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
This commit is contained in:
YHH
2026-01-05 22:17:30 +08:00
committed by GitHub
parent 12da6bd609
commit 30173f0764
49 changed files with 6073 additions and 103 deletions

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/**
* @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;
}

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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;
}
}

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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));
}
}

View File

@@ -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';

View File

@@ -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);
});
});
});

View File

@@ -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);
});
});
});

View File

@@ -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",

View File

@@ -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'
// ============================================================================

View File

@@ -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;
}
};
}

View File

@@ -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 });
}

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/**
* @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);
}

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@@ -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
);
}

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/**
* @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';

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@@ -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';