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
GitHub
450
packages/framework/math/src/Fixed32.ts
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450
packages/framework/math/src/Fixed32.ts
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/**
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* @zh Q16.16 定点数，用于确定性计算（帧同步）
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* @en Q16.16 fixed-point number for deterministic calculations (lockstep)
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*
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* @zh 使用 16 位整数部分 + 16 位小数部分，范围 ±32767.99998
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* @en Uses 16-bit integer + 16-bit fraction, range ±32767.99998
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*
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* @example
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* ```typescript
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* const a = Fixed32.from(3.14);
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* const b = Fixed32.from(2);
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* const c = a.mul(b); // 6.28
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* console.log(c.toNumber());
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* ```
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*/
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export class Fixed32 {
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/**
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* @zh 内部原始值（32位整数）
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* @en Internal raw value (32-bit integer)
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*/
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readonly raw: number;
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/**
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* @zh 小数位数
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* @en Fraction bits
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*/
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static readonly FRACTION_BITS = 16;
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/**
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* @zh 缩放因子 (2^16 = 65536)
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* @en Scale factor (2^16 = 65536)
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*/
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static readonly SCALE = 65536;
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/**
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* @zh 最大值 (约 32767.99998)
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* @en Maximum value (approximately 32767.99998)
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*/
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static readonly MAX_VALUE = 0x7FFFFFFF;
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/**
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* @zh 最小值 (约 -32768)
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* @en Minimum value (approximately -32768)
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*/
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static readonly MIN_VALUE = -0x80000000;
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/**
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* @zh 精度 (1/65536 ≈ 0.0000153)
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* @en Precision (1/65536 ≈ 0.0000153)
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*/
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static readonly EPSILON = 1;
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// ==================== 常量 ====================
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/** @zh 零 @en Zero */
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static readonly ZERO = new Fixed32(0);
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/** @zh 一 @en One */
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static readonly ONE = new Fixed32(Fixed32.SCALE);
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/** @zh 负一 @en Negative one */
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static readonly NEG_ONE = new Fixed32(-Fixed32.SCALE);
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/** @zh 二分之一 @en One half */
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static readonly HALF = new Fixed32(Fixed32.SCALE >> 1);
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/** @zh 圆周率 π @en Pi */
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static readonly PI = new Fixed32(205887); // π * 65536
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/** @zh 2π @en Two Pi */
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static readonly TWO_PI = new Fixed32(411775); // 2π * 65536
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/** @zh π/2 @en Pi divided by 2 */
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static readonly HALF_PI = new Fixed32(102944); // π/2 * 65536
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/** @zh 弧度转角度系数 (180/π) @en Radians to degrees factor */
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static readonly RAD_TO_DEG = new Fixed32(3754936); // (180/π) * 65536
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/** @zh 角度转弧度系数 (π/180) @en Degrees to radians factor */
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static readonly DEG_TO_RAD = new Fixed32(1144); // (π/180) * 65536
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// ==================== 构造 ====================
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/**
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* @zh 私有构造函数，使用静态方法创建实例
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* @en Private constructor, use static methods to create instances
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*/
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private constructor(raw: number) {
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// 确保是 32 位有符号整数
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this.raw = raw | 0;
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}
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/**
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* @zh 从浮点数创建定点数
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* @en Create fixed-point from floating-point number
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* @param n - @zh 浮点数值 @en Floating-point value
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*/
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static from(n: number): Fixed32 {
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return new Fixed32(Math.round(n * Fixed32.SCALE));
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}
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/**
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* @zh 从原始整数值创建定点数
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* @en Create fixed-point from raw integer value
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* @param raw - @zh 原始值 @en Raw value
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*/
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static fromRaw(raw: number): Fixed32 {
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return new Fixed32(raw);
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}
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/**
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* @zh 从整数创建定点数（无精度损失）
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* @en Create fixed-point from integer (no precision loss)
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* @param n - @zh 整数值 @en Integer value
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*/
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static fromInt(n: number): Fixed32 {
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return new Fixed32((n | 0) << Fixed32.FRACTION_BITS);
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}
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// ==================== 转换 ====================
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/**
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* @zh 转换为浮点数
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* @en Convert to floating-point number
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*/
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toNumber(): number {
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return this.raw / Fixed32.SCALE;
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}
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/**
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* @zh 获取原始整数值
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* @en Get raw integer value
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*/
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toRaw(): number {
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return this.raw;
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}
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/**
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* @zh 转换为整数（向下取整）
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* @en Convert to integer (floor)
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*/
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toInt(): number {
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return this.raw >> Fixed32.FRACTION_BITS;
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}
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/**
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* @zh 转换为字符串
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* @en Convert to string
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*/
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toString(): string {
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return `Fixed32(${this.toNumber().toFixed(5)})`;
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}
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// ==================== 基础运算 ====================
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/**
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* @zh 加法
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* @en Addition
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*/
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add(other: Fixed32): Fixed32 {
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return new Fixed32(this.raw + other.raw);
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}
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/**
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* @zh 减法
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* @en Subtraction
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*/
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sub(other: Fixed32): Fixed32 {
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return new Fixed32(this.raw - other.raw);
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}
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/**
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* @zh 乘法（使用 64 位中间结果防止溢出）
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* @en Multiplication (uses 64-bit intermediate to prevent overflow)
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*/
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mul(other: Fixed32): Fixed32 {
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// 拆分为高低 16 位进行乘法，避免溢出
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const a = this.raw;
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const b = other.raw;
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// 使用 BigInt 确保精度（JS 数字在大数时会丢失精度）
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// 或者使用拆分法
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const aLow = a & 0xFFFF;
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const aHigh = a >> 16;
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const bLow = b & 0xFFFF;
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const bHigh = b >> 16;
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// (aHigh * 2^16 + aLow) * (bHigh * 2^16 + bLow) / 2^16
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// = aHigh * bHigh * 2^16 + aHigh * bLow + aLow * bHigh + aLow * bLow / 2^16
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const lowLow = (aLow * bLow) >>> 16;
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const lowHigh = aLow * bHigh;
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const highLow = aHigh * bLow;
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const highHigh = aHigh * bHigh;
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const result = highHigh * Fixed32.SCALE + lowHigh + highLow + lowLow;
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return new Fixed32(result | 0);
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}
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/**
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* @zh 除法
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* @en Division
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* @throws @zh 除数为零时抛出错误 @en Throws when dividing by zero
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*/
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div(other: Fixed32): Fixed32 {
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if (other.raw === 0) {
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throw new Error('Fixed32: Division by zero');
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}
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// 先左移再除，保持精度
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const result = ((this.raw * Fixed32.SCALE) / other.raw) | 0;
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return new Fixed32(result);
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}
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/**
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* @zh 取模运算
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* @en Modulo operation
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*/
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mod(other: Fixed32): Fixed32 {
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return new Fixed32(this.raw % other.raw);
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}
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/**
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* @zh 取反
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* @en Negation
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*/
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neg(): Fixed32 {
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return new Fixed32(-this.raw);
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}
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/**
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* @zh 绝对值
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* @en Absolute value
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*/
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abs(): Fixed32 {
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return this.raw >= 0 ? this : new Fixed32(-this.raw);
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}
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// ==================== 比较运算 ====================
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/**
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* @zh 等于
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* @en Equal to
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*/
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eq(other: Fixed32): boolean {
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return this.raw === other.raw;
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}
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/**
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* @zh 不等于
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* @en Not equal to
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*/
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ne(other: Fixed32): boolean {
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return this.raw !== other.raw;
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}
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/**
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* @zh 小于
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* @en Less than
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*/
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lt(other: Fixed32): boolean {
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return this.raw < other.raw;
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}
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/**
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* @zh 小于等于
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* @en Less than or equal to
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*/
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le(other: Fixed32): boolean {
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return this.raw <= other.raw;
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}
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/**
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* @zh 大于
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* @en Greater than
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*/
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gt(other: Fixed32): boolean {
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return this.raw > other.raw;
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}
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/**
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* @zh 大于等于
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* @en Greater than or equal to
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*/
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ge(other: Fixed32): boolean {
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return this.raw >= other.raw;
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}
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/**
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* @zh 检查是否为零
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* @en Check if zero
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*/
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isZero(): boolean {
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return this.raw === 0;
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}
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/**
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* @zh 检查是否为正数
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* @en Check if positive
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*/
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isPositive(): boolean {
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return this.raw > 0;
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}
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/**
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* @zh 检查是否为负数
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* @en Check if negative
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*/
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isNegative(): boolean {
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return this.raw < 0;
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}
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// ==================== 数学函数 ====================
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/**
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* @zh 平方根（牛顿迭代法，确定性）
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* @en Square root (Newton's method, deterministic)
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*/
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static sqrt(x: Fixed32): Fixed32 {
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if (x.raw <= 0) return Fixed32.ZERO;
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// 牛顿迭代法
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let guess = x.raw;
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let prev = 0;
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// 固定迭代次数确保确定性
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for (let i = 0; i < 16; i++) {
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prev = guess;
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guess = ((guess + ((x.raw * Fixed32.SCALE) / guess) | 0) >> 1) | 0;
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if (guess === prev) break;
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}
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return new Fixed32(guess);
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}
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/**
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* @zh 向下取整
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* @en Floor
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*/
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static floor(x: Fixed32): Fixed32 {
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return new Fixed32(x.raw & ~(Fixed32.SCALE - 1));
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}
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/**
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* @zh 向上取整
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* @en Ceiling
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*/
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static ceil(x: Fixed32): Fixed32 {
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const frac = x.raw & (Fixed32.SCALE - 1);
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if (frac === 0) return x;
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return new Fixed32((x.raw & ~(Fixed32.SCALE - 1)) + Fixed32.SCALE);
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}
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/**
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* @zh 四舍五入
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* @en Round
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*/
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static round(x: Fixed32): Fixed32 {
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return new Fixed32((x.raw + (Fixed32.SCALE >> 1)) & ~(Fixed32.SCALE - 1));
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}
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/**
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* @zh 最小值
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* @en Minimum
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*/
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static min(a: Fixed32, b: Fixed32): Fixed32 {
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return a.raw < b.raw ? a : b;
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}
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/**
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* @zh 最大值
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* @en Maximum
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*/
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static max(a: Fixed32, b: Fixed32): Fixed32 {
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return a.raw > b.raw ? a : b;
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}
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/**
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* @zh 限制范围
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* @en Clamp to range
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*/
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static clamp(x: Fixed32, min: Fixed32, max: Fixed32): Fixed32 {
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if (x.raw < min.raw) return min;
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if (x.raw > max.raw) return max;
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return x;
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}
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/**
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* @zh 线性插值
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* @en Linear interpolation
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* @param a - @zh 起始值 @en Start value
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* @param b - @zh 结束值 @en End value
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* @param t - @zh 插值参数 (0-1) @en Interpolation parameter (0-1)
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*/
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static lerp(a: Fixed32, b: Fixed32, t: Fixed32): Fixed32 {
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// a + (b - a) * t
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return a.add(b.sub(a).mul(t));
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}
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/**
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* @zh 符号函数
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* @en Sign function
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* @returns @zh -1, 0, 或 1 @en -1, 0, or 1
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*/
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static sign(x: Fixed32): Fixed32 {
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if (x.raw > 0) return Fixed32.ONE;
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if (x.raw < 0) return Fixed32.NEG_ONE;
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return Fixed32.ZERO;
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}
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// ==================== 静态运算（便捷方法） ====================
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/**
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* @zh 加法（静态）
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* @en Addition (static)
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*/
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static add(a: Fixed32, b: Fixed32): Fixed32 {
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return a.add(b);
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}
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/**
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* @zh 减法（静态）
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* @en Subtraction (static)
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*/
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static sub(a: Fixed32, b: Fixed32): Fixed32 {
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return a.sub(b);
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}
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/**
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* @zh 乘法（静态）
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* @en Multiplication (static)
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*/
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static mul(a: Fixed32, b: Fixed32): Fixed32 {
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return a.mul(b);
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}
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/**
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* @zh 除法（静态）
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* @en Division (static)
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*/
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static div(a: Fixed32, b: Fixed32): Fixed32 {
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return a.div(b);
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}
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}
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/**
|
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* @zh Fixed32 数据接口，用于序列化
|
||||
* @en Fixed32 data interface for serialization
|
||||
*/
|
||||
export interface IFixed32 {
|
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raw: number;
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}
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298
packages/framework/math/src/FixedMath.ts
Normal file
298
packages/framework/math/src/FixedMath.ts
Normal file
@@ -0,0 +1,298 @@
|
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import { Fixed32 } from './Fixed32';
|
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|
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/**
|
||||
* @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
|
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* @en All trigonometric functions use precomputed lookup tables to ensure consistent results across all platforms
|
||||
*/
|
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export class FixedMath {
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/**
|
||||
* @zh 正弦表大小（每 90 度的采样点数）
|
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* @en Sine table size (samples per 90 degrees)
|
||||
*/
|
||||
private static readonly SIN_TABLE_SIZE = 1024;
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|
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/**
|
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* @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();
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/**
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||||
* @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++) {
|
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const angle = (i * Math.PI) / (2 * FixedMath.SIN_TABLE_SIZE);
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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;
|
||||
}
|
||||
}
|
||||
504
packages/framework/math/src/FixedVector2.ts
Normal file
504
packages/framework/math/src/FixedVector2.ts
Normal file
@@ -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';
|
||||
|
||||
|
||||
Reference in New Issue
Block a user