAQ
+
+### Q: Node menu is empty?
+
+A: Click the **Rescan** button to scan for blueprint node classes in your project. Make sure you have called `registerAllComponentNodes()`.
+
+### Q: Blueprint doesn't execute?
+
+A: Check:
+1. Entity has `BlueprintComponent` added
+2. `BlueprintExecutionSystem` is registered to scene
+3. `blueprintAsset` is correctly loaded
+4. `autoStart` is `true`
+
+### Q: How to trigger custom events?
+
+A: Trigger through VM:
+```typescript
+const bp = entity.getComponent(BlueprintComponent);
+bp.vm?.triggerCustomEvent('OnPickup', { item: itemEntity });
+```
+
+## Related Documentation
+
+- [Blueprint Runtime API](/en/modules/blueprint/) - BlueprintVM and core API
+- [Custom Nodes](/en/modules/blueprint/custom-nodes) - Detailed node creation guide
+- [Built-in Nodes](/en/modules/blueprint/nodes) - Built-in node reference
@@ -604,7 +604,7 @@ Use **Print** nodes to output variable values to the console.

 ## Next Steps

- [ECS Node Reference](./nodes) - Complete node list
- [Custom Nodes](./custom-nodes) - Create custom nodes
- [Runtime Integration](./vm) - Blueprint VM API
- [Examples](./examples) - More game logic examples
+- [ECS Node Reference](/en/modules/blueprint/nodes) - Complete node list
+- [Custom Nodes](/en/modules/blueprint/custom-nodes) - Create custom nodes
+- [Runtime Integration](/en/modules/blueprint/vm) - Blueprint VM API
+- [Examples](/en/modules/blueprint/examples) - More game logic examples
@@ -604,6 +604,6 @@ Blueprint-defined variables automatically generate Get and Set nodes:

 ## Related Documentation

- [Blueprint Editor Guide](./editor-guide) - Learn how to use the editor
- [Custom Nodes](./custom-nodes) - Create custom nodes
- [Blueprint VM](./vm) - Runtime API
+- [Blueprint Editor Guide](/en/modules/blueprint/editor-guide) - Learn how to use the editor
+- [Custom Nodes](/en/modules/blueprint/custom-nodes) - Create custom nodes
+- [Blueprint VM](/en/modules/blueprint/vm) - Runtime API
@@ -0,0 +1,326 @@
+---
+title: "Fixed-Point Numbers"
+description: "Deterministic fixed-point math library for lockstep games"
+---
+
+`@esengine/ecs-framework-math` provides deterministic fixed-point calculations designed for **Lockstep** architecture. Fixed-point numbers guarantee identical results across all platforms.
+
+## Why Fixed-Point?
+
+Floating-point numbers may produce different rounding results on different platforms:
+
+```typescript
+// Floating-point: may differ across platforms
+const a = 0.1 + 0.2;  // 0.30000000000000004 (some platforms)
+                      // 0.3 (other platforms)
+
+// Fixed-point: consistent everywhere
+const x = Fixed32.from(0.1);
+const y = Fixed32.from(0.2);
+const z = x.add(y);   // raw = 19661 (all platforms)
+```
+
+| Feature | Floating-Point | Fixed-Point |
+|---------|----------------|-------------|
+| Cross-platform consistency | ❌ May differ | ✅ Identical |
+| Network sync mode | State sync | Lockstep |
+| Game types | FPS, RPG | RTS, MOBA, Fighting |
+
+## Installation
+
+```bash
+npm install @esengine/ecs-framework-math
+```
+
+## Fixed32 Fixed-Point Number
+
+Q16.16 format: 16-bit integer + 16-bit fraction, range ±32767.99998.
+
+### Creating Fixed-Point Numbers
+
+```typescript
+import { Fixed32 } from '@esengine/ecs-framework-math';
+
+// From floating-point
+const speed = Fixed32.from(5.5);
+
+// From integer (no precision loss)
+const count = Fixed32.fromInt(10);
+
+// From raw value (after network receive)
+const received = Fixed32.fromRaw(360448);  // equals 5.5
+
+// Predefined constants
+Fixed32.ZERO        // 0
+Fixed32.ONE         // 1
+Fixed32.HALF        // 0.5
+Fixed32.PI          // π
+Fixed32.TWO_PI      // 2π
+Fixed32.HALF_PI     // π/2
+```
+
+### Basic Operations
+
+```typescript
+const a = Fixed32.from(10);
+const b = Fixed32.from(3);
+
+const sum = a.add(b);       // 13
+const diff = a.sub(b);      // 7
+const prod = a.mul(b);      // 30
+const quot = a.div(b);      // 3.333...
+const mod = a.mod(b);       // 1
+const neg = a.neg();        // -10
+const abs = neg.abs();      // 10
+```
+
+### Comparison Operations
+
+```typescript
+const x = Fixed32.from(5);
+const y = Fixed32.from(3);
+
+x.eq(y)     // false - equal
+x.ne(y)     // true  - not equal
+x.lt(y)     // false - less than
+x.le(y)     // false - less or equal
+x.gt(y)     // true  - greater than
+x.ge(y)     // true  - greater or equal
+
+x.isZero()      // false
+x.isPositive()  // true
+x.isNegative()  // false
+```
+
+### Math Functions
+
+```typescript
+// Square root (Newton's method, deterministic)
+const sqrt = Fixed32.sqrt(Fixed32.from(16));  // 4
+
+// Rounding
+Fixed32.floor(Fixed32.from(3.7))   // 3
+Fixed32.ceil(Fixed32.from(3.2))    // 4
+Fixed32.round(Fixed32.from(3.5))   // 4
+
+// Clamping
+Fixed32.clamp(value, min, max)
+
+// Linear interpolation
+Fixed32.lerp(from, to, t)
+
+// Min/Max
+Fixed32.min(a, b)
+Fixed32.max(a, b)
+```
+
+### Type Conversion
+
+```typescript
+const value = Fixed32.from(3.14159);
+
+// To float (for rendering)
+const float = value.toNumber();  // 3.14159
+
+// Get raw value (for network)
+const raw = value.toRaw();  // 205887
+
+// To integer (floor)
+const int = value.toInt();  // 3
+```
+
+## FixedVector2 Fixed-Point Vector
+
+Immutable 2D vector, all operations return new instances.
+
+### Creating Vectors
+
+```typescript
+import { FixedVector2, Fixed32 } from '@esengine/ecs-framework-math';
+
+// From floating-point
+const pos = FixedVector2.from(100, 200);
+
+// From raw values (after network receive)
+const received = FixedVector2.fromRaw(6553600, 13107200);
+
+// From Fixed32
+const vec = new FixedVector2(Fixed32.from(10), Fixed32.from(20));
+
+// Predefined constants
+FixedVector2.ZERO   // (0, 0)
+FixedVector2.ONE    // (1, 1)
+FixedVector2.RIGHT  // (1, 0)
+FixedVector2.LEFT   // (-1, 0)
+FixedVector2.UP     // (0, 1)
+FixedVector2.DOWN   // (0, -1)
+```
+
+### Vector Operations
+
+```typescript
+const a = FixedVector2.from(3, 4);
+const b = FixedVector2.from(1, 2);
+
+// Basic operations
+const sum = a.add(b);                    // (4, 6)
+const diff = a.sub(b);                   // (2, 2)
+const scaled = a.mul(Fixed32.from(2));   // (6, 8)
+const divided = a.div(Fixed32.from(2));  // (1.5, 2)
+
+// Vector products
+const dot = a.dot(b);    // 3*1 + 4*2 = 11
+const cross = a.cross(b); // 3*2 - 4*1 = 2
+
+// Length
+const lenSq = a.lengthSquared();  // 25
+const len = a.length();           // 5
+
+// Normalize
+const norm = a.normalize();  // (0.6, 0.8)
+
+// Distance
+const dist = a.distanceTo(b);  // sqrt((3-1)² + (4-2)²)
+```
+
+### Rotation and Angles
+
+```typescript
+import { FixedMath } from '@esengine/ecs-framework-math';
+
+const vec = FixedVector2.from(1, 0);
+const angle = Fixed32.from(Math.PI / 2);  // 90 degrees
+
+// Rotate vector
+const rotated = vec.rotate(angle);  // (0, 1)
+
+// Rotate around point
+const center = FixedVector2.from(5, 5);
+const around = vec.rotateAround(center, angle);
+
+// Get vector angle
+const vecAngle = vec.angle();
+
+// Angle between vectors
+const between = vec.angleTo(other);
+
+// Create unit vector from angle
+const dir = FixedVector2.fromAngle(angle);
+
+// From polar coordinates
+const polar = FixedVector2.fromPolar(length, angle);
+```
+
+### Type Conversion
+
+```typescript
+const pos = FixedVector2.from(100.5, 200.5);
+
+// To float object (for rendering)
+const obj = pos.toObject();  // { x: 100.5, y: 200.5 }
+
+// To array
+const arr = pos.toArray();  // [100.5, 200.5]
+
+// Get raw values (for network)
+const raw = pos.toRawObject();  // { x: 6586368, y: 13140992 }
+```
+
+## FixedMath Trigonometric Functions
+
+Deterministic trigonometric functions using lookup tables.
+
+```typescript
+import { FixedMath, Fixed32 } from '@esengine/ecs-framework-math';
+
+const angle = Fixed32.from(Math.PI / 6);  // 30 degrees
+
+// Trigonometric functions
+const sin = FixedMath.sin(angle);  // 0.5
+const cos = FixedMath.cos(angle);  // 0.866
+const tan = FixedMath.tan(angle);  // 0.577
+
+// Inverse trigonometric
+const atan = FixedMath.atan2(y, x);
+const asin = FixedMath.asin(value);
+const acos = FixedMath.acos(value);
+
+// Normalize angle to [-π, π]
+const normalized = FixedMath.normalizeAngle(angle);
+
+// Angle difference (shortest path)
+const delta = FixedMath.angleDelta(from, to);
+
+// Angle interpolation (handles 360° wrap)
+const lerped = FixedMath.lerpAngle(from, to, t);
+
+// Radian/degree conversion
+const deg = FixedMath.radToDeg(rad);
+const rad = FixedMath.degToRad(deg);
+```
+
+## Best Practices
+
+### 1. Use Fixed-Point Throughout
+
+```typescript
+// ✅ Correct: all game logic uses fixed-point
+function calculateDamage(baseDamage: Fixed32, multiplier: Fixed32): Fixed32 {
+    return baseDamage.mul(multiplier);
+}
+
+// ❌ Wrong: mixing floating-point
+function calculateDamage(baseDamage: number, multiplier: number): number {
+    return baseDamage * multiplier;  // may be inconsistent
+}
+```
+
+### 2. Only Convert to Float for Rendering
+
+```typescript
+// Game logic
+const position: FixedVector2 = calculatePosition(input);
+
+// Rendering
+const { x, y } = position.toObject();
+sprite.position.set(x, y);
+```
+
+### 3. Use Raw Values for Network
+
+```typescript
+// ✅ Correct: transmit raw integers
+const raw = position.toRawObject();
+send(JSON.stringify(raw));
+
+// ❌ Wrong: transmit floats
+const float = position.toObject();
+send(JSON.stringify(float));  // may lose precision
+```
+
+### 4. Use FixedMath for Trigonometry
+
+```typescript
+// ✅ Correct: use lookup tables
+const direction = FixedVector2.fromAngle(FixedMath.atan2(dy, dx));
+
+// ❌ Wrong: use Math library
+const angle = Math.atan2(dy.toNumber(), dx.toNumber());  // non-deterministic
+```
+
+## API Exports
+
+```typescript
+import {
+    Fixed32,
+    FixedVector2,
+    FixedMath,
+    type IFixed32,
+    type IFixedVector2
+} from '@esengine/ecs-framework-math';
+```
+
+## Related Docs
+
+- [State Sync](/en/modules/network/sync) - Fixed-point snapshot buffer
+- [Client Prediction](/en/modules/network/prediction) - Fixed-point client prediction
@@ -252,3 +252,145 @@ if (predictionSystem) {
    console.log('Current sequence:', predictionSystem.inputSequence);
 }
 ```
+
+---
+
+## Fixed-Point Client Prediction (Lockstep)
+
+Deterministic client prediction for **Lockstep** architecture.
+
+> See [Fixed-Point Numbers](/en/modules/network/fixed-point) for math basics
+
+### Basic Usage
+
+```typescript
+import {
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    type IFixedPredictor,
+    type IFixedStatePositionExtractor
+} from '@esengine/network';
+import { Fixed32, FixedVector2 } from '@esengine/ecs-framework-math';
+
+// Define game state
+interface GameState {
+    position: FixedVector2;
+    velocity: FixedVector2;
+}
+
+// Implement predictor (must use fixed-point arithmetic)
+const predictor: IFixedPredictor<GameState, PlayerInput> = {
+    predict(state: GameState, input: PlayerInput, deltaTime: Fixed32): GameState {
+        const speed = Fixed32.from(100);
+        const inputVec = FixedVector2.from(input.dx, input.dy);
+        const velocity = inputVec.normalize().mul(speed);
+        const displacement = velocity.mul(deltaTime);
+
+        return {
+            position: state.position.add(displacement),
+            velocity
+        };
+    }
+};
+
+// Create prediction
+const prediction = createFixedClientPrediction(predictor, {
+    maxUnacknowledgedInputs: 60,
+    fixedDeltaTime: Fixed32.from(1 / 60),
+    reconciliationThreshold: Fixed32.from(0.001),
+    enableSmoothReconciliation: false  // Usually disabled for lockstep
+});
+```
+
+### Record Input
+
+```typescript
+function onUpdate(input: PlayerInput, currentState: GameState) {
+    // Record input and get predicted state
+    const predicted = prediction.recordInput(input, currentState);
+
+    // Render predicted state
+    const pos = predicted.position.toObject();
+    sprite.position.set(pos.x, pos.y);
+
+    // Send input
+    socket.send(JSON.stringify({
+        frame: prediction.currentFrame,
+        input
+    }));
+}
+```
+
+### Server Reconciliation
+
+```typescript
+// Position extractor
+const posExtractor: IFixedStatePositionExtractor<GameState> = {
+    getPosition(state: GameState): FixedVector2 {
+        return state.position;
+    }
+};
+
+// When receiving server state
+function onServerState(serverState: GameState, serverFrame: number) {
+    const reconciled = prediction.reconcile(
+        serverState,
+        serverFrame,
+        posExtractor
+    );
+}
+```
+
+### Rollback and Replay
+
+```typescript
+// Rollback when desync detected
+const correctedState = prediction.rollbackAndResimulate(
+    serverFrame,
+    authoritativeState
+);
+
+// View historical state
+const historicalState = prediction.getStateAtFrame(100);
+```
+
+### Preset Movement Predictor
+
+```typescript
+import {
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+    type IFixedMovementInput,
+    type IFixedMovementState
+} from '@esengine/network';
+
+// Create movement predictor (speed 100 units/sec)
+const movePredictor = createFixedMovementPredictor(Fixed32.from(100));
+const posExtractor = createFixedMovementPositionExtractor();
+
+const prediction = createFixedClientPrediction<IFixedMovementState, IFixedMovementInput>(
+    movePredictor,
+    { fixedDeltaTime: Fixed32.from(1 / 60) }
+);
+
+// Input format
+const input: IFixedMovementInput = { dx: 1, dy: 0 };
+```
+
+### API Exports
+
+```typescript
+import {
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+    type IFixedInputSnapshot,
+    type IFixedPredictedState,
+    type IFixedPredictor,
+    type IFixedStatePositionExtractor,
+    type FixedClientPredictionConfig,
+    type IFixedMovementInput,
+    type IFixedMovementState
+} from '@esengine/network';
+```
@@ -235,3 +235,139 @@ const corrected = prediction.reconcile(serverState, serverSeq, applyInput);
 1. **Interpolation delay**: 100-150ms for typical networks
 2. **Prediction**: Use only for local player, interpolate remote players
 3. **Snapshot count**: Keep enough snapshots to handle network jitter
+
+---
+
+## Fixed-Point Sync (Lockstep)
+
+For **Lockstep** architecture, use fixed-point numbers to ensure cross-platform determinism.
+
+> See [Fixed-Point Numbers](/en/modules/network/fixed-point) for math basics
+
+### FixedTransformState
+
+Fixed-point transform state for network transmission:
+
+```typescript
+import {
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw
+} from '@esengine/network';
+
+// Create state
+const state = FixedTransformState.from(100, 200, Math.PI / 4);
+
+// Serialize (sender)
+const raw: IFixedTransformStateRaw = state.toRaw();
+socket.send(JSON.stringify({ type: 'sync', state: raw }));
+
+// Deserialize (receiver)
+const received = FixedTransformState.fromRaw(message.state);
+
+// Use for rendering
+const { x, y, rotation } = received.toFloat();
+sprite.position.set(x, y);
+```
+
+State with velocity (for extrapolation):
+
+```typescript
+const state = FixedTransformStateWithVelocity.from(
+    100, 200,    // position
+    0,           // rotation
+    5, 3,        // velocity
+    0.1          // angular velocity
+);
+```
+
+### Fixed-Point Interpolators
+
+```typescript
+import {
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator
+} from '@esengine/network';
+import { Fixed32 } from '@esengine/ecs-framework-math';
+
+// Linear interpolator
+const interpolator = createFixedTransformInterpolator();
+
+const from = FixedTransformState.from(0, 0, 0);
+const to = FixedTransformState.from(100, 50, Math.PI);
+const t = Fixed32.from(0.5);
+
+const result = interpolator.interpolate(from, to, t);
+
+// Hermite interpolator (smoother)
+const hermite = createFixedHermiteTransformInterpolator(100);
+```
+
+### Fixed-Point Snapshot Buffer
+
+Manages fixed-point state history for lockstep replay:
+
+```typescript
+import {
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer
+} from '@esengine/network';
+
+// Create buffer (max 30 snapshots, 2 frame delay)
+const buffer = createFixedSnapshotBuffer<FixedTransformState>(30, 2);
+
+// Add snapshots
+buffer.push({
+    frame: 100,
+    state: FixedTransformState.from(100, 200, 0)
+});
+
+// Get interpolation snapshots
+const result = buffer.getInterpolationSnapshots(103);
+if (result) {
+    const { from, to, t } = result;
+    const interpolated = interpolator.interpolate(from.state, to.state, t);
+}
+
+// Get latest/specific frame
+const latest = buffer.getLatest();
+const atFrame = buffer.getAtFrame(100);
+
+// Rollback replay
+const snapshotsToReplay = buffer.getSnapshotsAfter(98);
+
+// Clean up old snapshots
+buffer.removeSnapshotsBefore(95);
+```
+
+Sub-frame interpolation:
+
+```typescript
+// Use Fixed32 frame time (supports fractional frames)
+const frameTime = Fixed32.from(102.5);
+const result = buffer.getInterpolationSnapshotsFixed(frameTime);
+```
+
+### API Exports
+
+```typescript
+import {
+    // State classes
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw,
+    type IFixedTransformStateWithVelocityRaw,
+
+    // Interpolators
+    FixedTransformInterpolator,
+    FixedHermiteTransformInterpolator,
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator,
+
+    // Snapshot buffer
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer,
+    type IFixedStateSnapshot,
+    type IFixedInterpolationResult
+} from '@esengine/network';
+```
@@ -434,6 +434,6 @@ const found = hierarchySystem.findChild(parent, "Child");

 ## 下一步

- 了解 [实体类](./entity/) 的其他功能
- 了解 [场景管理](./scene/) 如何组织实体和系统
- 了解 [组件系统](./component/) 如何定义和使用组件
+- 了解 [实体类](/guide/entity/) 的其他功能
+- 了解 [场景管理](/guide/scene/) 如何组织实体和系统
+- 了解 [组件系统](/guide/component/) 如何定义和使用组件
@@ -0,0 +1,363 @@
+---
+title: "持久实体"
+---
+
+# 持久实体
+
+> **版本**: v2.3.0+
+
+持久实体是一种特殊类型的实体，在场景切换时会自动迁移到新场景。适用于需要跨场景保持状态的游戏对象，如玩家、游戏管理器、音频管理器等。
+
+## 基本概念
+
+在 ECS 框架中，实体有两种生命周期策略：
+
+| 策略 | 描述 | 默认 |
+|------|------|------|
+| `SceneLocal` | 场景局部实体，场景切换时销毁 | ✓ |
+| `Persistent` | 持久实体，场景切换时自动迁移 | |
+
+## 快速开始
+
+### 创建持久实体
+
+```typescript
+import { Scene } from '@esengine/ecs-framework';
+
+class GameScene extends Scene {
+  protected initialize(): void {
+    // 创建持久玩家实体
+    const player = this.createEntity('Player').setPersistent();
+    player.addComponent(new Position(100, 200));
+    player.addComponent(new PlayerData('Hero', 500));
+
+    // 创建普通敌人实体（场景切换时销毁）
+    const enemy = this.createEntity('Enemy');
+    enemy.addComponent(new Position(300, 200));
+    enemy.addComponent(new EnemyAI());
+  }
+}
+```
+
+### 场景切换时的行为
+
+```typescript
+import { Core, Scene } from '@esengine/ecs-framework';
+
+// 初始场景
+class Level1Scene extends Scene {
+  protected initialize(): void {
+    // 玩家 - 持久实体，将迁移到下一个场景
+    const player = this.createEntity('Player').setPersistent();
+    player.addComponent(new Position(0, 0));
+    player.addComponent(new Health(100));
+
+    // 敌人 - 场景局部实体，场景切换时销毁
+    const enemy = this.createEntity('Enemy');
+    enemy.addComponent(new Position(100, 100));
+  }
+}
+
+// 目标场景
+class Level2Scene extends Scene {
+  protected initialize(): void {
+    // 新敌人
+    const enemy = this.createEntity('Boss');
+    enemy.addComponent(new Position(200, 200));
+  }
+
+  public onStart(): void {
+    // 玩家已自动迁移到此场景
+    const player = this.findEntity('Player');
+    console.log(player !== null); // true
+
+    // 位置和生命值数据完整保留
+    const position = player?.getComponent(Position);
+    const health = player?.getComponent(Health);
+    console.log(position?.x, position?.y); // 0, 0
+    console.log(health?.value); // 100
+  }
+}
+
+// 切换场景
+Core.create({ debug: true });
+Core.setScene(new Level1Scene());
+
+// 稍后切换到 Level2
+Core.loadScene(new Level2Scene());
+// 玩家实体自动迁移，敌人实体被销毁
+```
+
+## API 参考
+
+### 实体方法
+
+#### setPersistent()
+
+将实体标记为持久实体，防止在场景切换时被销毁。
+
+```typescript
+public setPersistent(): this
+```
+
+**返回值**: 返回实体本身，支持链式调用
+
+**示例**:
+```typescript
+const player = scene.createEntity('Player')
+  .setPersistent();
+
+player.addComponent(new Position(100, 200));
+```
+
+#### setSceneLocal()
+
+将实体恢复为场景局部策略（默认）。
+
+```typescript
+public setSceneLocal(): this
+```
+
+**返回值**: 返回实体本身，支持链式调用
+
+**示例**:
+```typescript
+// 动态取消持久性
+player.setSceneLocal();
+```
+
+#### isPersistent
+
+检查实体是否为持久实体。
+
+```typescript
+public get isPersistent(): boolean
+```
+
+**示例**:
+```typescript
+if (entity.isPersistent) {
+  console.log('这是一个持久实体');
+}
+```
+
+#### lifecyclePolicy
+
+获取实体的生命周期策略。
+
+```typescript
+public get lifecyclePolicy(): EEntityLifecyclePolicy
+```
+
+**示例**:
+```typescript
+import { EEntityLifecyclePolicy } from '@esengine/ecs-framework';
+
+if (entity.lifecyclePolicy === EEntityLifecyclePolicy.Persistent) {
+  console.log('持久实体');
+}
+```
+
+### 场景方法
+
+#### findPersistentEntities()
+
+查找场景中所有持久实体。
+
+```typescript
+public findPersistentEntities(): Entity[]
+```
+
+**返回值**: 持久实体数组
+
+**示例**:
+```typescript
+const persistentEntities = scene.findPersistentEntities();
+console.log(`场景中有 ${persistentEntities.length} 个持久实体`);
+```
+
+#### extractPersistentEntities()
+
+提取并移除场景中所有持久实体（通常由框架内部调用）。
+
+```typescript
+public extractPersistentEntities(): Entity[]
+```
+
+**返回值**: 被提取的持久实体数组
+
+#### receiveMigratedEntities()
+
+接收迁移的实体（通常由框架内部调用）。
+
+```typescript
+public receiveMigratedEntities(entities: Entity[]): void
+```
+
+**参数**:
+- `entities` - 要接收的实体数组
+
+## 使用场景
+
+### 1. 跨关卡的玩家实体
+
+```typescript
+class PlayerSetupScene extends Scene {
+  protected initialize(): void {
+    // 玩家在所有关卡中保持状态
+    const player = this.createEntity('Player').setPersistent();
+    player.addComponent(new Transform(0, 0));
+    player.addComponent(new Health(100));
+    player.addComponent(new Inventory());
+    player.addComponent(new PlayerStats());
+  }
+}
+
+class Level1 extends Scene { /* ... */ }
+class Level2 extends Scene { /* ... */ }
+class Level3 extends Scene { /* ... */ }
+
+// 玩家实体在所有关卡之间自动迁移
+Core.setScene(new PlayerSetupScene());
+// ... 游戏进行
+Core.loadScene(new Level1());
+// ... 关卡完成
+Core.loadScene(new Level2());
+// 玩家数据（生命值、背包、属性）完整保留
+```
+
+### 2. 全局管理器
+
+```typescript
+class BootstrapScene extends Scene {
+  protected initialize(): void {
+    // 音频管理器 - 跨场景持久
+    const audioManager = this.createEntity('AudioManager').setPersistent();
+    audioManager.addComponent(new AudioController());
+
+    // 成就管理器 - 跨场景持久
+    const achievementManager = this.createEntity('AchievementManager').setPersistent();
+    achievementManager.addComponent(new AchievementTracker());
+
+    // 游戏设置 - 跨场景持久
+    const settings = this.createEntity('GameSettings').setPersistent();
+    settings.addComponent(new SettingsData());
+  }
+}
+```
+
+### 3. 动态切换持久性
+
+```typescript
+class GameScene extends Scene {
+  protected initialize(): void {
+    // 初始创建为普通实体
+    const companion = this.createEntity('Companion');
+    companion.addComponent(new Transform(0, 0));
+    companion.addComponent(new CompanionAI());
+
+    // 监听招募事件
+    this.eventSystem.on('companion:recruited', () => {
+      // 招募后变为持久实体
+      companion.setPersistent();
+      console.log('同伴加入队伍，将跟随玩家跨场景');
+    });
+
+    // 监听解散事件
+    this.eventSystem.on('companion:dismissed', () => {
+      // 解散后恢复为场景局部实体
+      companion.setSceneLocal();
+      console.log('同伴离开队伍，不再跨场景持久');
+    });
+  }
+}
+```
+
+## 最佳实践
+
+### 1. 明确标识持久实体
+
+```typescript
+// 推荐：创建时立即标记
+const player = this.createEntity('Player').setPersistent();
+
+// 不推荐：创建后再标记（容易遗忘）
+const player = this.createEntity('Player');
+// ... 大量代码 ...
+player.setPersistent(); // 容易忘记
+```
+
+### 2. 合理使用持久性
+
+```typescript
+// ✓ 适合持久化的实体
+const player = this.createEntity('Player').setPersistent();      // 玩家
+const gameManager = this.createEntity('GameManager').setPersistent(); // 全局管理器
+const audioManager = this.createEntity('AudioManager').setPersistent(); // 音频系统
+
+// ✗ 不应该持久化的实体
+const bullet = this.createEntity('Bullet'); // 临时对象
+const enemy = this.createEntity('Enemy');   // 关卡特定敌人
+const particle = this.createEntity('Particle'); // 特效粒子
+```
+
+### 3. 检查迁移的实体
+
+```typescript
+class NewScene extends Scene {
+  public onStart(): void {
+    // 检查预期的持久实体是否存在
+    const player = this.findEntity('Player');
+    if (!player) {
+      console.error('玩家实体未正确迁移！');
+      // 处理错误情况
+    }
+  }
+}
+```
+
+### 4. 避免循环引用
+
+```typescript
+// ✗ 避免：持久实体引用场景局部实体
+class BadScene extends Scene {
+  protected initialize(): void {
+    const player = this.createEntity('Player').setPersistent();
+    const enemy = this.createEntity('Enemy');
+
+    // 危险：player 是持久的但 enemy 不是
+    // 场景切换后，enemy 被销毁，引用变为无效
+    player.addComponent(new TargetComponent(enemy));
+  }
+}
+
+// ✓ 推荐：使用 ID 引用或事件系统
+class GoodScene extends Scene {
+  protected initialize(): void {
+    const player = this.createEntity('Player').setPersistent();
+    const enemy = this.createEntity('Enemy');
+
+    // 存储 ID 而非直接引用
+    player.addComponent(new TargetComponent(enemy.id));
+
+    // 或使用事件系统通信
+  }
+}
+```
+
+## 重要说明
+
+1. **已销毁的实体不会迁移**：如果实体在场景切换前被销毁，即使标记为持久也不会迁移。
+
+2. **组件数据完整保留**：迁移过程中所有组件及其状态都会被保留。
+
+3. **场景引用会更新**：迁移后，实体的 `scene` 属性将指向新场景。
+
+4. **查询系统会更新**：迁移的实体会自动注册到新场景的查询系统中。
+
+5. **延迟切换同样有效**：使用 `Core.loadScene()` 进行延迟切换时，持久实体同样会迁移。
+
+## 相关文档
+
+- [场景](/guide/scene/) - 了解场景基础知识
+- [场景管理器](/guide/scene-manager/) - 了解场景切换
@@ -16,7 +16,7 @@ ECS框架提供了平台适配器接口，允许用户为不同的运行环境

 ## 支持的平台

-### 🌐 [浏览器适配器](./platform-adapter/browser/)
+### 🌐 [浏览器适配器](/guide/platform-adapter/browser/)

 支持所有现代浏览器环境，包括 Chrome、Firefox、Safari、Edge 等。

@@ -30,7 +30,7 @@ ECS框架提供了平台适配器接口，允许用户为不同的运行环境

 ---

-### 📱 [微信小游戏适配器](./platform-adapter/wechat-minigame/)
+### 📱 [微信小游戏适配器](/guide/platform-adapter/wechat-minigame/)

 专为微信小游戏环境设计，处理微信小游戏的特殊限制和API。

@@ -44,7 +44,7 @@ ECS框架提供了平台适配器接口，允许用户为不同的运行环境

 ---

-### 🖥️ [Node.js适配器](./platform-adapter/nodejs/)
+### 🖥️ [Node.js适配器](/guide/platform-adapter/nodejs/)

 为 Node.js 服务器环境提供支持，适用于游戏服务器和计算服务器。

@@ -0,0 +1,439 @@
+---
+title: "场景管理器"
+---
+
+# SceneManager
+
+SceneManager 是 ECS Framework 提供的轻量级场景管理器，适用于 95% 的游戏应用。它提供简单直观的 API，支持场景切换和延迟加载。
+
+## 适用场景
+
+SceneManager 适用于：
+- 单人游戏
+- 简单多人游戏
+- 移动游戏
+- 需要场景切换的游戏（菜单、游戏、暂停等）
+- 不需要多 World 隔离的项目
+
+## 功能特性
+
+- 轻量级，零额外开销
+- 简单直观的 API
+- 支持延迟场景切换（避免在帧中途切换）
+- 自动 ECS 流式 API 管理
+- 自动场景生命周期处理
+- 与 Core 集成，自动更新
+- 支持 [持久实体](/guide/persistent-entity/) 跨场景迁移（v2.3.0+）
+
+## 基本用法
+
+### 推荐：使用 Core 的静态方法
+
+这是最简单且推荐的方式，适用于大多数应用：
+
+```typescript
+import { Core, Scene } from '@esengine/ecs-framework';
+
+// 1. 初始化 Core
+Core.create({ debug: true });
+
+// 2. 创建并设置场景
+class GameScene extends Scene {
+  protected initialize(): void {
+    this.name = "GameScene";
+
+    // 添加系统
+    this.addSystem(new MovementSystem());
+    this.addSystem(new RenderSystem());
+
+    // 创建初始实体
+    const player = this.createEntity("Player");
+    player.addComponent(new Transform(400, 300));
+    player.addComponent(new Health(100));
+  }
+
+  public onStart(): void {
+    console.log("游戏场景已启动");
+  }
+}
+
+// 3. 设置场景
+Core.setScene(new GameScene());
+
+// 4. 游戏循环（Core.update 自动更新场景）
+function gameLoop(deltaTime: number) {
+  Core.update(deltaTime);  // 自动更新所有服务和场景
+}
+
+// Laya 引擎集成
+Laya.timer.frameLoop(1, this, () => {
+  const deltaTime = Laya.timer.delta / 1000;
+  Core.update(deltaTime);
+});
+
+// Cocos Creator 集成
+update(deltaTime: number) {
+  Core.update(deltaTime);
+}
+```
+
+### 进阶：直接使用 SceneManager
+
+如果需要更多控制，可以直接使用 SceneManager：
+
+```typescript
+import { Core, SceneManager, Scene } from '@esengine/ecs-framework';
+
+// 初始化 Core
+Core.create({ debug: true });
+
+// 获取 SceneManager（已由 Core 自动创建并注册）
+const sceneManager = Core.services.resolve(SceneManager);
+
+// 设置场景
+const gameScene = new GameScene();
+sceneManager.setScene(gameScene);
+
+// 游戏循环（仍然使用 Core.update）
+function gameLoop(deltaTime: number) {
+  Core.update(deltaTime);  // Core 自动调用 sceneManager.update()
+}
+```
+
+**重要提示**：无论使用哪种方式，在游戏循环中只需调用 `Core.update()`。它会自动更新 SceneManager 和场景。无需手动调用 `sceneManager.update()`。
+
+## 场景切换
+
+### 立即切换
+
+使用 `Core.setScene()` 或 `sceneManager.setScene()` 立即切换场景：
+
+```typescript
+// 方法 1：使用 Core（推荐）
+Core.setScene(new MenuScene());
+
+// 方法 2：使用 SceneManager
+const sceneManager = Core.services.resolve(SceneManager);
+sceneManager.setScene(new MenuScene());
+```
+
+### 延迟切换
+
+使用 `Core.loadScene()` 或 `sceneManager.loadScene()` 进行延迟场景切换，在下一帧生效：
+
+```typescript
+// 方法 1：使用 Core（推荐）
+Core.loadScene(new GameOverScene());
+
+// 方法 2：使用 SceneManager
+const sceneManager = Core.services.resolve(SceneManager);
+sceneManager.loadScene(new GameOverScene());
+```
+
+在 System 中切换场景时，使用延迟切换：
+
+```typescript
+class GameOverSystem extends EntitySystem {
+  process(entities: readonly Entity[]): void {
+    const player = entities.find(e => e.name === 'Player');
+    const health = player?.getComponent(Health);
+
+    if (health && health.value <= 0) {
+      // 延迟切换到游戏结束场景（下一帧生效）
+      Core.loadScene(new GameOverScene());
+      // 当前帧继续执行，不会中断当前系统处理
+    }
+  }
+}
+```
+
+## API 参考
+
+### Core 静态方法（推荐）
+
+#### Core.setScene()
+
+立即切换场景。
+
+```typescript
+public static setScene<T extends IScene>(scene: T): T
+```
+
+**参数**:
+- `scene` - 要设置的场景实例
+
+**返回值**:
+- 返回设置的场景实例
+
+**示例**:
+```typescript
+const gameScene = Core.setScene(new GameScene());
+console.log(gameScene.name);
+```
+
+#### Core.loadScene()
+
+延迟场景加载（下一帧切换）。
+
+```typescript
+public static loadScene<T extends IScene>(scene: T): void
+```
+
+**参数**:
+- `scene` - 要加载的场景实例
+
+**示例**:
+```typescript
+Core.loadScene(new GameOverScene());
+```
+
+#### Core.scene
+
+获取当前活动场景。
+
+```typescript
+public static get scene(): IScene | null
+```
+
+**返回值**:
+- 当前场景实例，如果没有场景则返回 null
+
+**示例**:
+```typescript
+const currentScene = Core.scene;
+if (currentScene) {
+  console.log(`当前场景: ${currentScene.name}`);
+}
+```
+
+### SceneManager 方法（进阶）
+
+如果需要直接使用 SceneManager，通过服务容器获取：
+
+```typescript
+const sceneManager = Core.services.resolve(SceneManager);
+```
+
+#### setScene()
+
+立即切换场景。
+
+```typescript
+public setScene<T extends IScene>(scene: T): T
+```
+
+#### loadScene()
+
+延迟场景加载。
+
+```typescript
+public loadScene<T extends IScene>(scene: T): void
+```
+
+#### currentScene
+
+获取当前场景。
+
+```typescript
+public get currentScene(): IScene | null
+```
+
+#### hasScene
+
+检查是否有活动场景。
+
+```typescript
+public get hasScene(): boolean
+```
+
+#### hasPendingScene
+
+检查是否有待处理的场景切换。
+
+```typescript
+public get hasPendingScene(): boolean
+```
+
+## 最佳实践
+
+### 1. 使用 Core 的静态方法
+
+```typescript
+// 推荐：使用 Core 的静态方法
+Core.setScene(new GameScene());
+Core.loadScene(new MenuScene());
+const currentScene = Core.scene;
+
+// 不推荐：除非有特殊需求，否则不要直接使用 SceneManager
+const sceneManager = Core.services.resolve(SceneManager);
+sceneManager.setScene(new GameScene());
+```
+
+### 2. 只调用 Core.update()
+
+```typescript
+// 正确：只调用 Core.update()
+function gameLoop(deltaTime: number) {
+  Core.update(deltaTime);  // 自动更新所有服务和场景
+}
+
+// 错误：不要手动调用 sceneManager.update()
+function gameLoop(deltaTime: number) {
+  Core.update(deltaTime);
+  sceneManager.update();  // 重复更新，会导致问题！
+}
+```
+
+### 3. 使用延迟切换避免问题
+
+在 System 中切换场景时，使用 `loadScene()` 而不是 `setScene()`：
+
+```typescript
+// 推荐：延迟切换
+class HealthSystem extends EntitySystem {
+  process(entities: readonly Entity[]): void {
+    for (const entity of entities) {
+      const health = entity.getComponent(Health);
+      if (health.value <= 0) {
+        Core.loadScene(new GameOverScene());
+        // 当前帧继续处理其他实体
+      }
+    }
+  }
+}
+
+// 不推荐：立即切换可能导致问题
+class HealthSystem extends EntitySystem {
+  process(entities: readonly Entity[]): void {
+    for (const entity of entities) {
+      const health = entity.getComponent(Health);
+      if (health.value <= 0) {
+        Core.setScene(new GameOverScene());
+        // 场景立即切换，当前帧其他实体可能无法正确处理
+      }
+    }
+  }
+}
+```
+
+### 4. 场景职责分离
+
+每个场景应该只负责一个特定的游戏状态：
+
+```typescript
+// 好的设计 - 职责清晰
+class MenuScene extends Scene {
+  // 只处理菜单相关逻辑
+}
+
+class GameScene extends Scene {
+  // 只处理游戏逻辑
+}
+
+class PauseScene extends Scene {
+  // 只处理暂停界面逻辑
+}
+
+// 避免这种设计 - 职责混杂
+class MegaScene extends Scene {
+  // 包含菜单、游戏、暂停和所有其他逻辑
+}
+```
+
+### 5. 资源管理
+
+在场景的 `unload()` 方法中清理资源：
+
+```typescript
+class GameScene extends Scene {
+  private textures: Map<string, any> = new Map();
+  private sounds: Map<string, any> = new Map();
+
+  protected initialize(): void {
+    this.loadResources();
+  }
+
+  private loadResources(): void {
+    this.textures.set('player', loadTexture('player.png'));
+    this.sounds.set('bgm', loadSound('bgm.mp3'));
+  }
+
+  public unload(): void {
+    // 清理资源
+    this.textures.clear();
+    this.sounds.clear();
+    console.log('场景资源已清理');
+  }
+}
+```
+
+### 6. 事件驱动的场景切换
+
+使用事件系统触发场景切换，保持代码解耦：
+
+```typescript
+class GameScene extends Scene {
+  protected initialize(): void {
+    // 监听场景切换事件
+    this.eventSystem.on('goto:menu', () => {
+      Core.loadScene(new MenuScene());
+    });
+
+    this.eventSystem.on('goto:gameover', (data) => {
+      Core.loadScene(new GameOverScene());
+    });
+  }
+}
+
+// 在 System 中触发事件
+class GameLogicSystem extends EntitySystem {
+  process(entities: readonly Entity[]): void {
+    if (levelComplete) {
+      this.scene.eventSystem.emitSync('goto:gameover', {
+        score: 1000,
+        level: 5
+      });
+    }
+  }
+}
+```
+
+## 架构概览
+
+SceneManager 在 ECS Framework 中的位置：
+
+```
+Core（全局服务）
+  └── SceneManager（场景管理，自动更新）
+      └── Scene（当前场景）
+          ├── EntitySystem（系统）
+          ├── Entity（实体）
+          └── Component（组件）
+```
+
+## 与 WorldManager 的比较
+
+| 特性 | SceneManager | WorldManager |
+|------|--------------|--------------|
+| 适用场景 | 95% 的游戏应用 | 高级多世界隔离场景 |
+| 复杂度 | 简单 | 复杂 |
+| 场景数量 | 单场景（可切换） | 多个 World，每个包含多个场景 |
+| 性能开销 | 最小 | 较高 |
+| 使用方式 | `Core.setScene()` | `worldManager.createWorld()` |
+
+**何时使用 SceneManager**：
+- 单人游戏
+- 简单多人游戏
+- 移动游戏
+- 需要切换但不需要同时运行的场景
+
+**何时使用 WorldManager**：
+- MMO 游戏服务器（每个房间一个 World）
+- 游戏大厅系统（每个游戏房间完全隔离）
+- 需要运行多个完全独立的游戏实例
+
+## 相关文档
+
+- [持久实体](/guide/persistent-entity/) - 了解如何在场景切换时保持实体
+
+SceneManager 为大多数游戏提供了简单而强大的场景管理能力。通过 Core 的静态方法，你可以轻松管理场景切换。
@@ -305,11 +305,11 @@ const tree = BehaviorTreeBuilder.create('Timeout')

 ### Cocos Creator集成

-参见[Cocos Creator集成指南](./cocos-integration/)
+参见[Cocos Creator集成指南](/modules/behavior-tree/cocos-integration/)

 ### LayaAir集成

-参见[LayaAir集成指南](./laya-integration/)
+参见[LayaAir集成指南](/modules/behavior-tree/laya-integration/)

 ## 最佳实践

@@ -389,6 +389,6 @@ const tree = BehaviorTreeBuilder.create('AI')

 ## 下一步

- 查看[自定义节点执行器](./custom-actions/)学习如何创建自定义节点
- 阅读[最佳实践](./best-practices/)了解行为树设计技巧
- 参考[编辑器使用指南](./editor-guide/)学习可视化编辑
+- 查看[自定义节点执行器](/modules/behavior-tree/custom-actions/)学习如何创建自定义节点
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)了解行为树设计技巧
+- 参考[编辑器使用指南](/modules/behavior-tree/editor-guide/)学习可视化编辑
@@ -503,6 +503,6 @@ console.log(json);

 ## 下一步

- 学习[Cocos Creator 集成](./cocos-integration/)了解如何在游戏引擎中加载资源
- 查看[自定义节点执行器](./custom-actions/)创建自定义行为
- 阅读[最佳实践](./best-practices/)优化你的行为树设计
+- 学习[Cocos Creator 集成](/modules/behavior-tree/cocos-integration/)了解如何在游戏引擎中加载资源
+- 查看[自定义节点执行器](/modules/behavior-tree/custom-actions/)创建自定义行为
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)优化你的行为树设计
@@ -26,7 +26,7 @@ Root Selector

 ### 2. 单一职责原则

-每个节点应该只做一件事。要实现复杂动作,创建自定义执行器,参见[自定义节点执行器](./custom-actions/)。
+每个节点应该只做一件事。要实现复杂动作,创建自定义执行器,参见[自定义节点执行器](/modules/behavior-tree/custom-actions/)。

 ```typescript
 // 好的设计 - 使用内置节点
@@ -465,6 +465,6 @@ export class SmartUpdate implements INodeExecutor {

 ## 下一步

- 学习[自定义节点执行器](./custom-actions/)扩展行为树功能
- 探索[高级用法](./advanced-usage/)了解更多技巧
- 参考[核心概念](./core-concepts/)深入理解原理
+- 学习[自定义节点执行器](/modules/behavior-tree/custom-actions/)扩展行为树功能
+- 探索[高级用法](/modules/behavior-tree/advanced-usage/)了解更多技巧
+- 参考[核心概念](/modules/behavior-tree/core-concepts/)深入理解原理
@@ -8,7 +8,7 @@ title: "Cocos Creator 集成"

 - Cocos Creator 3.x 或更高版本
 - 基本的 TypeScript 知识
- 已完成[快速开始](./getting-started/)教程
+- 已完成[快速开始](/modules/behavior-tree/getting-started/)教程

 ## 安装

@@ -679,7 +679,7 @@ const updateInterval = sys.isNative ? 0.016 : 0.05;

 ## 下一步

- 查看[资产管理](./asset-management/)了解如何加载和管理行为树资产、使用子树
- 学习[高级用法](./advanced-usage/)了解性能优化和调试技巧
- 阅读[最佳实践](./best-practices/)优化你的 AI
- 学习[自定义节点执行器](./custom-actions/)创建自定义行为
+- 查看[资产管理](/modules/behavior-tree/asset-management/)了解如何加载和管理行为树资产、使用子树
+- 学习[高级用法](/modules/behavior-tree/advanced-usage/)了解性能优化和调试技巧
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)优化你的 AI
+- 学习[自定义节点执行器](/modules/behavior-tree/custom-actions/)创建自定义行为
@@ -192,7 +192,7 @@ const tree = BehaviorTreeBuilder.create('Actions')
    .build();
 ```

-要实现自定义动作,需要创建自定义执行器,参见[自定义节点执行器](./custom-actions/)。
+要实现自定义动作,需要创建自定义执行器,参见[自定义节点执行器](/modules/behavior-tree/custom-actions/)。

 #### Condition(条件)

@@ -487,7 +487,7 @@ NodeRuntimeState

 现在你已经理解了行为树的核心概念,接下来可以:

- 查看[快速开始](./getting-started/)创建第一个行为树
- 学习[自定义节点执行器](./custom-actions/)创建自定义节点
- 探索[高级用法](./advanced-usage/)了解更多功能
- 阅读[最佳实践](./best-practices/)学习设计模式
+- 查看[快速开始](/modules/behavior-tree/getting-started/)创建第一个行为树
+- 学习[自定义节点执行器](/modules/behavior-tree/custom-actions/)创建自定义节点
+- 探索[高级用法](/modules/behavior-tree/advanced-usage/)了解更多功能
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)学习设计模式
@@ -1123,6 +1123,6 @@ execute(context: NodeExecutionContext): TaskStatus {

 ## 下一步

- 学习[编辑器工作流](./editor-workflow/)了解如何在编辑器中使用自定义节点
- 阅读[最佳实践](./best-practices/)学习行为树设计模式
- 查看[高级用法](./advanced-usage/)了解更多功能
+- 学习[编辑器工作流](/modules/behavior-tree/editor-workflow/)了解如何在编辑器中使用自定义节点
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)学习行为树设计模式
+- 查看[高级用法](/modules/behavior-tree/advanced-usage/)了解更多功能
@@ -117,5 +117,5 @@ BehaviorTreeStarter.start(entity, tree);

 ## 下一步

- 查看[编辑器工作流](./editor-workflow/)了解完整的开发流程
- 查看[自定义节点执行器](./custom-actions/)学习如何扩展节点
+- 查看[编辑器工作流](/modules/behavior-tree/editor-workflow/)了解完整的开发流程
+- 查看[自定义节点执行器](/modules/behavior-tree/custom-actions/)学习如何扩展节点
@@ -112,7 +112,7 @@ setInterval(() => {

 ## 实现自定义执行器

-要扩展行为树的功能，需要创建自定义执行器（详见[自定义节点执行器](./custom-actions/)）：
+要扩展行为树的功能，需要创建自定义执行器（详见[自定义节点执行器](/modules/behavior-tree/custom-actions/)）：

 ```typescript
 import {
@@ -250,6 +250,6 @@ setInterval(() => {

 ## 下一步

- 查看[自定义节点执行器](./custom-actions/)学习如何创建自定义节点
- 查看[高级用法](./advanced-usage/)了解性能优化等高级特性
- 查看[最佳实践](./best-practices/)优化你的AI设计
+- 查看[自定义节点执行器](/modules/behavior-tree/custom-actions/)学习如何创建自定义节点
+- 查看[高级用法](/modules/behavior-tree/advanced-usage/)了解性能优化等高级特性
+- 查看[最佳实践](/modules/behavior-tree/best-practices/)优化你的AI设计
@@ -333,11 +333,11 @@ BehaviorTreeStarter.restart(entity);

 现在你已经创建了第一个行为树,接下来可以:

-1. 学习[核心概念](./core-concepts/)深入理解行为树原理
-2. 学习[资产管理](./asset-management/)了解如何加载和复用行为树、使用子树
-3. 查看[自定义节点执行器](./custom-actions/)学习如何创建自定义节点
-4. 根据你的场景查看集成教程：[Cocos Creator](./cocos-integration/) 或 [Node.js](./nodejs-usage.md)
-5. 查看[高级用法](./advanced-usage/)了解更多功能
+1. 学习[核心概念](/modules/behavior-tree/core-concepts/)深入理解行为树原理
+2. 学习[资产管理](/modules/behavior-tree/asset-management/)了解如何加载和复用行为树、使用子树
+3. 查看[自定义节点执行器](/modules/behavior-tree/custom-actions/)学习如何创建自定义节点
+4. 根据你的场景查看集成教程：[Cocos Creator](/modules/behavior-tree/cocos-integration/) 或 [Node.js](/modules/behavior-tree/nodejs-usage/)
+5. 查看[高级用法](/modules/behavior-tree/advanced-usage/)了解更多功能

 ## 常见问题

@@ -384,4 +384,4 @@ console.log('活动节点:', Array.from(runtime?.activeNodeIds || []));

 内置的`executeAction`和`executeCondition`节点只是占位符。要实现真正的自定义逻辑,你需要创建自定义执行器:

-参见[自定义节点执行器](./custom-actions/)学习如何创建。
+参见[自定义节点执行器](/modules/behavior-tree/custom-actions/)学习如何创建。
@@ -8,7 +8,7 @@ title: "Laya 引擎集成"

 - LayaAir 3.x 或更高版本
 - 基本的 TypeScript 知识
- 已完成[快速开始](./getting-started/)教程
+- 已完成[快速开始](/modules/behavior-tree/getting-started/)教程

 ## 安装

@@ -311,5 +311,5 @@ class AIManager {

 ## 下一步

- 查看[高级用法](./advanced-usage/)
- 学习[最佳实践](./best-practices/)
+- 查看[高级用法](/modules/behavior-tree/advanced-usage/)
+- 学习[最佳实践](/modules/behavior-tree/best-practices/)
@@ -577,6 +577,6 @@ function loadAIState(entity: Entity, savedState: any) {

 ## 下一步

- 查看[资产管理](./asset-management/)了解资源加载和子树
- 学习[自定义节点执行器](./custom-actions/)创建自定义行为
- 阅读[最佳实践](./best-practices/)优化你的服务端AI
+- 查看[资产管理](/modules/behavior-tree/asset-management/)了解资源加载和子树
+- 学习[自定义节点执行器](/modules/behavior-tree/custom-actions/)创建自定义行为
+- 阅读[最佳实践](/modules/behavior-tree/best-practices/)优化你的服务端AI
@@ -0,0 +1,383 @@
+---
+title: "Cocos Creator 蓝图编辑器"
+description: "在 Cocos Creator 中使用蓝图可视化脚本系统"
+---
+
+本文档介绍如何在 Cocos Creator 项目中安装和使用蓝图可视化脚本编辑器扩展。
+
+## 安装扩展
+
+### 1. 复制扩展到项目
+
+将 `cocos-node-editor` 扩展复制到你的 Cocos Creator 项目的 `extensions` 目录：
+
+```
+your-project/
+├── assets/
+├── extensions/
+│   └── cocos-node-editor/    # 蓝图编辑器扩展
+└── ...
+```
+
+### 2. 安装依赖
+
+在扩展目录中安装依赖：
+
+```bash
+cd extensions/cocos-node-editor
+npm install
+```
+
+### 3. 启用扩展
+
+1. 打开 Cocos Creator
+2. 进入 **扩展 → 扩展管理器**
+3. 找到 `cocos-node-editor` 并启用
+
+## 打开蓝图编辑器
+
+通过菜单 **面板 → Node Editor** 打开蓝图编辑器面板。
+
+## 编辑器界面
+
+### 工具栏
+
+| 按钮 | 快捷键 | 功能 |
+|------|--------|------|
+| 新建 | - | 创建空白蓝图 |
+| 加载 | - | 从文件加载蓝图 |
+| 保存 | `Ctrl+S` | 保存蓝图到文件 |
+| 撤销 | `Ctrl+Z` | 撤销上一步操作 |
+| 重做 | `Ctrl+Shift+Z` | 重做操作 |
+| 剪切 | `Ctrl+X` | 剪切选中节点 |
+| 复制 | `Ctrl+C` | 复制选中节点 |
+| 粘贴 | `Ctrl+V` | 粘贴节点 |
+| 删除 | `Delete` | 删除选中项 |
+| 重新扫描 | - | 重新扫描项目中的蓝图节点 |
+
+### 画布操作
+
+- **右键单击画布**：打开节点添加菜单
+- **拖拽节点**：移动节点位置
+- **点击节点**：选中节点
+- **Ctrl+点击**：多选节点
+- **拖拽引脚到引脚**：创建连接
+- **滚轮**：缩放画布
+- **中键拖拽**：平移画布
+
+### 节点菜单
+
+右键单击画布后会显示节点菜单：
+
+- 顶部搜索框可以快速搜索节点
+- 节点按类别分组显示
+- 按 `Enter` 快速添加第一个搜索结果
+- 按 `Esc` 关闭菜单
+
+## 蓝图文件格式
+
+蓝图保存为 `.blueprint.json` 文件，格式与运行时完全兼容：
+
+```json
+{
+  "version": 1,
+  "type": "blueprint",
+  "metadata": {
+    "name": "My Blueprint",
+    "createdAt": 1704307200000,
+    "modifiedAt": 1704307200000
+  },
+  "variables": [],
+  "nodes": [
+    {
+      "id": "node-1",
+      "type": "PrintString",
+      "position": { "x": 100, "y": 200 },
+      "data": {}
+    }
+  ],
+  "connections": [
+    {
+      "id": "conn-1",
+      "fromNodeId": "node-1",
+      "fromPin": "exec",
+      "toNodeId": "node-2",
+      "toPin": "exec"
+    }
+  ]
+}
+```
+
+## 在游戏中运行蓝图
+
+使用 ECS 系统方式管理和执行蓝图。
+
+### 1. 定义蓝图组件
+
+```typescript
+import { Component, ECSComponent, Property, Serialize } from '@esengine/ecs-framework';
+import type { BlueprintAsset } from '@esengine/blueprint';
+
+@ECSComponent('Blueprint')
+export class BlueprintComponent extends Component {
+    @Serialize()
+    @Property({ type: 'asset', label: 'Blueprint Asset' })
+    blueprintPath: string = '';
+
+    @Serialize()
+    @Property({ type: 'boolean', label: 'Auto Start' })
+    autoStart: boolean = true;
+
+    // 运行时数据（不序列化）
+    blueprintAsset: BlueprintAsset | null = null;
+    vm: BlueprintVM | null = null;
+    isStarted: boolean = false;
+}
+```
+
+### 2. 创建蓝图执行系统
+
+```typescript
+import { EntitySystem, Matcher, Entity } from '@esengine/ecs-framework';
+import {
+    BlueprintVM,
+    validateBlueprintAsset
+} from '@esengine/blueprint';
+import { BlueprintComponent } from './BlueprintComponent';
+
+export class BlueprintExecutionSystem extends EntitySystem {
+    constructor() {
+        super(Matcher.empty().all(BlueprintComponent));
+    }
+
+    protected override process(entities: readonly Entity[]): void {
+        const dt = Time.deltaTime;
+
+        for (const entity of entities) {
+            const bp = entity.getComponent(BlueprintComponent)!;
+
+            // 跳过没有蓝图资产的实体
+            if (!bp.blueprintAsset) continue;
+
+            // 初始化 VM
+            if (!bp.vm) {
+                bp.vm = new BlueprintVM(bp.blueprintAsset, entity, this.scene!);
+            }
+
+            // 自动启动
+            if (bp.autoStart && !bp.isStarted) {
+                bp.vm.start();
+                bp.isStarted = true;
+            }
+
+            // 更新蓝图
+            if (bp.isStarted) {
+                bp.vm.tick(dt);
+            }
+        }
+    }
+
+    protected override onRemoved(entity: Entity): void {
+        const bp = entity.getComponent(BlueprintComponent);
+        if (bp?.vm && bp.isStarted) {
+            bp.vm.stop();
+            bp.vm = null;
+            bp.isStarted = false;
+        }
+    }
+}
+```
+
+### 3. 加载蓝图并添加到实体
+
+```typescript
+import { resources, JsonAsset } from 'cc';
+import { validateBlueprintAsset } from '@esengine/blueprint';
+
+// 加载蓝图资产
+async function loadBlueprint(path: string): Promise<BlueprintAsset | null> {
+    return new Promise((resolve) => {
+        resources.load(path, JsonAsset, (err, asset) => {
+            if (err || !asset) {
+                console.error('Failed to load blueprint:', err);
+                resolve(null);
+                return;
+            }
+
+            const data = asset.json;
+            if (validateBlueprintAsset(data)) {
+                resolve(data as BlueprintAsset);
+            } else {
+                console.error('Invalid blueprint format');
+                resolve(null);
+            }
+        });
+    });
+}
+
+// 创建带蓝图的实体
+async function createBlueprintEntity(scene: IScene, blueprintPath: string): Promise<Entity> {
+    const entity = scene.createEntity('BlueprintEntity');
+
+    const bpComponent = entity.addComponent(BlueprintComponent);
+    bpComponent.blueprintPath = blueprintPath;
+    bpComponent.blueprintAsset = await loadBlueprint(blueprintPath);
+
+    return entity;
+}
+```
+
+### 4. 注册系统到场景
+
+```typescript
+// 在场景初始化时
+scene.addSystem(new BlueprintExecutionSystem());
+```
+
+## 创建自定义节点
+
+### 使用装饰器标记组件
+
+推荐使用装饰器让组件自动生成蓝图节点：
+
+```typescript
+import { Component, ECSComponent } from '@esengine/ecs-framework';
+import { BlueprintExpose, BlueprintProperty, BlueprintMethod } from '@esengine/blueprint';
+
+@ECSComponent('Health')
+@BlueprintExpose({ displayName: '生命值组件' })
+export class HealthComponent extends Component {
+    @BlueprintProperty({ displayName: '当前生命值', category: 'number' })
+    current: number = 100;
+
+    @BlueprintProperty({ displayName: '最大生命值', category: 'number' })
+    max: number = 100;
+
+    @BlueprintMethod({ displayName: '治疗', isExec: true })
+    heal(amount: number): void {
+        this.current = Math.min(this.current + amount, this.max);
+    }
+
+    @BlueprintMethod({ displayName: '受伤', isExec: true })
+    takeDamage(amount: number): void {
+        this.current = Math.max(this.current - amount, 0);
+    }
+
+    @BlueprintMethod({ displayName: '是否死亡' })
+    isDead(): boolean {
+        return this.current <= 0;
+    }
+}
+```
+
+### 注册组件节点
+
+```typescript
+import { registerAllComponentNodes } from '@esengine/blueprint';
+
+// 在应用启动时注册所有标记的组件
+registerAllComponentNodes();
+```
+
+### 手动定义节点（高级）
+
+如需完全自定义节点逻辑：
+
+```typescript
+import {
+    BlueprintNodeTemplate,
+    INodeExecutor,
+    RegisterNode,
+    ExecutionContext,
+    ExecutionResult
+} from '@esengine/blueprint';
+
+const MyNodeTemplate: BlueprintNodeTemplate = {
+    type: 'MyCustomNode',
+    title: '我的自定义节点',
+    category: 'custom',
+    description: '自定义节点示例',
+    inputs: [
+        { name: 'exec', type: 'exec', direction: 'input', isExec: true },
+        { name: 'value', type: 'number', direction: 'input', defaultValue: 0 }
+    ],
+    outputs: [
+        { name: 'exec', type: 'exec', direction: 'output', isExec: true },
+        { name: 'result', type: 'number', direction: 'output' }
+    ]
+};
+
+@RegisterNode(MyNodeTemplate)
+class MyNodeExecutor implements INodeExecutor {
+    execute(node: BlueprintNode, context: ExecutionContext): ExecutionResult {
+        const value = context.getInput<number>(node.id, 'value');
+        return {
+            outputs: { result: value * 2 },
+            nextExec: 'exec'
+        };
+    }
+}
+```
+
+## 节点类别
+
+| 类别 | 说明 | 颜色 |
+|------|------|------|
+| `event` | 事件节点 | 红色 |
+| `flow` | 流程控制 | 灰色 |
+| `entity` | 实体操作 | 蓝色 |
+| `component` | 组件访问 | 青色 |
+| `math` | 数学运算 | 绿色 |
+| `logic` | 逻辑运算 | 红色 |
+| `variable` | 变量访问 | 紫色 |
+| `time` | 时间工具 | 青色 |
+| `debug` | 调试工具 | 灰色 |
+| `custom` | 自定义节点 | 蓝灰色 |
+
+## 最佳实践
+
+1. **文件组织**
+   - 将蓝图文件放在 `assets/blueprints/` 目录下
+   - 使用有意义的文件名，如 `player-controller.blueprint.json`
+
+2. **组件设计**
+   - 使用 `@BlueprintExpose` 标记需要暴露给蓝图的组件
+   - 为属性和方法提供清晰的 `displayName`
+   - 将执行方法标记为 `isExec: true`
+
+3. **性能考虑**
+   - 避免在 Tick 事件中执行重计算
+   - 使用变量缓存中间结果
+   - 纯函数节点会自动缓存输出
+
+4. **调试技巧**
+   - 使用 Print 节点输出中间值
+   - 启用 `vm.debug = true` 查看执行日志
+
+## 常见问题
+
+### Q: 节点菜单是空的？
+
+A: 点击 **重新扫描** 按钮扫描项目中的蓝图节点类。确保已调用 `registerAllComponentNodes()`。
+
+### Q: 蓝图不执行？
+
+A: 检查：
+1. 实体是否添加了 `BlueprintComponent`
+2. `BlueprintExecutionSystem` 是否注册到场景
+3. `blueprintAsset` 是否正确加载
+4. `autoStart` 是否为 `true`
+
+### Q: 如何触发自定义事件？
+
+A: 通过 VM 触发：
+```typescript
+const bp = entity.getComponent(BlueprintComponent);
+bp.vm?.triggerCustomEvent('OnPickup', { item: itemEntity });
+```
+
+## 相关文档
+
+- [蓝图运行时 API](/modules/blueprint/) - BlueprintVM 和核心 API
+- [自定义节点](/modules/blueprint/custom-nodes) - 详细的节点创建指南
+- [内置节点](/modules/blueprint/nodes) - 内置节点参考
@@ -870,7 +870,7 @@ your-project/

 ## 下一步

- [ECS 节点参考](./nodes) - 完整节点列表
- [自定义节点](./custom-nodes) - 创建自定义节点
- [运行时集成](./vm) - 蓝图虚拟机 API
- [实际示例](./examples) - 更多游戏逻辑示例
+- [ECS 节点参考](/modules/blueprint/nodes) - 完整节点列表
+- [自定义节点](/modules/blueprint/custom-nodes) - 创建自定义节点
+- [运行时集成](/modules/blueprint/vm) - 蓝图虚拟机 API
+- [实际示例](/modules/blueprint/examples) - 更多游戏逻辑示例
@@ -535,6 +535,6 @@ description: "蓝图内置 ECS 操作节点完整参考"

 ## 相关文档

- [蓝图编辑器指南](./editor-guide) - 学习如何使用编辑器
- [自定义节点](./custom-nodes) - 创建自定义节点
- [蓝图虚拟机](./vm) - 运行时 API
+- [蓝图编辑器指南](/modules/blueprint/editor-guide) - 学习如何使用编辑器
+- [自定义节点](/modules/blueprint/custom-nodes) - 创建自定义节点
+- [蓝图虚拟机](/modules/blueprint/vm) - 运行时 API
@@ -0,0 +1,326 @@
+---
+title: "定点数"
+description: "用于帧同步的确定性定点数数学库"
+---
+
+`@esengine/ecs-framework-math` 提供确定性定点数计算，专为**帧同步 (Lockstep)** 设计。定点数在所有平台上保证产生完全相同的计算结果。
+
+## 为什么需要定点数？
+
+浮点数在不同平台上可能产生不同的舍入结果：
+
+```typescript
+// 浮点数：不同平台可能得到不同结果
+const a = 0.1 + 0.2;  // 0.30000000000000004 (某些平台)
+                      // 0.3 (其他平台)
+
+// 定点数：所有平台结果一致
+const x = Fixed32.from(0.1);
+const y = Fixed32.from(0.2);
+const z = x.add(y);   // raw = 19661 (所有平台)
+```
+
+| 特性 | 浮点数 | 定点数 |
+|------|--------|--------|
+| 跨平台一致性 | ❌ 可能不同 | ✅ 完全一致 |
+| 网络同步模式 | 状态同步 | 帧同步 (Lockstep) |
+| 适用游戏类型 | FPS、RPG | RTS、MOBA、格斗 |
+
+## 安装
+
+```bash
+npm install @esengine/ecs-framework-math
+```
+
+## Fixed32 定点数
+
+Q16.16 格式：16 位整数 + 16 位小数，范围 ±32767.99998。
+
+### 创建定点数
+
+```typescript
+import { Fixed32 } from '@esengine/ecs-framework-math';
+
+// 从浮点数创建
+const speed = Fixed32.from(5.5);
+
+// 从整数创建（无精度损失）
+const count = Fixed32.fromInt(10);
+
+// 从原始值创建（网络接收后使用）
+const received = Fixed32.fromRaw(360448);  // 等于 5.5
+
+// 预定义常量
+Fixed32.ZERO        // 0
+Fixed32.ONE         // 1
+Fixed32.HALF        // 0.5
+Fixed32.PI          // π
+Fixed32.TWO_PI      // 2π
+Fixed32.HALF_PI     // π/2
+```
+
+### 基本运算
+
+```typescript
+const a = Fixed32.from(10);
+const b = Fixed32.from(3);
+
+const sum = a.add(b);       // 13
+const diff = a.sub(b);      // 7
+const prod = a.mul(b);      // 30
+const quot = a.div(b);      // 3.333...
+const mod = a.mod(b);       // 1
+const neg = a.neg();        // -10
+const abs = neg.abs();      // 10
+```
+
+### 比较运算
+
+```typescript
+const x = Fixed32.from(5);
+const y = Fixed32.from(3);
+
+x.eq(y)     // false - 等于
+x.ne(y)     // true  - 不等于
+x.lt(y)     // false - 小于
+x.le(y)     // false - 小于等于
+x.gt(y)     // true  - 大于
+x.ge(y)     // true  - 大于等于
+
+x.isZero()      // false
+x.isPositive()  // true
+x.isNegative()  // false
+```
+
+### 数学函数
+
+```typescript
+// 平方根（牛顿迭代法，确定性）
+const sqrt = Fixed32.sqrt(Fixed32.from(16));  // 4
+
+// 取整
+Fixed32.floor(Fixed32.from(3.7))   // 3
+Fixed32.ceil(Fixed32.from(3.2))    // 4
+Fixed32.round(Fixed32.from(3.5))   // 4
+
+// 范围限制
+Fixed32.clamp(value, min, max)
+
+// 线性插值
+Fixed32.lerp(from, to, t)
+
+// 最大/最小值
+Fixed32.min(a, b)
+Fixed32.max(a, b)
+```
+
+### 类型转换
+
+```typescript
+const value = Fixed32.from(3.14159);
+
+// 转为浮点数（用于渲染）
+const float = value.toNumber();  // 3.14159
+
+// 获取原始值（用于网络传输）
+const raw = value.toRaw();  // 205887
+
+// 转为整数（向下取整）
+const int = value.toInt();  // 3
+```
+
+## FixedVector2 定点数向量
+
+不可变的 2D 向量类，所有运算返回新实例。
+
+### 创建向量
+
+```typescript
+import { FixedVector2, Fixed32 } from '@esengine/ecs-framework-math';
+
+// 从浮点数创建
+const pos = FixedVector2.from(100, 200);
+
+// 从原始值创建（网络接收后使用）
+const received = FixedVector2.fromRaw(6553600, 13107200);
+
+// 从 Fixed32 创建
+const vec = new FixedVector2(Fixed32.from(10), Fixed32.from(20));
+
+// 预定义常量
+FixedVector2.ZERO   // (0, 0)
+FixedVector2.ONE    // (1, 1)
+FixedVector2.RIGHT  // (1, 0)
+FixedVector2.LEFT   // (-1, 0)
+FixedVector2.UP     // (0, 1)
+FixedVector2.DOWN   // (0, -1)
+```
+
+### 向量运算
+
+```typescript
+const a = FixedVector2.from(3, 4);
+const b = FixedVector2.from(1, 2);
+
+// 基本运算
+const sum = a.add(b);                    // (4, 6)
+const diff = a.sub(b);                   // (2, 2)
+const scaled = a.mul(Fixed32.from(2));   // (6, 8)
+const divided = a.div(Fixed32.from(2));  // (1.5, 2)
+
+// 向量积
+const dot = a.dot(b);    // 3*1 + 4*2 = 11
+const cross = a.cross(b); // 3*2 - 4*1 = 2
+
+// 长度
+const lenSq = a.lengthSquared();  // 25
+const len = a.length();           // 5
+
+// 归一化
+const norm = a.normalize();  // (0.6, 0.8)
+
+// 距离
+const dist = a.distanceTo(b);  // sqrt((3-1)² + (4-2)²)
+```
+
+### 旋转和角度
+
+```typescript
+import { FixedMath } from '@esengine/ecs-framework-math';
+
+const vec = FixedVector2.from(1, 0);
+const angle = Fixed32.from(Math.PI / 2);  // 90度
+
+// 旋转向量
+const rotated = vec.rotate(angle);  // (0, 1)
+
+// 围绕点旋转
+const center = FixedVector2.from(5, 5);
+const around = vec.rotateAround(center, angle);
+
+// 获取向量角度
+const vecAngle = vec.angle();
+
+// 两向量夹角
+const between = vec.angleTo(other);
+
+// 从角度创建单位向量
+const dir = FixedVector2.fromAngle(angle);
+
+// 从极坐标创建
+const polar = FixedVector2.fromPolar(length, angle);
+```
+
+### 类型转换
+
+```typescript
+const pos = FixedVector2.from(100.5, 200.5);
+
+// 转为浮点对象（用于渲染）
+const obj = pos.toObject();  // { x: 100.5, y: 200.5 }
+
+// 转为数组
+const arr = pos.toArray();  // [100.5, 200.5]
+
+// 获取原始值（用于网络传输）
+const raw = pos.toRawObject();  // { x: 6586368, y: 13140992 }
+```
+
+## FixedMath 三角函数
+
+使用查找表实现确定性三角函数。
+
+```typescript
+import { FixedMath, Fixed32 } from '@esengine/ecs-framework-math';
+
+const angle = Fixed32.from(Math.PI / 6);  // 30度
+
+// 三角函数
+const sin = FixedMath.sin(angle);  // 0.5
+const cos = FixedMath.cos(angle);  // 0.866
+const tan = FixedMath.tan(angle);  // 0.577
+
+// 反三角函数
+const atan = FixedMath.atan2(y, x);
+const asin = FixedMath.asin(value);
+const acos = FixedMath.acos(value);
+
+// 角度规范化到 [-π, π]
+const normalized = FixedMath.normalizeAngle(angle);
+
+// 角度差（最短路径）
+const delta = FixedMath.angleDelta(from, to);
+
+// 角度插值（处理 360° 环绕）
+const lerped = FixedMath.lerpAngle(from, to, t);
+
+// 弧度/角度转换
+const deg = FixedMath.radToDeg(rad);
+const rad = FixedMath.degToRad(deg);
+```
+
+## 最佳实践
+
+### 1. 全程使用定点数计算
+
+```typescript
+// ✅ 正确：所有游戏逻辑使用定点数
+function calculateDamage(baseDamage: Fixed32, multiplier: Fixed32): Fixed32 {
+    return baseDamage.mul(multiplier);
+}
+
+// ❌ 错误：混用浮点数
+function calculateDamage(baseDamage: number, multiplier: number): number {
+    return baseDamage * multiplier;  // 可能不一致
+}
+```
+
+### 2. 只在渲染时转换为浮点数
+
+```typescript
+// 游戏逻辑层
+const position: FixedVector2 = calculatePosition(input);
+
+// 渲染层
+const { x, y } = position.toObject();
+sprite.position.set(x, y);
+```
+
+### 3. 使用原始值进行网络传输
+
+```typescript
+// ✅ 正确：传输整数原始值
+const raw = position.toRawObject();
+send(JSON.stringify(raw));
+
+// ❌ 错误：传输浮点数
+const float = position.toObject();
+send(JSON.stringify(float));  // 可能丢失精度
+```
+
+### 4. 使用 FixedMath 进行三角运算
+
+```typescript
+// ✅ 正确：使用查找表
+const direction = FixedVector2.fromAngle(FixedMath.atan2(dy, dx));
+
+// ❌ 错误：使用 Math 库
+const angle = Math.atan2(dy.toNumber(), dx.toNumber());  // 不确定
+```
+
+## API 导出
+
+```typescript
+import {
+    Fixed32,
+    FixedVector2,
+    FixedMath,
+    type IFixed32,
+    type IFixedVector2
+} from '@esengine/ecs-framework-math';
+```
+
+## 相关文档
+
+- [状态同步](/modules/network/sync) - 定点数快照缓冲区
+- [客户端预测](/modules/network/prediction) - 定点数客户端预测
@@ -252,3 +252,145 @@ if (predictionSystem) {
    console.log('Current sequence:', predictionSystem.inputSequence);
 }
 ```
+
+---
+
+## 定点数客户端预测（帧同步）
+
+用于**帧同步 (Lockstep)** 的确定性客户端预测。
+
+> 定点数基础知识请参考 [定点数文档](/modules/network/fixed-point)
+
+### 基本用法
+
+```typescript
+import {
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    type IFixedPredictor,
+    type IFixedStatePositionExtractor
+} from '@esengine/network';
+import { Fixed32, FixedVector2 } from '@esengine/ecs-framework-math';
+
+// 定义游戏状态
+interface GameState {
+    position: FixedVector2;
+    velocity: FixedVector2;
+}
+
+// 实现预测器（必须使用定点数运算）
+const predictor: IFixedPredictor<GameState, PlayerInput> = {
+    predict(state: GameState, input: PlayerInput, deltaTime: Fixed32): GameState {
+        const speed = Fixed32.from(100);
+        const inputVec = FixedVector2.from(input.dx, input.dy);
+        const velocity = inputVec.normalize().mul(speed);
+        const displacement = velocity.mul(deltaTime);
+
+        return {
+            position: state.position.add(displacement),
+            velocity
+        };
+    }
+};
+
+// 创建预测器
+const prediction = createFixedClientPrediction(predictor, {
+    maxUnacknowledgedInputs: 60,
+    fixedDeltaTime: Fixed32.from(1 / 60),
+    reconciliationThreshold: Fixed32.from(0.001),
+    enableSmoothReconciliation: false  // 帧同步通常关闭
+});
+```
+
+### 记录输入
+
+```typescript
+function onUpdate(input: PlayerInput, currentState: GameState) {
+    // 记录输入并获得预测状态
+    const predicted = prediction.recordInput(input, currentState);
+
+    // 渲染预测状态
+    const pos = predicted.position.toObject();
+    sprite.position.set(pos.x, pos.y);
+
+    // 发送输入
+    socket.send(JSON.stringify({
+        frame: prediction.currentFrame,
+        input
+    }));
+}
+```
+
+### 服务器校正
+
+```typescript
+// 位置提取器
+const posExtractor: IFixedStatePositionExtractor<GameState> = {
+    getPosition(state: GameState): FixedVector2 {
+        return state.position;
+    }
+};
+
+// 收到服务器状态
+function onServerState(serverState: GameState, serverFrame: number) {
+    const reconciled = prediction.reconcile(
+        serverState,
+        serverFrame,
+        posExtractor
+    );
+}
+```
+
+### 回滚重播
+
+```typescript
+// 发现不同步时回滚
+const correctedState = prediction.rollbackAndResimulate(
+    serverFrame,
+    authoritativeState
+);
+
+// 查看历史状态
+const historicalState = prediction.getStateAtFrame(100);
+```
+
+### 预设移动预测器
+
+```typescript
+import {
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+    type IFixedMovementInput,
+    type IFixedMovementState
+} from '@esengine/network';
+
+// 创建移动预测器（速度 100 单位/秒）
+const movePredictor = createFixedMovementPredictor(Fixed32.from(100));
+const posExtractor = createFixedMovementPositionExtractor();
+
+const prediction = createFixedClientPrediction<IFixedMovementState, IFixedMovementInput>(
+    movePredictor,
+    { fixedDeltaTime: Fixed32.from(1 / 60) }
+);
+
+// 输入格式
+const input: IFixedMovementInput = { dx: 1, dy: 0 };
+```
+
+### API 导出
+
+```typescript
+import {
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+    type IFixedInputSnapshot,
+    type IFixedPredictedState,
+    type IFixedPredictor,
+    type IFixedStatePositionExtractor,
+    type FixedClientPredictionConfig,
+    type IFixedMovementInput,
+    type IFixedMovementState
+} from '@esengine/network';
+```
@@ -340,3 +340,139 @@ if (!identity.bIsLocalPlayer) {
 3. **校正阈值**：根据游戏精度需求设置合适的阈值

 4. **快照数量**：保持足够的快照以应对网络抖动
+
+---
+
+## 定点数同步（帧同步）
+
+以下内容用于**帧同步 (Lockstep)** 架构，使用定点数确保跨平台确定性。
+
+> 定点数基础知识请参考 [定点数文档](/modules/network/fixed-point)
+
+### FixedTransformState
+
+定点数变换状态，用于网络传输：
+
+```typescript
+import {
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw
+} from '@esengine/network';
+
+// 创建状态
+const state = FixedTransformState.from(100, 200, Math.PI / 4);
+
+// 序列化（发送方）
+const raw: IFixedTransformStateRaw = state.toRaw();
+socket.send(JSON.stringify({ type: 'sync', state: raw }));
+
+// 反序列化（接收方）
+const received = FixedTransformState.fromRaw(message.state);
+
+// 用于渲染
+const { x, y, rotation } = received.toFloat();
+sprite.position.set(x, y);
+```
+
+带速度的状态（用于外推）：
+
+```typescript
+const state = FixedTransformStateWithVelocity.from(
+    100, 200,    // 位置
+    0,           // 旋转
+    5, 3,        // 速度
+    0.1          // 角速度
+);
+```
+
+### 定点数插值器
+
+```typescript
+import {
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator
+} from '@esengine/network';
+import { Fixed32 } from '@esengine/ecs-framework-math';
+
+// 线性插值器
+const interpolator = createFixedTransformInterpolator();
+
+const from = FixedTransformState.from(0, 0, 0);
+const to = FixedTransformState.from(100, 50, Math.PI);
+const t = Fixed32.from(0.5);
+
+const result = interpolator.interpolate(from, to, t);
+
+// Hermite 插值器（更平滑）
+const hermite = createFixedHermiteTransformInterpolator(100);
+```
+
+### 定点数快照缓冲区
+
+管理定点数状态历史，用于帧同步回放：
+
+```typescript
+import {
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer
+} from '@esengine/network';
+
+// 创建缓冲区（最多 30 快照，2 帧延迟）
+const buffer = createFixedSnapshotBuffer<FixedTransformState>(30, 2);
+
+// 添加快照
+buffer.push({
+    frame: 100,
+    state: FixedTransformState.from(100, 200, 0)
+});
+
+// 获取插值快照
+const result = buffer.getInterpolationSnapshots(103);
+if (result) {
+    const { from, to, t } = result;
+    const interpolated = interpolator.interpolate(from.state, to.state, t);
+}
+
+// 获取最新/指定帧快照
+const latest = buffer.getLatest();
+const atFrame = buffer.getAtFrame(100);
+
+// 回滚重播
+const snapshotsToReplay = buffer.getSnapshotsAfter(98);
+
+// 清理旧快照
+buffer.removeSnapshotsBefore(95);
+```
+
+子帧插值：
+
+```typescript
+// 使用 Fixed32 帧时间（支持小数帧）
+const frameTime = Fixed32.from(102.5);
+const result = buffer.getInterpolationSnapshotsFixed(frameTime);
+```
+
+### API 导出
+
+```typescript
+import {
+    // 状态类
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw,
+    type IFixedTransformStateWithVelocityRaw,
+
+    // 插值器
+    FixedTransformInterpolator,
+    FixedHermiteTransformInterpolator,
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator,
+
+    // 快照缓冲区
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer,
+    type IFixedStateSnapshot,
+    type IFixedInterpolationResult
+} from '@esengine/network';
+```
@@ -0,0 +1,450 @@
+/**
+ * @zh Q16.16 定点数，用于确定性计算（帧同步）
+ * @en Q16.16 fixed-point number for deterministic calculations (lockstep)
+ *
+ * @zh 使用 16 位整数部分 + 16 位小数部分，范围 ±32767.99998
+ * @en Uses 16-bit integer + 16-bit fraction, range ±32767.99998
+ *
+ * @example
+ * ```typescript
+ * const a = Fixed32.from(3.14);
+ * const b = Fixed32.from(2);
+ * const c = a.mul(b);  // 6.28
+ * console.log(c.toNumber());
+ * ```
+ */
+export class Fixed32 {
+    /**
+     * @zh 内部原始值（32位整数）
+     * @en Internal raw value (32-bit integer)
+     */
+    readonly raw: number;
+
+    /**
+     * @zh 小数位数
+     * @en Fraction bits
+     */
+    static readonly FRACTION_BITS = 16;
+
+    /**
+     * @zh 缩放因子 (2^16 = 65536)
+     * @en Scale factor (2^16 = 65536)
+     */
+    static readonly SCALE = 65536;
+
+    /**
+     * @zh 最大值 (约 32767.99998)
+     * @en Maximum value (approximately 32767.99998)
+     */
+    static readonly MAX_VALUE = 0x7FFFFFFF;
+
+    /**
+     * @zh 最小值 (约 -32768)
+     * @en Minimum value (approximately -32768)
+     */
+    static readonly MIN_VALUE = -0x80000000;
+
+    /**
+     * @zh 精度 (1/65536 ≈ 0.0000153)
+     * @en Precision (1/65536 ≈ 0.0000153)
+     */
+    static readonly EPSILON = 1;
+
+    // ==================== 常量 ====================
+
+    /** @zh 零 @en Zero */
+    static readonly ZERO = new Fixed32(0);
+
+    /** @zh 一 @en One */
+    static readonly ONE = new Fixed32(Fixed32.SCALE);
+
+    /** @zh 负一 @en Negative one */
+    static readonly NEG_ONE = new Fixed32(-Fixed32.SCALE);
+
+    /** @zh 二分之一 @en One half */
+    static readonly HALF = new Fixed32(Fixed32.SCALE >> 1);
+
+    /** @zh 圆周率 π @en Pi */
+    static readonly PI = new Fixed32(205887); // π * 65536
+
+    /** @zh 2π @en Two Pi */
+    static readonly TWO_PI = new Fixed32(411775); // 2π * 65536
+
+    /** @zh π/2 @en Pi divided by 2 */
+    static readonly HALF_PI = new Fixed32(102944); // π/2 * 65536
+
+    /** @zh 弧度转角度系数 (180/π) @en Radians to degrees factor */
+    static readonly RAD_TO_DEG = new Fixed32(3754936); // (180/π) * 65536
+
+    /** @zh 角度转弧度系数 (π/180) @en Degrees to radians factor */
+    static readonly DEG_TO_RAD = new Fixed32(1144); // (π/180) * 65536
+
+    // ==================== 构造 ====================
+
+    /**
+     * @zh 私有构造函数，使用静态方法创建实例
+     * @en Private constructor, use static methods to create instances
+     */
+    private constructor(raw: number) {
+        // 确保是 32 位有符号整数
+        this.raw = raw | 0;
+    }
+
+    /**
+     * @zh 从浮点数创建定点数
+     * @en Create fixed-point from floating-point number
+     * @param n - @zh 浮点数值 @en Floating-point value
+     */
+    static from(n: number): Fixed32 {
+        return new Fixed32(Math.round(n * Fixed32.SCALE));
+    }
+
+    /**
+     * @zh 从原始整数值创建定点数
+     * @en Create fixed-point from raw integer value
+     * @param raw - @zh 原始值 @en Raw value
+     */
+    static fromRaw(raw: number): Fixed32 {
+        return new Fixed32(raw);
+    }
+
+    /**
+     * @zh 从整数创建定点数（无精度损失）
+     * @en Create fixed-point from integer (no precision loss)
+     * @param n - @zh 整数值 @en Integer value
+     */
+    static fromInt(n: number): Fixed32 {
+        return new Fixed32((n | 0) << Fixed32.FRACTION_BITS);
+    }
+
+    // ==================== 转换 ====================
+
+    /**
+     * @zh 转换为浮点数
+     * @en Convert to floating-point number
+     */
+    toNumber(): number {
+        return this.raw / Fixed32.SCALE;
+    }
+
+    /**
+     * @zh 获取原始整数值
+     * @en Get raw integer value
+     */
+    toRaw(): number {
+        return this.raw;
+    }
+
+    /**
+     * @zh 转换为整数（向下取整）
+     * @en Convert to integer (floor)
+     */
+    toInt(): number {
+        return this.raw >> Fixed32.FRACTION_BITS;
+    }
+
+    /**
+     * @zh 转换为字符串
+     * @en Convert to string
+     */
+    toString(): string {
+        return `Fixed32(${this.toNumber().toFixed(5)})`;
+    }
+
+    // ==================== 基础运算 ====================
+
+    /**
+     * @zh 加法
+     * @en Addition
+     */
+    add(other: Fixed32): Fixed32 {
+        return new Fixed32(this.raw + other.raw);
+    }
+
+    /**
+     * @zh 减法
+     * @en Subtraction
+     */
+    sub(other: Fixed32): Fixed32 {
+        return new Fixed32(this.raw - other.raw);
+    }
+
+    /**
+     * @zh 乘法（使用 64 位中间结果防止溢出）
+     * @en Multiplication (uses 64-bit intermediate to prevent overflow)
+     */
+    mul(other: Fixed32): Fixed32 {
+        // 拆分为高低 16 位进行乘法，避免溢出
+        const a = this.raw;
+        const b = other.raw;
+
+        // 使用 BigInt 确保精度（JS 数字在大数时会丢失精度）
+        // 或者使用拆分法
+        const aLow = a & 0xFFFF;
+        const aHigh = a >> 16;
+        const bLow = b & 0xFFFF;
+        const bHigh = b >> 16;
+
+        // (aHigh * 2^16 + aLow) * (bHigh * 2^16 + bLow) / 2^16
+        // = aHigh * bHigh * 2^16 + aHigh * bLow + aLow * bHigh + aLow * bLow / 2^16
+        const lowLow = (aLow * bLow) >>> 16;
+        const lowHigh = aLow * bHigh;
+        const highLow = aHigh * bLow;
+        const highHigh = aHigh * bHigh;
+
+        const result = highHigh * Fixed32.SCALE + lowHigh + highLow + lowLow;
+        return new Fixed32(result | 0);
+    }
+
+    /**
+     * @zh 除法
+     * @en Division
+     * @throws @zh 除数为零时抛出错误 @en Throws when dividing by zero
+     */
+    div(other: Fixed32): Fixed32 {
+        if (other.raw === 0) {
+            throw new Error('Fixed32: Division by zero');
+        }
+        // 先左移再除，保持精度
+        const result = ((this.raw * Fixed32.SCALE) / other.raw) | 0;
+        return new Fixed32(result);
+    }
+
+    /**
+     * @zh 取模运算
+     * @en Modulo operation
+     */
+    mod(other: Fixed32): Fixed32 {
+        return new Fixed32(this.raw % other.raw);
+    }
+
+    /**
+     * @zh 取反
+     * @en Negation
+     */
+    neg(): Fixed32 {
+        return new Fixed32(-this.raw);
+    }
+
+    /**
+     * @zh 绝对值
+     * @en Absolute value
+     */
+    abs(): Fixed32 {
+        return this.raw >= 0 ? this : new Fixed32(-this.raw);
+    }
+
+    // ==================== 比较运算 ====================
+
+    /**
+     * @zh 等于
+     * @en Equal to
+     */
+    eq(other: Fixed32): boolean {
+        return this.raw === other.raw;
+    }
+
+    /**
+     * @zh 不等于
+     * @en Not equal to
+     */
+    ne(other: Fixed32): boolean {
+        return this.raw !== other.raw;
+    }
+
+    /**
+     * @zh 小于
+     * @en Less than
+     */
+    lt(other: Fixed32): boolean {
+        return this.raw < other.raw;
+    }
+
+    /**
+     * @zh 小于等于
+     * @en Less than or equal to
+     */
+    le(other: Fixed32): boolean {
+        return this.raw <= other.raw;
+    }
+
+    /**
+     * @zh 大于
+     * @en Greater than
+     */
+    gt(other: Fixed32): boolean {
+        return this.raw > other.raw;
+    }
+
+    /**
+     * @zh 大于等于
+     * @en Greater than or equal to
+     */
+    ge(other: Fixed32): boolean {
+        return this.raw >= other.raw;
+    }
+
+    /**
+     * @zh 检查是否为零
+     * @en Check if zero
+     */
+    isZero(): boolean {
+        return this.raw === 0;
+    }
+
+    /**
+     * @zh 检查是否为正数
+     * @en Check if positive
+     */
+    isPositive(): boolean {
+        return this.raw > 0;
+    }
+
+    /**
+     * @zh 检查是否为负数
+     * @en Check if negative
+     */
+    isNegative(): boolean {
+        return this.raw < 0;
+    }
+
+    // ==================== 数学函数 ====================
+
+    /**
+     * @zh 平方根（牛顿迭代法，确定性）
+     * @en Square root (Newton's method, deterministic)
+     */
+    static sqrt(x: Fixed32): Fixed32 {
+        if (x.raw <= 0) return Fixed32.ZERO;
+
+        // 牛顿迭代法
+        let guess = x.raw;
+        let prev = 0;
+
+        // 固定迭代次数确保确定性
+        for (let i = 0; i < 16; i++) {
+            prev = guess;
+            guess = ((guess + ((x.raw * Fixed32.SCALE) / guess) | 0) >> 1) | 0;
+            if (guess === prev) break;
+        }
+
+        return new Fixed32(guess);
+    }
+
+    /**
+     * @zh 向下取整
+     * @en Floor
+     */
+    static floor(x: Fixed32): Fixed32 {
+        return new Fixed32(x.raw & ~(Fixed32.SCALE - 1));
+    }
+
+    /**
+     * @zh 向上取整
+     * @en Ceiling
+     */
+    static ceil(x: Fixed32): Fixed32 {
+        const frac = x.raw & (Fixed32.SCALE - 1);
+        if (frac === 0) return x;
+        return new Fixed32((x.raw & ~(Fixed32.SCALE - 1)) + Fixed32.SCALE);
+    }
+
+    /**
+     * @zh 四舍五入
+     * @en Round
+     */
+    static round(x: Fixed32): Fixed32 {
+        return new Fixed32((x.raw + (Fixed32.SCALE >> 1)) & ~(Fixed32.SCALE - 1));
+    }
+
+    /**
+     * @zh 最小值
+     * @en Minimum
+     */
+    static min(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.raw < b.raw ? a : b;
+    }
+
+    /**
+     * @zh 最大值
+     * @en Maximum
+     */
+    static max(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.raw > b.raw ? a : b;
+    }
+
+    /**
+     * @zh 限制范围
+     * @en Clamp to range
+     */
+    static clamp(x: Fixed32, min: Fixed32, max: Fixed32): Fixed32 {
+        if (x.raw < min.raw) return min;
+        if (x.raw > max.raw) return max;
+        return x;
+    }
+
+    /**
+     * @zh 线性插值
+     * @en Linear interpolation
+     * @param a - @zh 起始值 @en Start value
+     * @param b - @zh 结束值 @en End value
+     * @param t - @zh 插值参数 (0-1) @en Interpolation parameter (0-1)
+     */
+    static lerp(a: Fixed32, b: Fixed32, t: Fixed32): Fixed32 {
+        // a + (b - a) * t
+        return a.add(b.sub(a).mul(t));
+    }
+
+    /**
+     * @zh 符号函数
+     * @en Sign function
+     * @returns @zh -1, 0, 或 1 @en -1, 0, or 1
+     */
+    static sign(x: Fixed32): Fixed32 {
+        if (x.raw > 0) return Fixed32.ONE;
+        if (x.raw < 0) return Fixed32.NEG_ONE;
+        return Fixed32.ZERO;
+    }
+
+    // ==================== 静态运算（便捷方法） ====================
+
+    /**
+     * @zh 加法（静态）
+     * @en Addition (static)
+     */
+    static add(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.add(b);
+    }
+
+    /**
+     * @zh 减法（静态）
+     * @en Subtraction (static)
+     */
+    static sub(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.sub(b);
+    }
+
+    /**
+     * @zh 乘法（静态）
+     * @en Multiplication (static)
+     */
+    static mul(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.mul(b);
+    }
+
+    /**
+     * @zh 除法（静态）
+     * @en Division (static)
+     */
+    static div(a: Fixed32, b: Fixed32): Fixed32 {
+        return a.div(b);
+    }
+}
+
+/**
+ * @zh Fixed32 数据接口，用于序列化
+ * @en Fixed32 data interface for serialization
+ */
+export interface IFixed32 {
+    raw: number;
+}
@@ -0,0 +1,298 @@
+import { Fixed32 } from './Fixed32';
+
+/**
+ * @zh 定点数数学函数库，使用查表法确保确定性
+ * @en Fixed-point math functions using lookup tables for determinism
+ *
+ * @zh 所有三角函数使用预计算的查找表，确保在所有平台上结果一致
+ * @en All trigonometric functions use precomputed lookup tables to ensure consistent results across all platforms
+ */
+export class FixedMath {
+    /**
+     * @zh 正弦表大小（每 90 度的采样点数）
+     * @en Sine table size (samples per 90 degrees)
+     */
+    private static readonly SIN_TABLE_SIZE = 1024;
+
+    /**
+     * @zh 正弦查找表（0 到 90 度）
+     * @en Sine lookup table (0 to 90 degrees)
+     */
+    private static readonly SIN_TABLE: Int32Array = FixedMath.generateSinTable();
+
+    /**
+     * @zh 生成正弦查找表
+     * @en Generate sine lookup table
+     */
+    private static generateSinTable(): Int32Array {
+        const table = new Int32Array(FixedMath.SIN_TABLE_SIZE + 1);
+        for (let i = 0; i <= FixedMath.SIN_TABLE_SIZE; i++) {
+            const angle = (i * Math.PI) / (2 * FixedMath.SIN_TABLE_SIZE);
+            table[i] = Math.round(Math.sin(angle) * Fixed32.SCALE);
+        }
+        return table;
+    }
+
+    /**
+     * @zh 正弦函数（确定性）
+     * @en Sine function (deterministic)
+     * @param angle - @zh 角度（弧度，定点数） @en Angle in radians (fixed-point)
+     */
+    static sin(angle: Fixed32): Fixed32 {
+        // 将角度规范化到 [0, 2π)
+        let raw = angle.raw % Fixed32.TWO_PI.raw;
+        if (raw < 0) raw += Fixed32.TWO_PI.raw;
+
+        const halfPi = Fixed32.HALF_PI.raw;
+        const pi = Fixed32.PI.raw;
+        const threeHalfPi = halfPi * 3;
+
+        let tableAngle: number;
+        let negative = false;
+
+        if (raw <= halfPi) {
+            // 第一象限: [0, π/2]
+            tableAngle = raw;
+        } else if (raw <= pi) {
+            // 第二象限: (π/2, π]
+            tableAngle = pi - raw;
+        } else if (raw <= threeHalfPi) {
+            // 第三象限: (π, 3π/2]
+            tableAngle = raw - pi;
+            negative = true;
+        } else {
+            // 第四象限: (3π/2, 2π)
+            tableAngle = Fixed32.TWO_PI.raw - raw;
+            negative = true;
+        }
+
+        // 计算表索引 (tableAngle 范围是 [0, π/2])
+        const tableIndex = Math.min(
+            ((tableAngle * FixedMath.SIN_TABLE_SIZE) / halfPi) | 0,
+            FixedMath.SIN_TABLE_SIZE
+        );
+
+        const result = FixedMath.SIN_TABLE[tableIndex];
+        return Fixed32.fromRaw(negative ? -result : result);
+    }
+
+    /**
+     * @zh 余弦函数（确定性）
+     * @en Cosine function (deterministic)
+     * @param angle - @zh 角度（弧度，定点数） @en Angle in radians (fixed-point)
+     */
+    static cos(angle: Fixed32): Fixed32 {
+        // cos(x) = sin(x + π/2)
+        return FixedMath.sin(angle.add(Fixed32.HALF_PI));
+    }
+
+    /**
+     * @zh 正切函数（确定性）
+     * @en Tangent function (deterministic)
+     * @param angle - @zh 角度（弧度，定点数） @en Angle in radians (fixed-point)
+     */
+    static tan(angle: Fixed32): Fixed32 {
+        const cosVal = FixedMath.cos(angle);
+        if (cosVal.isZero()) {
+            // 返回最大值表示无穷大
+            return Fixed32.fromRaw(Fixed32.MAX_VALUE);
+        }
+        return FixedMath.sin(angle).div(cosVal);
+    }
+
+    /**
+     * @zh 反正切函数 atan2（确定性）
+     * @en Arc tangent of y/x (deterministic)
+     * @param y - @zh Y 坐标 @en Y coordinate
+     * @param x - @zh X 坐标 @en X coordinate
+     * @returns @zh 角度（弧度，范围 -π 到 π）@en Angle in radians (range -π to π)
+     */
+    static atan2(y: Fixed32, x: Fixed32): Fixed32 {
+        const yRaw = y.raw;
+        const xRaw = x.raw;
+
+        if (xRaw === 0 && yRaw === 0) {
+            return Fixed32.ZERO;
+        }
+
+        // 使用 CORDIC 算法的简化版本
+        const absY = Math.abs(yRaw);
+        const absX = Math.abs(xRaw);
+
+        let angle: number;
+
+        if (absX >= absY) {
+            // |y/x| <= 1，使用泰勒展开近似
+            angle = FixedMath.atanApprox(absY, absX);
+        } else {
+            // |y/x| > 1，使用恒等式 atan(y/x) = π/2 - atan(x/y)
+            angle = Fixed32.HALF_PI.raw - FixedMath.atanApprox(absX, absY);
+        }
+
+        // 根据象限调整
+        if (xRaw < 0) {
+            angle = Fixed32.PI.raw - angle;
+        }
+        if (yRaw < 0) {
+            angle = -angle;
+        }
+
+        return Fixed32.fromRaw(angle);
+    }
+
+    /**
+     * @zh atan 近似计算（内部使用）
+     * @en Approximate atan calculation (internal use)
+     */
+    private static atanApprox(num: number, den: number): number {
+        if (den === 0) return Fixed32.HALF_PI.raw;
+
+        // 使用多项式近似: atan(x) ≈ x - x³/3 + x⁵/5
+        // 对于 |x| <= 1 精度足够
+        const ratio = ((num * Fixed32.SCALE) / den) | 0;
+
+        // 简化的多项式: atan(x) ≈ x * (1 - x²/3)
+        // 更精确的版本: atan(x) ≈ x / (1 + 0.28125 * x²)
+        const x2 = ((ratio * ratio) / Fixed32.SCALE) | 0;
+        const factor = Fixed32.SCALE + ((x2 * 18432) / Fixed32.SCALE | 0); // 0.28125 * 65536 ≈ 18432
+        const result = ((ratio * Fixed32.SCALE) / factor) | 0;
+
+        return result;
+    }
+
+    /**
+     * @zh 反正弦函数（确定性）
+     * @en Arc sine function (deterministic)
+     * @param x - @zh 值（范围 -1 到 1）@en Value (range -1 to 1)
+     */
+    static asin(x: Fixed32): Fixed32 {
+        // asin(x) = atan2(x, sqrt(1 - x²))
+        const one = Fixed32.ONE;
+        const x2 = x.mul(x);
+        const sqrt = Fixed32.sqrt(one.sub(x2));
+        return FixedMath.atan2(x, sqrt);
+    }
+
+    /**
+     * @zh 反余弦函数（确定性）
+     * @en Arc cosine function (deterministic)
+     * @param x - @zh 值（范围 -1 到 1）@en Value (range -1 to 1)
+     */
+    static acos(x: Fixed32): Fixed32 {
+        // acos(x) = π/2 - asin(x)
+        return Fixed32.HALF_PI.sub(FixedMath.asin(x));
+    }
+
+    /**
+     * @zh 角度规范化到 [-π, π]
+     * @en Normalize angle to [-π, π]
+     */
+    static normalizeAngle(angle: Fixed32): Fixed32 {
+        let raw = angle.raw % Fixed32.TWO_PI.raw;
+
+        if (raw > Fixed32.PI.raw) {
+            raw -= Fixed32.TWO_PI.raw;
+        } else if (raw < -Fixed32.PI.raw) {
+            raw += Fixed32.TWO_PI.raw;
+        }
+
+        return Fixed32.fromRaw(raw);
+    }
+
+    /**
+     * @zh 角度差值（最短路径）
+     * @en Angle difference (shortest path)
+     */
+    static angleDelta(from: Fixed32, to: Fixed32): Fixed32 {
+        return FixedMath.normalizeAngle(to.sub(from));
+    }
+
+    /**
+     * @zh 角度线性插值（最短路径）
+     * @en Angle linear interpolation (shortest path)
+     */
+    static lerpAngle(from: Fixed32, to: Fixed32, t: Fixed32): Fixed32 {
+        const delta = FixedMath.angleDelta(from, to);
+        return from.add(delta.mul(t));
+    }
+
+    /**
+     * @zh 弧度转角度
+     * @en Radians to degrees
+     */
+    static radToDeg(rad: Fixed32): Fixed32 {
+        return rad.mul(Fixed32.RAD_TO_DEG);
+    }
+
+    /**
+     * @zh 角度转弧度
+     * @en Degrees to radians
+     */
+    static degToRad(deg: Fixed32): Fixed32 {
+        return deg.mul(Fixed32.DEG_TO_RAD);
+    }
+
+    /**
+     * @zh 幂函数（整数次幂）
+     * @en Power function (integer exponent)
+     */
+    static pow(base: Fixed32, exp: number): Fixed32 {
+        if (exp === 0) return Fixed32.ONE;
+        if (exp < 0) {
+            base = Fixed32.ONE.div(base);
+            exp = -exp;
+        }
+
+        let result = Fixed32.ONE;
+        while (exp > 0) {
+            if (exp & 1) {
+                result = result.mul(base);
+            }
+            base = base.mul(base);
+            exp >>= 1;
+        }
+
+        return result;
+    }
+
+    /**
+     * @zh 指数函数近似（e^x）
+     * @en Exponential function approximation (e^x)
+     */
+    static exp(x: Fixed32): Fixed32 {
+        // 使用泰勒展开: e^x ≈ 1 + x + x²/2 + x³/6 + x⁴/24
+        const one = Fixed32.ONE;
+        const x2 = x.mul(x);
+        const x3 = x2.mul(x);
+        const x4 = x3.mul(x);
+
+        return one
+            .add(x)
+            .add(x2.div(Fixed32.from(2)))
+            .add(x3.div(Fixed32.from(6)))
+            .add(x4.div(Fixed32.from(24)));
+    }
+
+    /**
+     * @zh 自然对数近似
+     * @en Natural logarithm approximation
+     */
+    static ln(x: Fixed32): Fixed32 {
+        if (x.raw <= 0) {
+            throw new Error('FixedMath.ln: argument must be positive');
+        }
+
+        // 使用牛顿迭代法: y_{n+1} = y_n + 2 * (x - exp(y_n)) / (x + exp(y_n))
+        let y = Fixed32.ZERO;
+        const two = Fixed32.from(2);
+
+        for (let i = 0; i < 10; i++) {
+            const expY = FixedMath.exp(y);
+            const diff = x.sub(expY);
+            const sum = x.add(expY);
+            y = y.add(two.mul(diff).div(sum));
+        }
+
+        return y;
+    }
+}
@@ -0,0 +1,504 @@
+import { Fixed32, type IFixed32 } from './Fixed32';
+import { FixedMath } from './FixedMath';
+
+/**
+ * @zh 定点数 2D 向量数据接口
+ * @en Fixed-point 2D vector data interface
+ */
+export interface IFixedVector2 {
+    x: IFixed32;
+    y: IFixed32;
+}
+
+/**
+ * @zh 定点数 2D 向量类，用于确定性计算（帧同步）
+ * @en Fixed-point 2D vector class for deterministic calculations (lockstep)
+ *
+ * @zh 所有运算返回新实例，保证不可变性
+ * @en All operations return new instances, ensuring immutability
+ *
+ * @example
+ * ```typescript
+ * const a = FixedVector2.from(3, 4);
+ * const b = FixedVector2.from(1, 2);
+ * const c = a.add(b);  // (4, 6)
+ * const len = a.length();  // 5
+ * ```
+ */
+export class FixedVector2 {
+    /** @zh X 分量 @en X component */
+    readonly x: Fixed32;
+
+    /** @zh Y 分量 @en Y component */
+    readonly y: Fixed32;
+
+    // ==================== 常量 ====================
+
+    /** @zh 零向量 (0, 0) @en Zero vector */
+    static readonly ZERO = new FixedVector2(Fixed32.ZERO, Fixed32.ZERO);
+
+    /** @zh 单位向量 (1, 1) @en One vector */
+    static readonly ONE = new FixedVector2(Fixed32.ONE, Fixed32.ONE);
+
+    /** @zh 右方向 (1, 0) @en Right direction */
+    static readonly RIGHT = new FixedVector2(Fixed32.ONE, Fixed32.ZERO);
+
+    /** @zh 左方向 (-1, 0) @en Left direction */
+    static readonly LEFT = new FixedVector2(Fixed32.NEG_ONE, Fixed32.ZERO);
+
+    /** @zh 上方向 (0, 1) @en Up direction */
+    static readonly UP = new FixedVector2(Fixed32.ZERO, Fixed32.ONE);
+
+    /** @zh 下方向 (0, -1) @en Down direction */
+    static readonly DOWN = new FixedVector2(Fixed32.ZERO, Fixed32.NEG_ONE);
+
+    // ==================== 构造 ====================
+
+    /**
+     * @zh 创建定点数向量
+     * @en Create fixed-point vector
+     */
+    constructor(x: Fixed32, y: Fixed32) {
+        this.x = x;
+        this.y = y;
+    }
+
+    /**
+     * @zh 从浮点数创建向量
+     * @en Create vector from floating-point numbers
+     */
+    static from(x: number, y: number): FixedVector2 {
+        return new FixedVector2(Fixed32.from(x), Fixed32.from(y));
+    }
+
+    /**
+     * @zh 从原始整数值创建向量
+     * @en Create vector from raw integer values
+     */
+    static fromRaw(rawX: number, rawY: number): FixedVector2 {
+        return new FixedVector2(Fixed32.fromRaw(rawX), Fixed32.fromRaw(rawY));
+    }
+
+    /**
+     * @zh 从整数创建向量
+     * @en Create vector from integers
+     */
+    static fromInt(x: number, y: number): FixedVector2 {
+        return new FixedVector2(Fixed32.fromInt(x), Fixed32.fromInt(y));
+    }
+
+    /**
+     * @zh 从普通向量接口创建
+     * @en Create from plain vector interface
+     */
+    static fromObject(obj: { x: number; y: number }): FixedVector2 {
+        return FixedVector2.from(obj.x, obj.y);
+    }
+
+    // ==================== 转换 ====================
+
+    /**
+     * @zh 转换为浮点数对象（用于渲染）
+     * @en Convert to floating-point object (for rendering)
+     */
+    toObject(): { x: number; y: number } {
+        return {
+            x: this.x.toNumber(),
+            y: this.y.toNumber()
+        };
+    }
+
+    /**
+     * @zh 转换为数组
+     * @en Convert to array
+     */
+    toArray(): [number, number] {
+        return [this.x.toNumber(), this.y.toNumber()];
+    }
+
+    /**
+     * @zh 获取原始值对象（用于网络传输）
+     * @en Get raw values object (for network transmission)
+     */
+    toRawObject(): { x: number; y: number } {
+        return {
+            x: this.x.toRaw(),
+            y: this.y.toRaw()
+        };
+    }
+
+    /**
+     * @zh 转换为字符串
+     * @en Convert to string
+     */
+    toString(): string {
+        return `FixedVector2(${this.x.toNumber().toFixed(3)}, ${this.y.toNumber().toFixed(3)})`;
+    }
+
+    /**
+     * @zh 克隆向量
+     * @en Clone vector
+     */
+    clone(): FixedVector2 {
+        return new FixedVector2(this.x, this.y);
+    }
+
+    // ==================== 基础运算 ====================
+
+    /**
+     * @zh 向量加法
+     * @en Vector addition
+     */
+    add(other: FixedVector2): FixedVector2 {
+        return new FixedVector2(this.x.add(other.x), this.y.add(other.y));
+    }
+
+    /**
+     * @zh 向量减法
+     * @en Vector subtraction
+     */
+    sub(other: FixedVector2): FixedVector2 {
+        return new FixedVector2(this.x.sub(other.x), this.y.sub(other.y));
+    }
+
+    /**
+     * @zh 标量乘法
+     * @en Scalar multiplication
+     */
+    mul(scalar: Fixed32): FixedVector2 {
+        return new FixedVector2(this.x.mul(scalar), this.y.mul(scalar));
+    }
+
+    /**
+     * @zh 标量除法
+     * @en Scalar division
+     */
+    div(scalar: Fixed32): FixedVector2 {
+        return new FixedVector2(this.x.div(scalar), this.y.div(scalar));
+    }
+
+    /**
+     * @zh 分量乘法
+     * @en Component-wise multiplication
+     */
+    mulComponents(other: FixedVector2): FixedVector2 {
+        return new FixedVector2(this.x.mul(other.x), this.y.mul(other.y));
+    }
+
+    /**
+     * @zh 分量除法
+     * @en Component-wise division
+     */
+    divComponents(other: FixedVector2): FixedVector2 {
+        return new FixedVector2(this.x.div(other.x), this.y.div(other.y));
+    }
+
+    /**
+     * @zh 取反
+     * @en Negate
+     */
+    neg(): FixedVector2 {
+        return new FixedVector2(this.x.neg(), this.y.neg());
+    }
+
+    // ==================== 向量运算 ====================
+
+    /**
+     * @zh 点积
+     * @en Dot product
+     */
+    dot(other: FixedVector2): Fixed32 {
+        return this.x.mul(other.x).add(this.y.mul(other.y));
+    }
+
+    /**
+     * @zh 叉积（2D 返回标量）
+     * @en Cross product (returns scalar in 2D)
+     */
+    cross(other: FixedVector2): Fixed32 {
+        return this.x.mul(other.y).sub(this.y.mul(other.x));
+    }
+
+    /**
+     * @zh 长度的平方
+     * @en Length squared
+     */
+    lengthSquared(): Fixed32 {
+        return this.dot(this);
+    }
+
+    /**
+     * @zh 长度（模）
+     * @en Length (magnitude)
+     */
+    length(): Fixed32 {
+        return Fixed32.sqrt(this.lengthSquared());
+    }
+
+    /**
+     * @zh 归一化（转换为单位向量）
+     * @en Normalize (convert to unit vector)
+     */
+    normalize(): FixedVector2 {
+        const len = this.length();
+        if (len.isZero()) {
+            return FixedVector2.ZERO;
+        }
+        return this.div(len);
+    }
+
+    /**
+     * @zh 到另一个向量的距离平方
+     * @en Distance squared to another vector
+     */
+    distanceSquaredTo(other: FixedVector2): Fixed32 {
+        const dx = this.x.sub(other.x);
+        const dy = this.y.sub(other.y);
+        return dx.mul(dx).add(dy.mul(dy));
+    }
+
+    /**
+     * @zh 到另一个向量的距离
+     * @en Distance to another vector
+     */
+    distanceTo(other: FixedVector2): Fixed32 {
+        return Fixed32.sqrt(this.distanceSquaredTo(other));
+    }
+
+    /**
+     * @zh 获取垂直向量（顺时针旋转90度）
+     * @en Get perpendicular vector (clockwise 90 degrees)
+     */
+    perpendicular(): FixedVector2 {
+        return new FixedVector2(this.y, this.x.neg());
+    }
+
+    /**
+     * @zh 获取垂直向量（逆时针旋转90度）
+     * @en Get perpendicular vector (counter-clockwise 90 degrees)
+     */
+    perpendicularCCW(): FixedVector2 {
+        return new FixedVector2(this.y.neg(), this.x);
+    }
+
+    /**
+     * @zh 投影到另一个向量上
+     * @en Project onto another vector
+     */
+    projectOnto(onto: FixedVector2): FixedVector2 {
+        const dot = this.dot(onto);
+        const lenSq = onto.lengthSquared();
+        if (lenSq.isZero()) {
+            return FixedVector2.ZERO;
+        }
+        return onto.mul(dot.div(lenSq));
+    }
+
+    /**
+     * @zh 反射向量（关于法线）
+     * @en Reflect vector (about normal)
+     */
+    reflect(normal: FixedVector2): FixedVector2 {
+        const dot = this.dot(normal);
+        const two = Fixed32.from(2);
+        return this.sub(normal.mul(two.mul(dot)));
+    }
+
+    // ==================== 旋转和角度 ====================
+
+    /**
+     * @zh 旋转向量（顺时针为正，左手坐标系）
+     * @en Rotate vector (clockwise positive, left-hand coordinate system)
+     * @param angle - @zh 旋转角度（弧度）@en Rotation angle in radians
+     */
+    rotate(angle: Fixed32): FixedVector2 {
+        const cos = FixedMath.cos(angle);
+        const sin = FixedMath.sin(angle);
+        // 顺时针旋转: x' = x*cos + y*sin, y' = -x*sin + y*cos
+        return new FixedVector2(
+            this.x.mul(cos).add(this.y.mul(sin)),
+            this.x.neg().mul(sin).add(this.y.mul(cos))
+        );
+    }
+
+    /**
+     * @zh 围绕一个点旋转
+     * @en Rotate around a point
+     */
+    rotateAround(center: FixedVector2, angle: Fixed32): FixedVector2 {
+        return this.sub(center).rotate(angle).add(center);
+    }
+
+    /**
+     * @zh 获取向量角度（弧度）
+     * @en Get vector angle in radians
+     */
+    angle(): Fixed32 {
+        return FixedMath.atan2(this.y, this.x);
+    }
+
+    /**
+     * @zh 获取与另一个向量的夹角
+     * @en Get angle between this and another vector
+     */
+    angleTo(other: FixedVector2): Fixed32 {
+        const cross = this.cross(other);
+        const dot = this.dot(other);
+        return FixedMath.atan2(cross, dot);
+    }
+
+    /**
+     * @zh 从极坐标创建向量
+     * @en Create vector from polar coordinates
+     */
+    static fromPolar(length: Fixed32, angle: Fixed32): FixedVector2 {
+        return new FixedVector2(
+            length.mul(FixedMath.cos(angle)),
+            length.mul(FixedMath.sin(angle))
+        );
+    }
+
+    /**
+     * @zh 从角度创建单位向量
+     * @en Create unit vector from angle
+     */
+    static fromAngle(angle: Fixed32): FixedVector2 {
+        return new FixedVector2(FixedMath.cos(angle), FixedMath.sin(angle));
+    }
+
+    // ==================== 比较运算 ====================
+
+    /**
+     * @zh 检查是否相等
+     * @en Check equality
+     */
+    equals(other: FixedVector2): boolean {
+        return this.x.eq(other.x) && this.y.eq(other.y);
+    }
+
+    /**
+     * @zh 检查是否为零向量
+     * @en Check if zero vector
+     */
+    isZero(): boolean {
+        return this.x.isZero() && this.y.isZero();
+    }
+
+    // ==================== 限制和插值 ====================
+
+    /**
+     * @zh 限制长度
+     * @en Clamp length
+     */
+    clampLength(maxLength: Fixed32): FixedVector2 {
+        const lenSq = this.lengthSquared();
+        const maxLenSq = maxLength.mul(maxLength);
+        if (lenSq.gt(maxLenSq)) {
+            return this.normalize().mul(maxLength);
+        }
+        return this;
+    }
+
+    /**
+     * @zh 限制分量范围
+     * @en Clamp components
+     */
+    clamp(min: FixedVector2, max: FixedVector2): FixedVector2 {
+        return new FixedVector2(
+            Fixed32.clamp(this.x, min.x, max.x),
+            Fixed32.clamp(this.y, min.y, max.y)
+        );
+    }
+
+    /**
+     * @zh 线性插值
+     * @en Linear interpolation
+     */
+    lerp(target: FixedVector2, t: Fixed32): FixedVector2 {
+        return new FixedVector2(
+            Fixed32.lerp(this.x, target.x, t),
+            Fixed32.lerp(this.y, target.y, t)
+        );
+    }
+
+    /**
+     * @zh 向目标移动固定距离
+     * @en Move towards target by fixed distance
+     */
+    moveTowards(target: FixedVector2, maxDistance: Fixed32): FixedVector2 {
+        const diff = target.sub(this);
+        const dist = diff.length();
+
+        if (dist.isZero() || dist.le(maxDistance)) {
+            return target;
+        }
+
+        return this.add(diff.div(dist).mul(maxDistance));
+    }
+
+    // ==================== 静态方法 ====================
+
+    /**
+     * @zh 向量加法（静态）
+     * @en Vector addition (static)
+     */
+    static add(a: FixedVector2, b: FixedVector2): FixedVector2 {
+        return a.add(b);
+    }
+
+    /**
+     * @zh 向量减法（静态）
+     * @en Vector subtraction (static)
+     */
+    static sub(a: FixedVector2, b: FixedVector2): FixedVector2 {
+        return a.sub(b);
+    }
+
+    /**
+     * @zh 点积（静态）
+     * @en Dot product (static)
+     */
+    static dot(a: FixedVector2, b: FixedVector2): Fixed32 {
+        return a.dot(b);
+    }
+
+    /**
+     * @zh 叉积（静态）
+     * @en Cross product (static)
+     */
+    static cross(a: FixedVector2, b: FixedVector2): Fixed32 {
+        return a.cross(b);
+    }
+
+    /**
+     * @zh 距离（静态）
+     * @en Distance (static)
+     */
+    static distance(a: FixedVector2, b: FixedVector2): Fixed32 {
+        return a.distanceTo(b);
+    }
+
+    /**
+     * @zh 线性插值（静态）
+     * @en Linear interpolation (static)
+     */
+    static lerp(a: FixedVector2, b: FixedVector2, t: Fixed32): FixedVector2 {
+        return a.lerp(b, t);
+    }
+
+    /**
+     * @zh 获取两个向量的最小分量
+     * @en Get minimum components of two vectors
+     */
+    static min(a: FixedVector2, b: FixedVector2): FixedVector2 {
+        return new FixedVector2(Fixed32.min(a.x, b.x), Fixed32.min(a.y, b.y));
+    }
+
+    /**
+     * @zh 获取两个向量的最大分量
+     * @en Get maximum components of two vectors
+     */
+    static max(a: FixedVector2, b: FixedVector2): FixedVector2 {
+        return new FixedVector2(Fixed32.max(a.x, b.x), Fixed32.max(a.y, b.y));
+    }
+}
@@ -3,6 +3,7 @@
 *
 * 2D数学库，为游戏开发提供完整的数学工具
 * - 基础数学类（向量、矩阵、几何形状）
+ * - 定点数数学（用于帧同步确定性计算）
 * - 碰撞检测算法
 * - 动画插值和缓动函数
 * - 数学工具函数
@@ -16,6 +17,11 @@ export { Matrix3 } from './Matrix3';
 export { Rectangle } from './Rectangle';
 export { Circle } from './Circle';

+// 定点数数学（帧同步确定性计算）
+export { Fixed32, type IFixed32 } from './Fixed32';
+export { FixedVector2, type IFixedVector2 } from './FixedVector2';
+export { FixedMath } from './FixedMath';
+
 // 数学工具
 export { MathUtils } from './MathUtils';

@@ -0,0 +1,225 @@
+import { Fixed32 } from '../src/Fixed32';
+import { FixedMath } from '../src/FixedMath';
+
+describe('Fixed32', () => {
+    describe('创建和转换', () => {
+        test('from 应正确从浮点数创建', () => {
+            const a = Fixed32.from(3.5);
+            expect(a.toNumber()).toBeCloseTo(3.5, 4);
+        });
+
+        test('fromInt 应正确从整数创建', () => {
+            const a = Fixed32.fromInt(42);
+            expect(a.toInt()).toBe(42);
+            expect(a.toNumber()).toBe(42);
+        });
+
+        test('fromRaw 应正确从原始值创建', () => {
+            const raw = 65536 * 2; // 2.0
+            const a = Fixed32.fromRaw(raw);
+            expect(a.toNumber()).toBe(2);
+        });
+
+        test('常量应正确', () => {
+            expect(Fixed32.ZERO.toNumber()).toBe(0);
+            expect(Fixed32.ONE.toNumber()).toBe(1);
+            expect(Fixed32.HALF.toNumber()).toBe(0.5);
+            expect(Fixed32.PI.toNumber()).toBeCloseTo(Math.PI, 3);
+        });
+    });
+
+    describe('基础运算', () => {
+        test('add 应正确计算', () => {
+            const a = Fixed32.from(2.5);
+            const b = Fixed32.from(1.5);
+            expect(a.add(b).toNumber()).toBeCloseTo(4, 4);
+        });
+
+        test('sub 应正确计算', () => {
+            const a = Fixed32.from(5);
+            const b = Fixed32.from(3);
+            expect(a.sub(b).toNumber()).toBeCloseTo(2, 4);
+        });
+
+        test('mul 应正确计算', () => {
+            const a = Fixed32.from(3);
+            const b = Fixed32.from(4);
+            expect(a.mul(b).toNumber()).toBeCloseTo(12, 4);
+        });
+
+        test('mul 应正确处理小数', () => {
+            const a = Fixed32.from(2.5);
+            const b = Fixed32.from(1.5);
+            expect(a.mul(b).toNumber()).toBeCloseTo(3.75, 4);
+        });
+
+        test('div 应正确计算', () => {
+            const a = Fixed32.from(10);
+            const b = Fixed32.from(4);
+            expect(a.div(b).toNumber()).toBeCloseTo(2.5, 4);
+        });
+
+        test('div 应抛出除零错误', () => {
+            const a = Fixed32.from(10);
+            expect(() => a.div(Fixed32.ZERO)).toThrow('Division by zero');
+        });
+
+        test('neg 应正确取反', () => {
+            const a = Fixed32.from(5);
+            expect(a.neg().toNumber()).toBeCloseTo(-5, 4);
+        });
+
+        test('abs 应正确取绝对值', () => {
+            const a = Fixed32.from(-5);
+            expect(a.abs().toNumber()).toBeCloseTo(5, 4);
+        });
+    });
+
+    describe('比较运算', () => {
+        test('eq 应正确比较', () => {
+            const a = Fixed32.from(5);
+            const b = Fixed32.from(5);
+            const c = Fixed32.from(6);
+            expect(a.eq(b)).toBe(true);
+            expect(a.eq(c)).toBe(false);
+        });
+
+        test('lt/le/gt/ge 应正确比较', () => {
+            const a = Fixed32.from(3);
+            const b = Fixed32.from(5);
+            expect(a.lt(b)).toBe(true);
+            expect(a.le(b)).toBe(true);
+            expect(b.gt(a)).toBe(true);
+            expect(b.ge(a)).toBe(true);
+        });
+    });
+
+    describe('数学函数', () => {
+        test('sqrt 应正确计算', () => {
+            const a = Fixed32.from(16);
+            expect(Fixed32.sqrt(a).toNumber()).toBeCloseTo(4, 3);
+
+            const b = Fixed32.from(2);
+            expect(Fixed32.sqrt(b).toNumber()).toBeCloseTo(Math.sqrt(2), 3);
+        });
+
+        test('floor/ceil/round 应正确计算', () => {
+            const a = Fixed32.from(3.7);
+            expect(Fixed32.floor(a).toNumber()).toBeCloseTo(3, 4);
+            expect(Fixed32.ceil(a).toNumber()).toBeCloseTo(4, 4);
+            expect(Fixed32.round(a).toNumber()).toBeCloseTo(4, 4);
+
+            const b = Fixed32.from(3.2);
+            expect(Fixed32.round(b).toNumber()).toBeCloseTo(3, 4);
+        });
+
+        test('min/max/clamp 应正确计算', () => {
+            const a = Fixed32.from(3);
+            const b = Fixed32.from(5);
+            expect(Fixed32.min(a, b).toNumber()).toBe(3);
+            expect(Fixed32.max(a, b).toNumber()).toBe(5);
+
+            const x = Fixed32.from(7);
+            expect(Fixed32.clamp(x, a, b).toNumber()).toBe(5);
+        });
+
+        test('lerp 应正确插值', () => {
+            const a = Fixed32.from(0);
+            const b = Fixed32.from(10);
+            const t = Fixed32.from(0.5);
+            expect(Fixed32.lerp(a, b, t).toNumber()).toBeCloseTo(5, 4);
+        });
+    });
+
+    describe('确定性', () => {
+        test('相同输入应产生相同输出', () => {
+            const results: number[] = [];
+            for (let i = 0; i < 100; i++) {
+                const a = Fixed32.from(3.14159);
+                const b = Fixed32.from(2.71828);
+                const result = a.mul(b).add(Fixed32.sqrt(a)).toRaw();
+                results.push(result);
+            }
+            // 所有结果应该完全相同
+            expect(new Set(results).size).toBe(1);
+        });
+    });
+});
+
+describe('FixedMath', () => {
+    describe('三角函数', () => {
+        test('sin 应正确计算', () => {
+            expect(FixedMath.sin(Fixed32.ZERO).toNumber()).toBeCloseTo(0, 3);
+            expect(FixedMath.sin(Fixed32.HALF_PI).toNumber()).toBeCloseTo(1, 3);
+            expect(FixedMath.sin(Fixed32.PI).toNumber()).toBeCloseTo(0, 2);
+        });
+
+        test('cos 应正确计算', () => {
+            expect(FixedMath.cos(Fixed32.ZERO).toNumber()).toBeCloseTo(1, 3);
+            expect(FixedMath.cos(Fixed32.HALF_PI).toNumber()).toBeCloseTo(0, 2);
+            expect(FixedMath.cos(Fixed32.PI).toNumber()).toBeCloseTo(-1, 3);
+        });
+
+        test('sin²x + cos²x = 1', () => {
+            const angles = [0, 0.5, 1, 1.5, 2, 2.5, 3];
+            for (const a of angles) {
+                const angle = Fixed32.from(a);
+                const sin = FixedMath.sin(angle);
+                const cos = FixedMath.cos(angle);
+                const sum = sin.mul(sin).add(cos.mul(cos));
+                expect(sum.toNumber()).toBeCloseTo(1, 2);
+            }
+        });
+
+        test('atan2 应正确计算', () => {
+            // atan2(0, 1) = 0
+            expect(FixedMath.atan2(Fixed32.ZERO, Fixed32.ONE).toNumber()).toBeCloseTo(0, 3);
+
+            // atan2(1, 0) = π/2
+            expect(FixedMath.atan2(Fixed32.ONE, Fixed32.ZERO).toNumber()).toBeCloseTo(Math.PI / 2, 2);
+
+            // atan2(1, 1) = π/4
+            expect(FixedMath.atan2(Fixed32.ONE, Fixed32.ONE).toNumber()).toBeCloseTo(Math.PI / 4, 2);
+        });
+    });
+
+    describe('角度函数', () => {
+        test('radToDeg/degToRad 应正确转换', () => {
+            const rad = Fixed32.PI;
+            const deg = FixedMath.radToDeg(rad);
+            expect(deg.toNumber()).toBeCloseTo(180, 1);
+
+            const deg90 = Fixed32.from(90);
+            const rad90 = FixedMath.degToRad(deg90);
+            expect(rad90.toNumber()).toBeCloseTo(Math.PI / 2, 2);
+        });
+
+        test('normalizeAngle 应正确规范化', () => {
+            const angle1 = Fixed32.from(Math.PI * 3); // 3π -> π
+            expect(Math.abs(FixedMath.normalizeAngle(angle1).toNumber())).toBeLessThanOrEqual(Math.PI + 0.1);
+
+            const angle2 = Fixed32.from(-Math.PI * 3); // -3π -> -π
+            expect(Math.abs(FixedMath.normalizeAngle(angle2).toNumber())).toBeLessThanOrEqual(Math.PI + 0.1);
+        });
+
+        test('lerpAngle 应走最短路径', () => {
+            const from = Fixed32.from(0.1);
+            const to = Fixed32.from(-0.1);
+            const t = Fixed32.HALF;
+            const result = FixedMath.lerpAngle(from, to, t);
+            expect(result.toNumber()).toBeCloseTo(0, 2);
+        });
+    });
+
+    describe('确定性', () => {
+        test('三角函数应产生确定性结果', () => {
+            const results: number[] = [];
+            for (let i = 0; i < 100; i++) {
+                const angle = Fixed32.from(1.234);
+                const result = FixedMath.sin(angle).toRaw();
+                results.push(result);
+            }
+            expect(new Set(results).size).toBe(1);
+        });
+    });
+});
@@ -0,0 +1,242 @@
+import { Fixed32 } from '../src/Fixed32';
+import { FixedVector2 } from '../src/FixedVector2';
+
+describe('FixedVector2', () => {
+    describe('创建和转换', () => {
+        test('from 应正确从浮点数创建', () => {
+            const v = FixedVector2.from(3, 4);
+            const obj = v.toObject();
+            expect(obj.x).toBeCloseTo(3, 4);
+            expect(obj.y).toBeCloseTo(4, 4);
+        });
+
+        test('fromInt 应正确从整数创建', () => {
+            const v = FixedVector2.fromInt(5, 6);
+            expect(v.x.toInt()).toBe(5);
+            expect(v.y.toInt()).toBe(6);
+        });
+
+        test('常量应正确', () => {
+            expect(FixedVector2.ZERO.isZero()).toBe(true);
+            expect(FixedVector2.ONE.x.toNumber()).toBe(1);
+            expect(FixedVector2.ONE.y.toNumber()).toBe(1);
+            expect(FixedVector2.RIGHT.x.toNumber()).toBe(1);
+            expect(FixedVector2.RIGHT.y.toNumber()).toBe(0);
+        });
+
+        test('toRawObject 应返回原始值', () => {
+            const v = FixedVector2.from(1, 2);
+            const raw = v.toRawObject();
+            expect(raw.x).toBe(Fixed32.from(1).toRaw());
+            expect(raw.y).toBe(Fixed32.from(2).toRaw());
+        });
+    });
+
+    describe('基础运算', () => {
+        test('add 应正确计算', () => {
+            const a = FixedVector2.from(1, 2);
+            const b = FixedVector2.from(3, 4);
+            const result = a.add(b).toObject();
+            expect(result.x).toBeCloseTo(4, 4);
+            expect(result.y).toBeCloseTo(6, 4);
+        });
+
+        test('sub 应正确计算', () => {
+            const a = FixedVector2.from(5, 7);
+            const b = FixedVector2.from(2, 3);
+            const result = a.sub(b).toObject();
+            expect(result.x).toBeCloseTo(3, 4);
+            expect(result.y).toBeCloseTo(4, 4);
+        });
+
+        test('mul 应正确计算标量乘法', () => {
+            const v = FixedVector2.from(3, 4);
+            const result = v.mul(Fixed32.from(2)).toObject();
+            expect(result.x).toBeCloseTo(6, 4);
+            expect(result.y).toBeCloseTo(8, 4);
+        });
+
+        test('div 应正确计算标量除法', () => {
+            const v = FixedVector2.from(6, 8);
+            const result = v.div(Fixed32.from(2)).toObject();
+            expect(result.x).toBeCloseTo(3, 4);
+            expect(result.y).toBeCloseTo(4, 4);
+        });
+
+        test('neg 应正确取反', () => {
+            const v = FixedVector2.from(3, -4);
+            const result = v.neg().toObject();
+            expect(result.x).toBeCloseTo(-3, 4);
+            expect(result.y).toBeCloseTo(4, 4);
+        });
+    });
+
+    describe('向量运算', () => {
+        test('dot 应正确计算点积', () => {
+            const a = FixedVector2.from(1, 2);
+            const b = FixedVector2.from(3, 4);
+            // 1*3 + 2*4 = 11
+            expect(a.dot(b).toNumber()).toBeCloseTo(11, 4);
+        });
+
+        test('cross 应正确计算叉积', () => {
+            const a = FixedVector2.from(1, 0);
+            const b = FixedVector2.from(0, 1);
+            // 1*1 - 0*0 = 1
+            expect(a.cross(b).toNumber()).toBeCloseTo(1, 4);
+        });
+
+        test('length 应正确计算', () => {
+            const v = FixedVector2.from(3, 4);
+            expect(v.length().toNumber()).toBeCloseTo(5, 3);
+        });
+
+        test('lengthSquared 应正确计算', () => {
+            const v = FixedVector2.from(3, 4);
+            expect(v.lengthSquared().toNumber()).toBeCloseTo(25, 4);
+        });
+
+        test('normalize 应正确归一化', () => {
+            const v = FixedVector2.from(3, 4);
+            const n = v.normalize();
+            expect(n.length().toNumber()).toBeCloseTo(1, 2);
+            expect(n.x.toNumber()).toBeCloseTo(0.6, 2);
+            expect(n.y.toNumber()).toBeCloseTo(0.8, 2);
+        });
+
+        test('normalize 零向量应返回零向量', () => {
+            const v = FixedVector2.ZERO;
+            const n = v.normalize();
+            expect(n.isZero()).toBe(true);
+        });
+
+        test('distanceTo 应正确计算', () => {
+            const a = FixedVector2.from(0, 0);
+            const b = FixedVector2.from(3, 4);
+            expect(a.distanceTo(b).toNumber()).toBeCloseTo(5, 3);
+        });
+
+        test('perpendicular 应正确计算', () => {
+            const v = FixedVector2.from(1, 0);
+            const perp = v.perpendicular();
+            // 顺时针 90 度: (1, 0) -> (0, -1)
+            expect(perp.x.toNumber()).toBeCloseTo(0, 4);
+            expect(perp.y.toNumber()).toBeCloseTo(-1, 4);
+        });
+    });
+
+    describe('旋转和角度', () => {
+        test('rotate 应正确旋转', () => {
+            const v = FixedVector2.from(1, 0);
+            const angle = Fixed32.HALF_PI; // 90 度
+            const rotated = v.rotate(angle);
+            // 顺时针旋转 90 度: (1, 0) -> (0, -1)
+            expect(rotated.x.toNumber()).toBeCloseTo(0, 2);
+            expect(rotated.y.toNumber()).toBeCloseTo(-1, 2);
+        });
+
+        test('angle 应正确计算', () => {
+            const v = FixedVector2.from(1, 0);
+            expect(v.angle().toNumber()).toBeCloseTo(0, 3);
+
+            const v2 = FixedVector2.from(0, 1);
+            expect(v2.angle().toNumber()).toBeCloseTo(Math.PI / 2, 2);
+        });
+
+        test('fromAngle 应正确创建', () => {
+            const v = FixedVector2.fromAngle(Fixed32.ZERO);
+            expect(v.x.toNumber()).toBeCloseTo(1, 3);
+            expect(v.y.toNumber()).toBeCloseTo(0, 3);
+        });
+
+        test('fromPolar 应正确创建', () => {
+            const v = FixedVector2.fromPolar(Fixed32.from(5), Fixed32.ZERO);
+            expect(v.x.toNumber()).toBeCloseTo(5, 3);
+            expect(v.y.toNumber()).toBeCloseTo(0, 3);
+        });
+    });
+
+    describe('插值和限制', () => {
+        test('lerp 应正确插值', () => {
+            const a = FixedVector2.from(0, 0);
+            const b = FixedVector2.from(10, 20);
+            const result = a.lerp(b, Fixed32.HALF).toObject();
+            expect(result.x).toBeCloseTo(5, 4);
+            expect(result.y).toBeCloseTo(10, 4);
+        });
+
+        test('clampLength 应正确限制长度', () => {
+            const v = FixedVector2.from(6, 8); // 长度 10
+            const clamped = v.clampLength(Fixed32.from(5));
+            expect(clamped.length().toNumber()).toBeCloseTo(5, 2);
+        });
+
+        test('moveTowards 应正确移动', () => {
+            const a = FixedVector2.from(0, 0);
+            const b = FixedVector2.from(10, 0);
+            const result = a.moveTowards(b, Fixed32.from(3));
+            expect(result.x.toNumber()).toBeCloseTo(3, 3);
+            expect(result.y.toNumber()).toBeCloseTo(0, 3);
+        });
+    });
+
+    describe('比较运算', () => {
+        test('equals 应正确比较', () => {
+            const a = FixedVector2.from(3, 4);
+            const b = FixedVector2.from(3, 4);
+            const c = FixedVector2.from(3, 5);
+            expect(a.equals(b)).toBe(true);
+            expect(a.equals(c)).toBe(false);
+        });
+
+        test('isZero 应正确判断', () => {
+            expect(FixedVector2.ZERO.isZero()).toBe(true);
+            expect(FixedVector2.ONE.isZero()).toBe(false);
+        });
+    });
+
+    describe('确定性', () => {
+        test('向量运算应产生确定性结果', () => {
+            const results: string[] = [];
+            for (let i = 0; i < 100; i++) {
+                const a = FixedVector2.from(3.14159, 2.71828);
+                const b = FixedVector2.from(1.41421, 1.73205);
+                const result = a.add(b).mul(Fixed32.from(0.5)).normalize();
+                results.push(`${result.x.toRaw()},${result.y.toRaw()}`);
+            }
+            expect(new Set(results).size).toBe(1);
+        });
+
+        test('旋转应产生确定性结果', () => {
+            const results: string[] = [];
+            for (let i = 0; i < 100; i++) {
+                const v = FixedVector2.from(1, 0);
+                const angle = Fixed32.from(0.7853981634); // π/4
+                const rotated = v.rotate(angle);
+                results.push(`${rotated.x.toRaw()},${rotated.y.toRaw()}`);
+            }
+            expect(new Set(results).size).toBe(1);
+        });
+    });
+
+    describe('静态方法', () => {
+        test('distance 应正确计算', () => {
+            const a = FixedVector2.from(0, 0);
+            const b = FixedVector2.from(3, 4);
+            expect(FixedVector2.distance(a, b).toNumber()).toBeCloseTo(5, 3);
+        });
+
+        test('min/max 应正确计算', () => {
+            const a = FixedVector2.from(1, 5);
+            const b = FixedVector2.from(3, 2);
+
+            const min = FixedVector2.min(a, b);
+            expect(min.x.toNumber()).toBeCloseTo(1, 4);
+            expect(min.y.toNumber()).toBeCloseTo(2, 4);
+
+            const max = FixedVector2.max(a, b);
+            expect(max.x.toNumber()).toBeCloseTo(3, 4);
+            expect(max.y.toNumber()).toBeCloseTo(5, 4);
+        });
+    });
+});
@@ -32,6 +32,7 @@
    },
    "peerDependencies": {
        "@esengine/ecs-framework": "workspace:*",
+        "@esengine/ecs-framework-math": "workspace:*",
        "@esengine/blueprint": "workspace:*"
    },
    "peerDependenciesMeta": {
@@ -42,6 +43,7 @@
    "devDependencies": {
        "@esengine/blueprint": "workspace:*",
        "@esengine/ecs-framework": "workspace:*",
+        "@esengine/ecs-framework-math": "workspace:*",
        "@esengine/build-config": "workspace:*",
        "rimraf": "^5.0.5",
        "tsup": "^8.0.0",
@@ -138,6 +138,11 @@ export type {
    ComponentSyncEvent,
    ComponentSyncEventListener,
    ComponentSyncConfig,
+    // Fixed-point sync types
+    IFixedTransformStateRaw,
+    IFixedTransformStateWithVelocityRaw,
+    IFixedInterpolator,
+    IFixedExtrapolator,
 } from './sync'

 export {
@@ -158,6 +163,15 @@ export {
    // Component sync
    ComponentSyncSystem,
    createComponentSyncSystem,
+    // Fixed-point sync (Deterministic Lockstep)
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    createZeroFixedTransformState,
+    createZeroFixedTransformStateWithVelocity,
+    FixedTransformInterpolator,
+    FixedHermiteTransformInterpolator,
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator,
 } from './sync'

 // ============================================================================
@@ -0,0 +1,485 @@
+/**
+ * @zh 定点数客户端预测
+ * @en Fixed-point Client Prediction
+ *
+ * @zh 用于帧同步的确定性客户端预测和回滚
+ * @en Deterministic client prediction and rollback for lockstep
+ */
+
+import { Fixed32, FixedVector2 } from '@esengine/ecs-framework-math';
+
+// =============================================================================
+// 定点数输入快照接口 | Fixed Input Snapshot Interface
+// =============================================================================
+
+/**
+ * @zh 定点数输入快照
+ * @en Fixed-point input snapshot
+ */
+export interface IFixedInputSnapshot<TInput> {
+    /**
+     * @zh 输入帧号
+     * @en Input frame number
+     */
+    readonly frame: number;
+
+    /**
+     * @zh 输入数据
+     * @en Input data
+     */
+    readonly input: TInput;
+}
+
+/**
+ * @zh 定点数预测状态
+ * @en Fixed-point predicted state
+ */
+export interface IFixedPredictedState<TState> {
+    /**
+     * @zh 状态数据
+     * @en State data
+     */
+    readonly state: TState;
+
+    /**
+     * @zh 对应的帧号
+     * @en Corresponding frame number
+     */
+    readonly frame: number;
+}
+
+// =============================================================================
+// 定点数预测器接口 | Fixed Predictor Interface
+// =============================================================================
+
+/**
+ * @zh 定点数状态预测器接口
+ * @en Fixed-point state predictor interface
+ *
+ * @zh 必须使用定点数运算确保确定性
+ * @en Must use fixed-point arithmetic to ensure determinism
+ */
+export interface IFixedPredictor<TState, TInput> {
+    /**
+     * @zh 根据当前状态和输入预测下一状态
+     * @en Predict next state based on current state and input
+     *
+     * @param state - @zh 当前状态 @en Current state
+     * @param input - @zh 输入 @en Input
+     * @param deltaTime - @zh 固定时间步长（定点数）@en Fixed delta time (fixed-point)
+     * @returns @zh 预测的状态 @en Predicted state
+     */
+    predict(state: TState, input: TInput, deltaTime: Fixed32): TState;
+}
+
+/**
+ * @zh 状态位置提取器接口
+ * @en State position extractor interface
+ */
+export interface IFixedStatePositionExtractor<TState> {
+    /**
+     * @zh 从状态中提取位置
+     * @en Extract position from state
+     */
+    getPosition(state: TState): FixedVector2;
+}
+
+// =============================================================================
+// 定点数客户端预测配置 | Fixed Client Prediction Config
+// =============================================================================
+
+/**
+ * @zh 定点数客户端预测配置
+ * @en Fixed-point client prediction configuration
+ */
+export interface FixedClientPredictionConfig {
+    /**
+     * @zh 最大未确认输入数量
+     * @en Maximum unacknowledged inputs
+     */
+    maxUnacknowledgedInputs: number;
+
+    /**
+     * @zh 固定时间步长（定点数）
+     * @en Fixed delta time (fixed-point)
+     */
+    fixedDeltaTime: Fixed32;
+
+    /**
+     * @zh 校正阈值（定点数，超过此值才进行校正）
+     * @en Reconciliation threshold (fixed-point, correction only above this value)
+     */
+    reconciliationThreshold: Fixed32;
+
+    /**
+     * @zh 是否启用平滑校正（帧同步通常关闭）
+     * @en Enable smooth reconciliation (usually disabled for lockstep)
+     */
+    enableSmoothReconciliation: boolean;
+
+    /**
+     * @zh 平滑校正速度（定点数）
+     * @en Smooth reconciliation speed (fixed-point)
+     */
+    reconciliationSpeed: Fixed32;
+}
+
+// =============================================================================
+// 定点数客户端预测管理器 | Fixed Client Prediction Manager
+// =============================================================================
+
+/**
+ * @zh 定点数客户端预测管理器
+ * @en Fixed-point client prediction manager
+ *
+ * @zh 提供确定性的客户端预测和服务器状态回滚校正
+ * @en Provides deterministic client prediction and server state rollback reconciliation
+ */
+export class FixedClientPrediction<TState, TInput> {
+    private readonly _predictor: IFixedPredictor<TState, TInput>;
+    private readonly _config: FixedClientPredictionConfig;
+    private readonly _pendingInputs: IFixedInputSnapshot<TInput>[] = [];
+    private _lastAcknowledgedFrame: number = 0;
+    private _currentFrame: number = 0;
+    private _lastServerState: TState | null = null;
+    private _predictedState: TState | null = null;
+    private _correctionOffset: FixedVector2 = FixedVector2.ZERO;
+    private _stateHistory: Map<number, TState> = new Map();
+    private readonly _maxHistorySize: number = 120;
+
+    constructor(
+        predictor: IFixedPredictor<TState, TInput>,
+        config?: Partial<FixedClientPredictionConfig>
+    ) {
+        this._predictor = predictor;
+        this._config = {
+            maxUnacknowledgedInputs: 60,
+            fixedDeltaTime: Fixed32.from(1 / 60),
+            reconciliationThreshold: Fixed32.from(0.001),
+            enableSmoothReconciliation: false,
+            reconciliationSpeed: Fixed32.from(10),
+            ...config
+        };
+    }
+
+    /**
+     * @zh 获取当前预测状态
+     * @en Get current predicted state
+     */
+    get predictedState(): TState | null {
+        return this._predictedState;
+    }
+
+    /**
+     * @zh 获取校正偏移（用于渲染平滑）
+     * @en Get correction offset (for render smoothing)
+     */
+    get correctionOffset(): FixedVector2 {
+        return this._correctionOffset;
+    }
+
+    /**
+     * @zh 获取待确认输入数量
+     * @en Get pending input count
+     */
+    get pendingInputCount(): number {
+        return this._pendingInputs.length;
+    }
+
+    /**
+     * @zh 获取当前帧号
+     * @en Get current frame number
+     */
+    get currentFrame(): number {
+        return this._currentFrame;
+    }
+
+    /**
+     * @zh 获取最后确认帧号
+     * @en Get last acknowledged frame
+     */
+    get lastAcknowledgedFrame(): number {
+        return this._lastAcknowledgedFrame;
+    }
+
+    /**
+     * @zh 记录并预测输入
+     * @en Record and predict input
+     *
+     * @param input - @zh 输入数据 @en Input data
+     * @param currentState - @zh 当前状态 @en Current state
+     * @returns @zh 预测的状态 @en Predicted state
+     */
+    recordInput(input: TInput, currentState: TState): TState {
+        this._currentFrame++;
+
+        const inputSnapshot: IFixedInputSnapshot<TInput> = {
+            frame: this._currentFrame,
+            input
+        };
+
+        this._pendingInputs.push(inputSnapshot);
+
+        while (this._pendingInputs.length > this._config.maxUnacknowledgedInputs) {
+            this._pendingInputs.shift();
+        }
+
+        this._predictedState = this._predictor.predict(
+            currentState,
+            input,
+            this._config.fixedDeltaTime
+        );
+
+        this._stateHistory.set(this._currentFrame, this._predictedState);
+        this._cleanupHistory();
+
+        return this._predictedState;
+    }
+
+    /**
+     * @zh 获取指定帧的输入
+     * @en Get input at specific frame
+     */
+    getInputAtFrame(frame: number): IFixedInputSnapshot<TInput> | null {
+        return this._pendingInputs.find(i => i.frame === frame) ?? null;
+    }
+
+    /**
+     * @zh 获取所有待确认输入
+     * @en Get all pending inputs
+     */
+    getPendingInputs(): readonly IFixedInputSnapshot<TInput>[] {
+        return this._pendingInputs;
+    }
+
+    /**
+     * @zh 处理服务器状态并进行回滚校正
+     * @en Process server state and perform rollback reconciliation
+     *
+     * @param serverState - @zh 服务器权威状态 @en Server authoritative state
+     * @param serverFrame - @zh 服务器状态对应的帧号 @en Server state frame number
+     * @param positionExtractor - @zh 状态位置提取器 @en State position extractor
+     * @returns @zh 校正后的状态 @en Reconciled state
+     */
+    reconcile(
+        serverState: TState,
+        serverFrame: number,
+        positionExtractor: IFixedStatePositionExtractor<TState>
+    ): TState {
+        this._lastServerState = serverState;
+        this._lastAcknowledgedFrame = serverFrame;
+
+        while (this._pendingInputs.length > 0 && this._pendingInputs[0].frame <= serverFrame) {
+            this._pendingInputs.shift();
+        }
+
+        const localStateAtServerFrame = this._stateHistory.get(serverFrame);
+
+        if (localStateAtServerFrame) {
+            const serverPos = positionExtractor.getPosition(serverState);
+            const localPos = positionExtractor.getPosition(localStateAtServerFrame);
+            const error = serverPos.sub(localPos);
+            const errorMagnitude = error.length();
+
+            if (errorMagnitude.gt(this._config.reconciliationThreshold)) {
+                if (this._config.enableSmoothReconciliation) {
+                    const t = Fixed32.min(
+                        Fixed32.ONE,
+                        this._config.reconciliationSpeed.mul(this._config.fixedDeltaTime)
+                    );
+                    this._correctionOffset = this._correctionOffset.add(error.mul(t));
+
+                    const decayRate = Fixed32.from(0.9);
+                    this._correctionOffset = this._correctionOffset.mul(decayRate);
+                } else {
+                    this._correctionOffset = FixedVector2.ZERO;
+                }
+
+                let state = serverState;
+                for (const inputSnapshot of this._pendingInputs) {
+                    state = this._predictor.predict(
+                        state,
+                        inputSnapshot.input,
+                        this._config.fixedDeltaTime
+                    );
+                    this._stateHistory.set(inputSnapshot.frame, state);
+                }
+                this._predictedState = state;
+
+                return state;
+            }
+        }
+
+        let state = serverState;
+        for (const inputSnapshot of this._pendingInputs) {
+            state = this._predictor.predict(
+                state,
+                inputSnapshot.input,
+                this._config.fixedDeltaTime
+            );
+        }
+        this._predictedState = state;
+
+        return state;
+    }
+
+    /**
+     * @zh 回滚到指定帧并重新模拟
+     * @en Rollback to specific frame and re-simulate
+     *
+     * @param targetFrame - @zh 目标帧号 @en Target frame number
+     * @param authoritativeState - @zh 权威状态 @en Authoritative state
+     * @returns @zh 重新模拟后的当前状态 @en Re-simulated current state
+     */
+    rollbackAndResimulate(targetFrame: number, authoritativeState: TState): TState {
+        this._stateHistory.set(targetFrame, authoritativeState);
+
+        let state = authoritativeState;
+        const inputsToResimulate = this._pendingInputs.filter(i => i.frame > targetFrame);
+
+        for (const inputSnapshot of inputsToResimulate) {
+            state = this._predictor.predict(
+                state,
+                inputSnapshot.input,
+                this._config.fixedDeltaTime
+            );
+            this._stateHistory.set(inputSnapshot.frame, state);
+        }
+
+        this._predictedState = state;
+        return state;
+    }
+
+    /**
+     * @zh 获取历史状态
+     * @en Get historical state
+     */
+    getStateAtFrame(frame: number): TState | null {
+        return this._stateHistory.get(frame) ?? null;
+    }
+
+    /**
+     * @zh 清空预测状态
+     * @en Clear prediction state
+     */
+    clear(): void {
+        this._pendingInputs.length = 0;
+        this._lastAcknowledgedFrame = 0;
+        this._currentFrame = 0;
+        this._lastServerState = null;
+        this._predictedState = null;
+        this._correctionOffset = FixedVector2.ZERO;
+        this._stateHistory.clear();
+    }
+
+    private _cleanupHistory(): void {
+        if (this._stateHistory.size > this._maxHistorySize) {
+            const sortedFrames = Array.from(this._stateHistory.keys()).sort((a, b) => a - b);
+            const framesToRemove = sortedFrames.slice(
+                0,
+                this._stateHistory.size - this._maxHistorySize
+            );
+            for (const frame of framesToRemove) {
+                this._stateHistory.delete(frame);
+            }
+        }
+    }
+}
+
+// =============================================================================
+// 工厂函数 | Factory Functions
+// =============================================================================
+
+/**
+ * @zh 创建定点数客户端预测管理器
+ * @en Create fixed-point client prediction manager
+ */
+export function createFixedClientPrediction<TState, TInput>(
+    predictor: IFixedPredictor<TState, TInput>,
+    config?: Partial<FixedClientPredictionConfig>
+): FixedClientPrediction<TState, TInput> {
+    return new FixedClientPrediction(predictor, config);
+}
+
+// =============================================================================
+// 预设预测器 | Preset Predictors
+// =============================================================================
+
+/**
+ * @zh 移动输入类型
+ * @en Movement input type
+ */
+export interface IFixedMovementInput {
+    /**
+     * @zh X方向输入 (-1, 0, 1)
+     * @en X direction input (-1, 0, 1)
+     */
+    readonly dx: number;
+
+    /**
+     * @zh Y方向输入 (-1, 0, 1)
+     * @en Y direction input (-1, 0, 1)
+     */
+    readonly dy: number;
+}
+
+/**
+ * @zh 移动状态类型
+ * @en Movement state type
+ */
+export interface IFixedMovementState {
+    /**
+     * @zh 位置
+     * @en Position
+     */
+    readonly position: FixedVector2;
+
+    /**
+     * @zh 速度
+     * @en Velocity
+     */
+    readonly velocity: FixedVector2;
+}
+
+/**
+ * @zh 创建简单移动预测器
+ * @en Create simple movement predictor
+ *
+ * @param speed - @zh 移动速度（定点数）@en Movement speed (fixed-point)
+ */
+export function createFixedMovementPredictor(
+    speed: Fixed32
+): IFixedPredictor<IFixedMovementState, IFixedMovementInput> {
+    return {
+        predict(
+            state: IFixedMovementState,
+            input: IFixedMovementInput,
+            deltaTime: Fixed32
+        ): IFixedMovementState {
+            const inputVec = FixedVector2.from(input.dx, input.dy);
+            const normalizedInput =
+                inputVec.lengthSquared().gt(Fixed32.ZERO) ? inputVec.normalize() : inputVec;
+
+            const velocity = normalizedInput.mul(speed);
+            const displacement = velocity.mul(deltaTime);
+            const newPosition = state.position.add(displacement);
+
+            return {
+                position: newPosition,
+                velocity
+            };
+        }
+    };
+}
+
+/**
+ * @zh 创建移动状态位置提取器
+ * @en Create movement state position extractor
+ */
+export function createFixedMovementPositionExtractor(): IFixedStatePositionExtractor<IFixedMovementState> {
+    return {
+        getPosition(state: IFixedMovementState): FixedVector2 {
+            return state.position;
+        }
+    };
+}
@@ -0,0 +1,304 @@
+/**
+ * @zh 定点数快照缓冲区
+ * @en Fixed-point Snapshot Buffer
+ *
+ * @zh 用于帧同步确定性计算的快照缓冲区
+ * @en Snapshot buffer for deterministic lockstep calculations
+ */
+
+import { Fixed32 } from '@esengine/ecs-framework-math';
+
+// =============================================================================
+// 定点数快照接口 | Fixed Snapshot Interfaces
+// =============================================================================
+
+/**
+ * @zh 定点数状态快照
+ * @en Fixed-point state snapshot
+ */
+export interface IFixedStateSnapshot<T> {
+    /**
+     * @zh 帧号（定点数时间戳）
+     * @en Frame number (fixed-point timestamp)
+     */
+    readonly frame: number;
+
+    /**
+     * @zh 状态数据
+     * @en State data
+     */
+    readonly state: T;
+}
+
+/**
+ * @zh 定点数快照缓冲区配置
+ * @en Fixed-point snapshot buffer configuration
+ */
+export interface IFixedSnapshotBufferConfig {
+    /**
+     * @zh 最大快照数量
+     * @en Maximum snapshot count
+     */
+    maxSize: number;
+
+    /**
+     * @zh 插值延迟帧数
+     * @en Interpolation delay in frames
+     */
+    interpolationDelayFrames: number;
+}
+
+/**
+ * @zh 插值结果
+ * @en Interpolation result
+ */
+export interface IFixedInterpolationResult<T> {
+    /**
+     * @zh 前一个快照
+     * @en Previous snapshot
+     */
+    readonly from: IFixedStateSnapshot<T>;
+
+    /**
+     * @zh 后一个快照
+     * @en Next snapshot
+     */
+    readonly to: IFixedStateSnapshot<T>;
+
+    /**
+     * @zh 插值因子 (0-1)
+     * @en Interpolation factor (0-1)
+     */
+    readonly t: Fixed32;
+}
+
+// =============================================================================
+// 定点数快照缓冲区实现 | Fixed Snapshot Buffer Implementation
+// =============================================================================
+
+/**
+ * @zh 定点数快照缓冲区
+ * @en Fixed-point snapshot buffer
+ *
+ * @zh 使用帧号而非毫秒时间戳，确保跨平台确定性
+ * @en Uses frame numbers instead of millisecond timestamps for cross-platform determinism
+ */
+export class FixedSnapshotBuffer<T> {
+    private readonly _buffer: IFixedStateSnapshot<T>[] = [];
+    private readonly _maxSize: number;
+    private readonly _interpolationDelayFrames: number;
+
+    constructor(config: IFixedSnapshotBufferConfig) {
+        this._maxSize = config.maxSize;
+        this._interpolationDelayFrames = config.interpolationDelayFrames;
+    }
+
+    /**
+     * @zh 获取缓冲区大小
+     * @en Get buffer size
+     */
+    get size(): number {
+        return this._buffer.length;
+    }
+
+    /**
+     * @zh 获取插值延迟帧数
+     * @en Get interpolation delay in frames
+     */
+    get interpolationDelayFrames(): number {
+        return this._interpolationDelayFrames;
+    }
+
+    /**
+     * @zh 添加快照
+     * @en Add snapshot
+     *
+     * @param snapshot - @zh 状态快照 @en State snapshot
+     */
+    push(snapshot: IFixedStateSnapshot<T>): void {
+        let insertIndex = this._buffer.length;
+        for (let i = this._buffer.length - 1; i >= 0; i--) {
+            if (this._buffer[i].frame <= snapshot.frame) {
+                insertIndex = i + 1;
+                break;
+            }
+            if (i === 0) {
+                insertIndex = 0;
+            }
+        }
+
+        this._buffer.splice(insertIndex, 0, snapshot);
+
+        while (this._buffer.length > this._maxSize) {
+            this._buffer.shift();
+        }
+    }
+
+    /**
+     * @zh 根据帧号获取插值快照
+     * @en Get interpolation snapshots by frame number
+     *
+     * @param currentFrame - @zh 当前帧号 @en Current frame number
+     * @returns @zh 插值结果（包含定点数插值因子）或 null @en Interpolation result with fixed-point factor or null
+     */
+    getInterpolationSnapshots(currentFrame: number): IFixedInterpolationResult<T> | null {
+        if (this._buffer.length < 2) {
+            return null;
+        }
+
+        const targetFrame = currentFrame - this._interpolationDelayFrames;
+
+        for (let i = 0; i < this._buffer.length - 1; i++) {
+            const prev = this._buffer[i];
+            const next = this._buffer[i + 1];
+
+            if (prev.frame <= targetFrame && next.frame >= targetFrame) {
+                const duration = next.frame - prev.frame;
+                let t: Fixed32;
+                if (duration > 0) {
+                    const elapsed = targetFrame - prev.frame;
+                    t = Fixed32.from(elapsed).div(Fixed32.from(duration));
+                    t = Fixed32.clamp(t, Fixed32.ZERO, Fixed32.ONE);
+                } else {
+                    t = Fixed32.ZERO;
+                }
+                return { from: prev, to: next, t };
+            }
+        }
+
+        if (targetFrame > this._buffer[this._buffer.length - 1].frame) {
+            const prev = this._buffer[this._buffer.length - 2];
+            const next = this._buffer[this._buffer.length - 1];
+            const duration = next.frame - prev.frame;
+            let t: Fixed32;
+            if (duration > 0) {
+                const elapsed = targetFrame - prev.frame;
+                t = Fixed32.from(elapsed).div(Fixed32.from(duration));
+                t = Fixed32.min(t, Fixed32.from(2));
+            } else {
+                t = Fixed32.ONE;
+            }
+            return { from: prev, to: next, t };
+        }
+
+        return null;
+    }
+
+    /**
+     * @zh 根据精确帧时间获取插值快照（支持子帧插值）
+     * @en Get interpolation snapshots by precise frame time (supports sub-frame interpolation)
+     *
+     * @param frameTime - @zh 精确帧时间（定点数）@en Precise frame time (fixed-point)
+     * @returns @zh 插值结果或 null @en Interpolation result or null
+     */
+    getInterpolationSnapshotsFixed(frameTime: Fixed32): IFixedInterpolationResult<T> | null {
+        if (this._buffer.length < 2) {
+            return null;
+        }
+
+        const targetFrame = frameTime.sub(Fixed32.from(this._interpolationDelayFrames));
+
+        for (let i = 0; i < this._buffer.length - 1; i++) {
+            const prev = this._buffer[i];
+            const next = this._buffer[i + 1];
+            const prevFrame = Fixed32.from(prev.frame);
+            const nextFrame = Fixed32.from(next.frame);
+
+            if (prevFrame.le(targetFrame) && nextFrame.ge(targetFrame)) {
+                const duration = nextFrame.sub(prevFrame);
+                let t: Fixed32;
+                if (duration.gt(Fixed32.ZERO)) {
+                    t = targetFrame.sub(prevFrame).div(duration);
+                    t = Fixed32.clamp(t, Fixed32.ZERO, Fixed32.ONE);
+                } else {
+                    t = Fixed32.ZERO;
+                }
+                return { from: prev, to: next, t };
+            }
+        }
+
+        const lastFrame = Fixed32.from(this._buffer[this._buffer.length - 1].frame);
+        if (targetFrame.gt(lastFrame)) {
+            const prev = this._buffer[this._buffer.length - 2];
+            const next = this._buffer[this._buffer.length - 1];
+            const prevFrame = Fixed32.from(prev.frame);
+            const nextFrame = Fixed32.from(next.frame);
+            const duration = nextFrame.sub(prevFrame);
+            let t: Fixed32;
+            if (duration.gt(Fixed32.ZERO)) {
+                t = targetFrame.sub(prevFrame).div(duration);
+                t = Fixed32.min(t, Fixed32.from(2));
+            } else {
+                t = Fixed32.ONE;
+            }
+            return { from: prev, to: next, t };
+        }
+
+        return null;
+    }
+
+    /**
+     * @zh 获取最新快照
+     * @en Get latest snapshot
+     */
+    getLatest(): IFixedStateSnapshot<T> | null {
+        return this._buffer.length > 0 ? this._buffer[this._buffer.length - 1] : null;
+    }
+
+    /**
+     * @zh 获取特定帧号的快照
+     * @en Get snapshot at specific frame
+     */
+    getAtFrame(frame: number): IFixedStateSnapshot<T> | null {
+        for (const snapshot of this._buffer) {
+            if (snapshot.frame === frame) {
+                return snapshot;
+            }
+        }
+        return null;
+    }
+
+    /**
+     * @zh 获取特定帧号之后的所有快照
+     * @en Get all snapshots after specific frame
+     */
+    getSnapshotsAfter(frame: number): IFixedStateSnapshot<T>[] {
+        return this._buffer.filter(s => s.frame > frame);
+    }
+
+    /**
+     * @zh 移除指定帧号之前的所有快照
+     * @en Remove all snapshots before specific frame
+     */
+    removeSnapshotsBefore(frame: number): void {
+        while (this._buffer.length > 0 && this._buffer[0].frame < frame) {
+            this._buffer.shift();
+        }
+    }
+
+    /**
+     * @zh 清空缓冲区
+     * @en Clear buffer
+     */
+    clear(): void {
+        this._buffer.length = 0;
+    }
+}
+
+// =============================================================================
+// 工厂函数 | Factory Functions
+// =============================================================================
+
+/**
+ * @zh 创建定点数快照缓冲区
+ * @en Create fixed-point snapshot buffer
+ *
+ * @param maxSize - @zh 最大快照数量（默认 30）@en Maximum snapshot count (default 30)
+ * @param interpolationDelayFrames - @zh 插值延迟帧数（默认 2）@en Interpolation delay frames (default 2)
+ */
+export function createFixedSnapshotBuffer<T>(
+    maxSize: number = 30,
+    interpolationDelayFrames: number = 2
+): FixedSnapshotBuffer<T> {
+    return new FixedSnapshotBuffer<T>({ maxSize, interpolationDelayFrames });
+}
@@ -0,0 +1,229 @@
+/**
+ * @zh 定点数变换插值器
+ * @en Fixed-point Transform Interpolator
+ *
+ * @zh 用于帧同步确定性计算的插值器
+ * @en Interpolator for deterministic lockstep calculations
+ */
+
+import { Fixed32, FixedVector2, FixedMath } from '@esengine/ecs-framework-math';
+import {
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw,
+    type IFixedTransformStateWithVelocityRaw
+} from './FixedTransformState';
+
+// =============================================================================
+// 插值器接口 | Interpolator Interface
+// =============================================================================
+
+/**
+ * @zh 定点数插值器接口
+ * @en Fixed-point interpolator interface
+ */
+export interface IFixedInterpolator<T> {
+    /**
+     * @zh 在两个状态之间插值
+     * @en Interpolate between two states
+     * @param from - @zh 起始状态 @en Start state
+     * @param to - @zh 结束状态 @en End state
+     * @param t - @zh 插值因子 (0-1) @en Interpolation factor (0-1)
+     */
+    interpolate(from: T, to: T, t: Fixed32): T;
+}
+
+/**
+ * @zh 定点数外推器接口
+ * @en Fixed-point extrapolator interface
+ */
+export interface IFixedExtrapolator<T> {
+    /**
+     * @zh 基于速度外推状态
+     * @en Extrapolate state based on velocity
+     * @param state - @zh 当前状态 @en Current state
+     * @param deltaTime - @zh 时间增量 @en Time delta
+     */
+    extrapolate(state: T, deltaTime: Fixed32): T;
+}
+
+// =============================================================================
+// 定点数变换插值器 | Fixed Transform Interpolator
+// =============================================================================
+
+/**
+ * @zh 定点数变换状态插值器
+ * @en Fixed-point transform state interpolator
+ */
+export class FixedTransformInterpolator
+    implements IFixedInterpolator<FixedTransformState>, IFixedExtrapolator<FixedTransformStateWithVelocity> {
+
+    /**
+     * @zh 在两个变换状态之间插值
+     * @en Interpolate between two transform states
+     */
+    interpolate(from: FixedTransformState, to: FixedTransformState, t: Fixed32): FixedTransformState {
+        return new FixedTransformState(
+            from.position.lerp(to.position, t),
+            FixedMath.lerpAngle(from.rotation, to.rotation, t)
+        );
+    }
+
+    /**
+     * @zh 基于速度外推变换状态
+     * @en Extrapolate transform state based on velocity
+     */
+    extrapolate(
+        state: FixedTransformStateWithVelocity,
+        deltaTime: Fixed32
+    ): FixedTransformStateWithVelocity {
+        return new FixedTransformStateWithVelocity(
+            state.position.add(state.velocity.mul(deltaTime)),
+            state.rotation.add(state.angularVelocity.mul(deltaTime)),
+            state.velocity,
+            state.angularVelocity
+        );
+    }
+
+    /**
+     * @zh 使用原始值进行插值
+     * @en Interpolate using raw values
+     */
+    interpolateRaw(
+        from: IFixedTransformStateRaw,
+        to: IFixedTransformStateRaw,
+        t: number
+    ): IFixedTransformStateRaw {
+        const fromState = FixedTransformState.fromRaw(from);
+        const toState = FixedTransformState.fromRaw(to);
+        const tFixed = Fixed32.from(t);
+        return this.interpolate(fromState, toState, tFixed).toRaw();
+    }
+
+    /**
+     * @zh 使用原始值进行外推
+     * @en Extrapolate using raw values
+     */
+    extrapolateRaw(
+        state: IFixedTransformStateWithVelocityRaw,
+        deltaTimeMs: number
+    ): IFixedTransformStateWithVelocityRaw {
+        const fixedState = FixedTransformStateWithVelocity.fromRaw(state);
+        const deltaTime = Fixed32.from(deltaTimeMs / 1000); // ms to seconds
+        return this.extrapolate(fixedState, deltaTime).toRaw();
+    }
+}
+
+// =============================================================================
+// 赫尔米特插值器 | Hermite Interpolator
+// =============================================================================
+
+/**
+ * @zh 定点数赫尔米特变换插值器（更平滑的曲线）
+ * @en Fixed-point Hermite transform interpolator (smoother curves)
+ */
+export class FixedHermiteTransformInterpolator
+    implements IFixedInterpolator<FixedTransformStateWithVelocity> {
+
+    /**
+     * @zh 快照间隔时间（秒）
+     * @en Snapshot interval in seconds
+     */
+    private readonly snapshotInterval: Fixed32;
+
+    constructor(snapshotIntervalMs: number = 100) {
+        this.snapshotInterval = Fixed32.from(snapshotIntervalMs / 1000);
+    }
+
+    /**
+     * @zh 使用赫尔米特插值
+     * @en Use Hermite interpolation
+     */
+    interpolate(
+        from: FixedTransformStateWithVelocity,
+        to: FixedTransformStateWithVelocity,
+        t: Fixed32
+    ): FixedTransformStateWithVelocity {
+        const t2 = t.mul(t);
+        const t3 = t2.mul(t);
+
+        const two = Fixed32.from(2);
+        const three = Fixed32.from(3);
+        const six = Fixed32.from(6);
+        const four = Fixed32.from(4);
+
+        // Hermite basis functions
+        // h00 = 2t³ - 3t² + 1
+        const h00 = two.mul(t3).sub(three.mul(t2)).add(Fixed32.ONE);
+        // h10 = t³ - 2t² + t
+        const h10 = t3.sub(two.mul(t2)).add(t);
+        // h01 = -2t³ + 3t²
+        const h01 = two.neg().mul(t3).add(three.mul(t2));
+        // h11 = t³ - t²
+        const h11 = t3.sub(t2);
+
+        const dt = this.snapshotInterval;
+
+        // Position interpolation
+        const x = h00.mul(from.position.x)
+            .add(h10.mul(from.velocity.x).mul(dt))
+            .add(h01.mul(to.position.x))
+            .add(h11.mul(to.velocity.x).mul(dt));
+
+        const y = h00.mul(from.position.y)
+            .add(h10.mul(from.velocity.y).mul(dt))
+            .add(h01.mul(to.position.y))
+            .add(h11.mul(to.velocity.y).mul(dt));
+
+        // Velocity derivatives
+        // dh00 = 6t² - 6t
+        const dh00 = six.mul(t2).sub(six.mul(t));
+        // dh10 = 3t² - 4t + 1
+        const dh10 = three.mul(t2).sub(four.mul(t)).add(Fixed32.ONE);
+        // dh01 = -6t² + 6t
+        const dh01 = six.neg().mul(t2).add(six.mul(t));
+        // dh11 = 3t² - 2t
+        const dh11 = three.mul(t2).sub(two.mul(t));
+
+        const velocityX = dh00.mul(from.position.x)
+            .add(dh10.mul(from.velocity.x).mul(dt))
+            .add(dh01.mul(to.position.x))
+            .add(dh11.mul(to.velocity.x).mul(dt))
+            .div(dt);
+
+        const velocityY = dh00.mul(from.position.y)
+            .add(dh10.mul(from.velocity.y).mul(dt))
+            .add(dh01.mul(to.position.y))
+            .add(dh11.mul(to.velocity.y).mul(dt))
+            .div(dt);
+
+        return new FixedTransformStateWithVelocity(
+            new FixedVector2(x, y),
+            FixedMath.lerpAngle(from.rotation, to.rotation, t),
+            new FixedVector2(velocityX, velocityY),
+            Fixed32.lerp(from.angularVelocity, to.angularVelocity, t)
+        );
+    }
+}
+
+// =============================================================================
+// 工厂函数 | Factory Functions
+// =============================================================================
+
+/**
+ * @zh 创建定点数变换插值器
+ * @en Create fixed-point transform interpolator
+ */
+export function createFixedTransformInterpolator(): FixedTransformInterpolator {
+    return new FixedTransformInterpolator();
+}
+
+/**
+ * @zh 创建定点数赫尔米特变换插值器
+ * @en Create fixed-point Hermite transform interpolator
+ */
+export function createFixedHermiteTransformInterpolator(
+    snapshotIntervalMs?: number
+): FixedHermiteTransformInterpolator {
+    return new FixedHermiteTransformInterpolator(snapshotIntervalMs);
+}
@@ -0,0 +1,265 @@
+/**
+ * @zh 定点数变换状态
+ * @en Fixed-point Transform State
+ *
+ * @zh 用于帧同步确定性计算的变换状态
+ * @en Transform state for deterministic lockstep calculations
+ */
+
+import { Fixed32, FixedVector2 } from '@esengine/ecs-framework-math';
+
+// =============================================================================
+// 定点数变换状态接口 | Fixed Transform State Interface
+// =============================================================================
+
+/**
+ * @zh 定点数变换状态（原始值）
+ * @en Fixed-point transform state (raw values)
+ *
+ * @zh 用于网络传输的原始整数格式，确保跨平台一致性
+ * @en Raw integer format for network transmission, ensures cross-platform consistency
+ */
+export interface IFixedTransformStateRaw {
+    /**
+     * @zh X 坐标原始值
+     * @en X coordinate raw value
+     */
+    x: number;
+
+    /**
+     * @zh Y 坐标原始值
+     * @en Y coordinate raw value
+     */
+    y: number;
+
+    /**
+     * @zh 旋转角度原始值（弧度 * 65536）
+     * @en Rotation raw value (radians * 65536)
+     */
+    rotation: number;
+}
+
+/**
+ * @zh 带速度的定点数变换状态（原始值）
+ * @en Fixed-point transform state with velocity (raw values)
+ */
+export interface IFixedTransformStateWithVelocityRaw extends IFixedTransformStateRaw {
+    /**
+     * @zh X 速度原始值
+     * @en X velocity raw value
+     */
+    velocityX: number;
+
+    /**
+     * @zh Y 速度原始值
+     * @en Y velocity raw value
+     */
+    velocityY: number;
+
+    /**
+     * @zh 角速度原始值
+     * @en Angular velocity raw value
+     */
+    angularVelocity: number;
+}
+
+// =============================================================================
+// 定点数变换状态类 | Fixed Transform State Class
+// =============================================================================
+
+/**
+ * @zh 定点数变换状态
+ * @en Fixed-point transform state
+ */
+export class FixedTransformState {
+    readonly position: FixedVector2;
+    readonly rotation: Fixed32;
+
+    constructor(position: FixedVector2, rotation: Fixed32) {
+        this.position = position;
+        this.rotation = rotation;
+    }
+
+    /**
+     * @zh 从原始值创建
+     * @en Create from raw values
+     */
+    static fromRaw(raw: IFixedTransformStateRaw): FixedTransformState {
+        return new FixedTransformState(
+            FixedVector2.fromRaw(raw.x, raw.y),
+            Fixed32.fromRaw(raw.rotation)
+        );
+    }
+
+    /**
+     * @zh 从浮点数创建
+     * @en Create from floating-point numbers
+     */
+    static from(x: number, y: number, rotation: number): FixedTransformState {
+        return new FixedTransformState(
+            FixedVector2.from(x, y),
+            Fixed32.from(rotation)
+        );
+    }
+
+    /**
+     * @zh 转换为原始值（用于网络传输）
+     * @en Convert to raw values (for network transmission)
+     */
+    toRaw(): IFixedTransformStateRaw {
+        return {
+            x: this.position.x.toRaw(),
+            y: this.position.y.toRaw(),
+            rotation: this.rotation.toRaw()
+        };
+    }
+
+    /**
+     * @zh 转换为浮点数对象（用于渲染）
+     * @en Convert to floating-point object (for rendering)
+     */
+    toFloat(): { x: number; y: number; rotation: number } {
+        return {
+            x: this.position.x.toNumber(),
+            y: this.position.y.toNumber(),
+            rotation: this.rotation.toNumber()
+        };
+    }
+
+    /**
+     * @zh 检查是否相等
+     * @en Check equality
+     */
+    equals(other: FixedTransformState): boolean {
+        return this.position.equals(other.position) && this.rotation.eq(other.rotation);
+    }
+}
+
+/**
+ * @zh 带速度的定点数变换状态
+ * @en Fixed-point transform state with velocity
+ */
+export class FixedTransformStateWithVelocity {
+    readonly position: FixedVector2;
+    readonly rotation: Fixed32;
+    readonly velocity: FixedVector2;
+    readonly angularVelocity: Fixed32;
+
+    constructor(
+        position: FixedVector2,
+        rotation: Fixed32,
+        velocity: FixedVector2,
+        angularVelocity: Fixed32
+    ) {
+        this.position = position;
+        this.rotation = rotation;
+        this.velocity = velocity;
+        this.angularVelocity = angularVelocity;
+    }
+
+    /**
+     * @zh 从原始值创建
+     * @en Create from raw values
+     */
+    static fromRaw(raw: IFixedTransformStateWithVelocityRaw): FixedTransformStateWithVelocity {
+        return new FixedTransformStateWithVelocity(
+            FixedVector2.fromRaw(raw.x, raw.y),
+            Fixed32.fromRaw(raw.rotation),
+            FixedVector2.fromRaw(raw.velocityX, raw.velocityY),
+            Fixed32.fromRaw(raw.angularVelocity)
+        );
+    }
+
+    /**
+     * @zh 从浮点数创建
+     * @en Create from floating-point numbers
+     */
+    static from(
+        x: number,
+        y: number,
+        rotation: number,
+        velocityX: number,
+        velocityY: number,
+        angularVelocity: number
+    ): FixedTransformStateWithVelocity {
+        return new FixedTransformStateWithVelocity(
+            FixedVector2.from(x, y),
+            Fixed32.from(rotation),
+            FixedVector2.from(velocityX, velocityY),
+            Fixed32.from(angularVelocity)
+        );
+    }
+
+    /**
+     * @zh 转换为原始值
+     * @en Convert to raw values
+     */
+    toRaw(): IFixedTransformStateWithVelocityRaw {
+        return {
+            x: this.position.x.toRaw(),
+            y: this.position.y.toRaw(),
+            rotation: this.rotation.toRaw(),
+            velocityX: this.velocity.x.toRaw(),
+            velocityY: this.velocity.y.toRaw(),
+            angularVelocity: this.angularVelocity.toRaw()
+        };
+    }
+
+    /**
+     * @zh 转换为浮点数对象
+     * @en Convert to floating-point object
+     */
+    toFloat(): {
+        x: number;
+        y: number;
+        rotation: number;
+        velocityX: number;
+        velocityY: number;
+        angularVelocity: number;
+    } {
+        return {
+            x: this.position.x.toNumber(),
+            y: this.position.y.toNumber(),
+            rotation: this.rotation.toNumber(),
+            velocityX: this.velocity.x.toNumber(),
+            velocityY: this.velocity.y.toNumber(),
+            angularVelocity: this.angularVelocity.toNumber()
+        };
+    }
+
+    /**
+     * @zh 检查是否相等
+     * @en Check equality
+     */
+    equals(other: FixedTransformStateWithVelocity): boolean {
+        return this.position.equals(other.position) &&
+            this.rotation.eq(other.rotation) &&
+            this.velocity.equals(other.velocity) &&
+            this.angularVelocity.eq(other.angularVelocity);
+    }
+}
+
+// =============================================================================
+// 工具函数 | Utility Functions
+// =============================================================================
+
+/**
+ * @zh 创建零状态
+ * @en Create zero state
+ */
+export function createZeroFixedTransformState(): FixedTransformState {
+    return new FixedTransformState(FixedVector2.ZERO, Fixed32.ZERO);
+}
+
+/**
+ * @zh 创建带速度的零状态
+ * @en Create zero state with velocity
+ */
+export function createZeroFixedTransformStateWithVelocity(): FixedTransformStateWithVelocity {
+    return new FixedTransformStateWithVelocity(
+        FixedVector2.ZERO,
+        Fixed32.ZERO,
+        FixedVector2.ZERO,
+        Fixed32.ZERO
+    );
+}
@@ -0,0 +1,63 @@
+/**
+ * @zh 定点数网络同步模块
+ * @en Fixed-point network sync module
+ *
+ * @zh 用于帧同步确定性计算的网络同步类型和工具
+ * @en Network sync types and utilities for deterministic lockstep calculations
+ */
+
+// =============================================================================
+// 变换状态 | Transform State
+// =============================================================================
+
+export {
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    createZeroFixedTransformState,
+    createZeroFixedTransformStateWithVelocity,
+    type IFixedTransformStateRaw,
+    type IFixedTransformStateWithVelocityRaw,
+} from './FixedTransformState';
+
+// =============================================================================
+// 插值器 | Interpolators
+// =============================================================================
+
+export {
+    FixedTransformInterpolator,
+    FixedHermiteTransformInterpolator,
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator,
+    type IFixedInterpolator,
+    type IFixedExtrapolator,
+} from './FixedTransformInterpolator';
+
+// =============================================================================
+// 快照缓冲区 | Snapshot Buffer
+// =============================================================================
+
+export {
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer,
+    type IFixedStateSnapshot,
+    type IFixedSnapshotBufferConfig,
+    type IFixedInterpolationResult,
+} from './FixedSnapshotBuffer';
+
+// =============================================================================
+// 客户端预测 | Client Prediction
+// =============================================================================
+
+export {
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+    type IFixedInputSnapshot,
+    type IFixedPredictedState,
+    type IFixedPredictor,
+    type IFixedStatePositionExtractor,
+    type FixedClientPredictionConfig,
+    type IFixedMovementInput,
+    type IFixedMovementState,
+} from './FixedClientPrediction';
@@ -78,3 +78,49 @@ export {
    ComponentSyncSystem,
    createComponentSyncSystem
 } from './ComponentSync';
+
+// =============================================================================
+// 定点数同步 | Fixed-point Sync (Deterministic Lockstep)
+// =============================================================================
+
+export {
+    // Transform State
+    FixedTransformState,
+    FixedTransformStateWithVelocity,
+    createZeroFixedTransformState,
+    createZeroFixedTransformStateWithVelocity,
+    // Interpolators
+    FixedTransformInterpolator,
+    FixedHermiteTransformInterpolator,
+    createFixedTransformInterpolator,
+    createFixedHermiteTransformInterpolator,
+    // Snapshot Buffer
+    FixedSnapshotBuffer,
+    createFixedSnapshotBuffer,
+    // Client Prediction
+    FixedClientPrediction,
+    createFixedClientPrediction,
+    createFixedMovementPredictor,
+    createFixedMovementPositionExtractor,
+} from './fixed';
+
+export type {
+    // Transform State Types
+    IFixedTransformStateRaw,
+    IFixedTransformStateWithVelocityRaw,
+    // Interpolator Types
+    IFixedInterpolator,
+    IFixedExtrapolator,
+    // Snapshot Buffer Types
+    IFixedStateSnapshot,
+    IFixedSnapshotBufferConfig,
+    IFixedInterpolationResult,
+    // Client Prediction Types
+    IFixedInputSnapshot,
+    IFixedPredictedState,
+    IFixedPredictor,
+    IFixedStatePositionExtractor,
+    FixedClientPredictionConfig,
+    IFixedMovementInput,
+    IFixedMovementState,
+} from './fixed';
@@ -1628,6 +1628,9 @@ importers:
      '@esengine/ecs-framework':
        specifier: workspace:*
        version: link:../core/dist
+      '@esengine/ecs-framework-math':
+        specifier: workspace:*
+        version: link:../math
      rimraf:
        specifier: ^5.0.5
        version: 5.0.10
@@ -1652,10 +1655,10 @@ importers:
        version: 5.0.10
      tsrpc-cli:
        specifier: ^2.4.5
-        version: 2.4.5(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@20.19.27)
+        version: 2.4.5(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@22.19.3)
      tsup:
        specifier: ^8.0.0
-        version: 8.5.1(@microsoft/api-extractor@7.55.2(@types/node@20.19.27))(@swc/core@1.15.7(@swc/helpers@0.5.18))(jiti@2.6.1)(postcss@8.5.6)(tsx@4.21.0)(typescript@5.9.3)(yaml@2.8.2)
+        version: 8.5.1(@microsoft/api-extractor@7.55.2(@types/node@22.19.3))(@swc/core@1.15.7(@swc/helpers@0.5.18))(jiti@2.6.1)(postcss@8.5.6)(tsx@4.21.0)(typescript@5.9.3)(yaml@2.8.2)
      typescript:
        specifier: ^5.3.3
        version: 5.9.3
@@ -13266,6 +13269,13 @@ snapshots:
    optionalDependencies:
      '@types/node': 20.19.27

+  '@inquirer/external-editor@1.0.3(@types/node@22.19.3)':
+    dependencies:
+      chardet: 2.1.1
+      iconv-lite: 0.7.1
+    optionalDependencies:
+      '@types/node': 22.19.3
+
  '@ioredis/commands@1.4.0': {}

  '@isaacs/balanced-match@4.0.1': {}
@@ -15063,7 +15073,6 @@ snapshots:
  '@types/node@22.19.3':
    dependencies:
      undici-types: 6.21.0
-    optional: true

  '@types/normalize-package-data@2.4.4': {}

@@ -15294,6 +15303,14 @@ snapshots:
    optionalDependencies:
      vite: 5.4.21(@types/node@20.19.27)(lightningcss@1.30.2)(terser@5.44.1)

+  '@vitest/mocker@2.1.9(vite@5.4.21(@types/node@22.19.3)(lightningcss@1.30.2)(terser@5.44.1))':
+    dependencies:
+      '@vitest/spy': 2.1.9
+      estree-walker: 3.0.3
+      magic-string: 0.30.21
+    optionalDependencies:
+      vite: 5.4.21(@types/node@22.19.3)(lightningcss@1.30.2)(terser@5.44.1)
+
  '@vitest/pretty-format@2.1.9':
    dependencies:
      tinyrainbow: 1.2.0
@@ -17859,6 +17876,26 @@ snapshots:
    transitivePeerDependencies:
      - '@types/node'

+  inquirer@8.2.7(@types/node@22.19.3):
+    dependencies:
+      '@inquirer/external-editor': 1.0.3(@types/node@22.19.3)
+      ansi-escapes: 4.3.2
+      chalk: 4.1.2
+      cli-cursor: 3.1.0
+      cli-width: 3.0.0
+      figures: 3.2.0
+      lodash: 4.17.21
+      mute-stream: 0.0.8
+      ora: 5.4.1
+      run-async: 2.4.1
+      rxjs: 7.8.2
+      string-width: 4.2.3
+      strip-ansi: 6.0.1
+      through: 2.3.8
+      wrap-ansi: 6.2.0
+    transitivePeerDependencies:
+      - '@types/node'
+
  into-stream@7.0.0:
    dependencies:
      from2: 2.3.0
@@ -21457,27 +21494,6 @@ snapshots:
      '@ts-morph/common': 0.22.0
      code-block-writer: 12.0.0

-  ts-node@10.9.2(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@20.19.27)(typescript@4.9.5):
-    dependencies:
-      '@cspotcode/source-map-support': 0.8.1
-      '@tsconfig/node10': 1.0.12
-      '@tsconfig/node12': 1.0.11
-      '@tsconfig/node14': 1.0.3
-      '@tsconfig/node16': 1.0.4
-      '@types/node': 20.19.27
-      acorn: 8.15.0
-      acorn-walk: 8.3.4
-      arg: 4.1.3
-      create-require: 1.1.1
-      diff: 4.0.2
-      make-error: 1.3.6
-      typescript: 4.9.5
-      v8-compile-cache-lib: 3.0.1
-      yn: 3.1.1
-    optionalDependencies:
-      '@swc/core': 1.15.7(@swc/helpers@0.5.18)
-      '@swc/wasm': 1.15.7
-
  ts-node@10.9.2(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@20.19.27)(typescript@5.9.3):
    dependencies:
      '@cspotcode/source-map-support': 0.8.1
@@ -21500,6 +21516,27 @@ snapshots:
      '@swc/wasm': 1.15.7
    optional: true

+  ts-node@10.9.2(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@22.19.3)(typescript@4.9.5):
+    dependencies:
+      '@cspotcode/source-map-support': 0.8.1
+      '@tsconfig/node10': 1.0.12
+      '@tsconfig/node12': 1.0.11
+      '@tsconfig/node14': 1.0.3
+      '@tsconfig/node16': 1.0.4
+      '@types/node': 22.19.3
+      acorn: 8.15.0
+      acorn-walk: 8.3.4
+      arg: 4.1.3
+      create-require: 1.1.1
+      diff: 4.0.2
+      make-error: 1.3.6
+      typescript: 4.9.5
+      v8-compile-cache-lib: 3.0.1
+      yn: 3.1.1
+    optionalDependencies:
+      '@swc/core': 1.15.7(@swc/helpers@0.5.18)
+      '@swc/wasm': 1.15.7
+
  tsbuffer-proto-generator@1.7.2:
    dependencies:
      k8w-crypto: 0.2.0
@@ -21536,18 +21573,18 @@ snapshots:

  tslib@2.8.1: {}

-  tsrpc-cli@2.4.5(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@20.19.27):
+  tsrpc-cli@2.4.5(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@22.19.3):
    dependencies:
      chalk: 4.1.2
      chokidar: 3.6.0
      fs-extra: 10.1.0
      glob: 7.2.3
-      inquirer: 8.2.7(@types/node@20.19.27)
+      inquirer: 8.2.7(@types/node@22.19.3)
      k8w-extend-native: 1.4.6
      minimist: 1.2.8
      ora: 5.4.1
      os-locale: 5.0.0
-      ts-node: 10.9.2(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@20.19.27)(typescript@4.9.5)
+      ts-node: 10.9.2(@swc/core@1.15.7(@swc/helpers@0.5.18))(@swc/wasm@1.15.7)(@types/node@22.19.3)(typescript@4.9.5)
      tsbuffer: 2.2.23
      tsbuffer-proto-generator: 1.7.2
      tsbuffer-schema: 2.2.0
@@ -22249,7 +22286,7 @@ snapshots:
  vitest@2.1.9(@types/node@22.19.3)(jsdom@20.0.3)(lightningcss@1.30.2)(terser@5.44.1):
    dependencies:
      '@vitest/expect': 2.1.9
-      '@vitest/mocker': 2.1.9(vite@5.4.21(@types/node@20.19.27)(lightningcss@1.30.2)(terser@5.44.1))
+      '@vitest/mocker': 2.1.9(vite@5.4.21(@types/node@22.19.3)(lightningcss@1.30.2)(terser@5.44.1))
      '@vitest/pretty-format': 2.1.9
      '@vitest/runner': 2.1.9
      '@vitest/snapshot': 2.1.9