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221 lines
7.8 KiB
221 lines
7.8 KiB
import { isVector2 } from './is';
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const VECTOR_ZERO = [0, 0, 0];
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/**
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* <zh/> 两个向量求和
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*
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* <en/> Adds two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量的和 | <en/> The sum of the two vectors
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*/
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export function add(a, b) {
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return a.map((v, i) => v + b[i]);
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}
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/**
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* <zh/> 两个向量求差
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*
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* <en/> Subtracts two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量的差 | <en/> The difference of the two vectors
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*/
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export function subtract(a, b) {
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return a.map((v, i) => v - b[i]);
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}
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/**
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* <zh/> 两个向量求积或者向量和标量求积
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*
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* <en/> Multiplies two vectors or a vector and a scalar
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* @param a - <zh/> 向量 | <en/> The vector
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* @param b - <zh/> 向量或者标量 | <en/> The vector or scalar
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* @returns <zh/> 两个向量的积或者向量和标量的积 | <en/> The product of the two vectors or the product of the vector and scalar
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*/
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export function multiply(a, b) {
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if (typeof b === 'number')
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return a.map((v) => v * b);
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return a.map((v, i) => v * b[i]);
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}
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/**
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* <zh/> 两个向量求商或者向量和标量求商
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*
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* <en/> Divides two vectors or a vector and a scalar
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* @param a - <zh/> 向量 | <en/> The vector
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* @param b - <zh/> 向量或者标量 | <en/> The vector or scalar
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* @returns <zh/> 两个向量的商或者向量和标量的商 | <en/> The quotient of the two vectors or the quotient of the vector and scalar
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*/
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export function divide(a, b) {
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if (typeof b === 'number')
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return a.map((v) => v / b);
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return a.map((v, i) => v / b[i]);
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}
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/**
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* <zh/> 两个向量求点积
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*
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* <en/> Calculates the dot product of two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量的点积 | <en/> The dot product of the two vectors
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*/
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export function dot(a, b) {
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return a.reduce((sum, v, i) => sum + v * b[i], 0);
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}
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/**
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* <zh/> 两个二维向量求叉积
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*
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* <en/> Calculates the cross product of two vectors in three-dimensional Euclidean space
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量的叉积 | <en/> The cross product of the two vectors
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*/
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export function cross(a, b) {
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const a2 = toVector3(a);
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const b2 = toVector3(b);
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return [a2[1] * b2[2] - a2[2] * b2[1], a2[2] * b2[0] - a2[0] * b2[2], a2[0] * b2[1] - a2[1] * b2[0]];
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}
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/**
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* <zh/> 向量缩放
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*
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* <en/> Scales a vector by a scalar number
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* @param a - <zh/> 向量 | <en/> The vector to scale
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* @param s - <zh/> 缩放系数 | <en/> Scale factor
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* @returns <zh/> 缩放后的向量 | <en/> The scaled vector
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*/
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export function scale(a, s) {
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return a.map((v) => v * s);
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}
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/**
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* <zh/> 计算两个向量间的欧几里得距离
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*
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* <en/> Calculates the Euclidean distance between two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量间的距离 | <en/> The distance between the two vectors
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*/
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export function distance(a, b) {
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return Math.sqrt(a.reduce((sum, v, i) => sum + Math.pow((v - b[i] || 0), 2), 0));
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}
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/**
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* <zh/> 计算两个向量间的曼哈顿距离
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*
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* <en/> Calculates the Manhattan distance between two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns <zh/> 两个向量间的距离 | <en/> The distance between the two vectors
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*/
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export function manhattanDistance(a, b) {
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return a.reduce((sum, v, i) => sum + Math.abs(v - b[i]), 0);
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}
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/**
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* <zh/> 标准化向量（使长度为 1）
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*
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* <en/> Normalizes a vector (making its length 1)
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* @param a - <zh/> 要标准化的向量 | <en/> The vector to normalize
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* @returns <zh/> 标准化后的向量 | <en/> The normalized vector
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*/
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export function normalize(a) {
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const length = a.reduce((sum, v) => sum + Math.pow(v, 2), 0);
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return a.map((v) => v / Math.sqrt(length));
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}
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/**
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* <zh/> 计算两个向量间的夹角，输出为锐角余弦值
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*
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* <en/> Get the angle between two vectors
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @param clockwise - <zh/> 是否顺时针 | <en/> Whether to calculate the angle in a clockwise direction
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* @returns <zh/> 弧度值 | <en/> The angle in radians
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*/
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export function angle(a, b, clockwise = false) {
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const determinant = a[0] * b[1] - a[1] * b[0];
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let angle = Math.acos(multiply(a, b).reduce((sum, v) => sum + v, 0) /
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(distance(a, VECTOR_ZERO) * distance(b, VECTOR_ZERO)));
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// If clockwise is true and determinant is negative, adjust the angle
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if (clockwise && determinant < 0) {
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angle = 2 * Math.PI - angle;
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}
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return angle;
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}
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/**
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* <zh/> 判断两个向量是否完全相等（使用 === 比较）
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*
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* <en/> Returns whether or not the vectors exactly have the same elements in the same position (when compared with ===)
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* @param a - <zh/> 第一个向量 | <en/> The first vector
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* @param b - <zh/> 第二个向量 | <en/> The second vector
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* @returns - <zh/> 是否相等 | <en/> Whether or not the vectors are equal
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*/
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export function exactEquals(a, b) {
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return a.every((v, i) => v === b[i]);
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}
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/**
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* <zh/> 计算向量的垂直向量
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*
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* <en/> Calculates the perpendicular vector to a given vector
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* @param a - <zh/> 原始向量 | <en/> The original vector
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* @param clockwise - <zh/> 是否顺时针 | <en/> Whether to calculate the perpendicular vector in a clockwise direction
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* @returns <zh/> 原始向量的垂直向量 | <en/> The perpendicular vector to the original vector
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*/
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export function perpendicular(a, clockwise = true) {
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return clockwise ? [-a[1], a[0]] : [a[1], -a[0]];
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}
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/**
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* <zh/> 计算向量的模
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*
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* <en/> Calculates the modulus of a vector
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* @param a - <zh/> 原始向量 | <en/> The original vector
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* @param b - <zh/> 模 | <en/> The modulus
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* @returns - <zh/> 向量的模 | <en/> The modulus of the vector
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*/
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export function mod(a, b) {
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return a.map((v) => v % b);
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}
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/**
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* <zh/> 向量强制转换为二维向量
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*
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* <en/> Force vector to be two-dimensional
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* @param a - <zh/> 原始向量 | <en/> The original vector
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* @returns <zh/> 二维向量 | <en/> Two-dimensional vector
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*/
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export function toVector2(a) {
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return [a[0], a[1]];
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}
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/**
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* <zh/> 向量强制转换为三维向量
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*
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* <en/> Force vector to be three-dimensional
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* @param a - <zh/> 原始向量 | <en/> The original vector
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* @returns - <zh/> 三维向量 | <en/> Three-dimensional vector
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*/
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export function toVector3(a) {
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return isVector2(a) ? [a[0], a[1], 0] : a;
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}
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/**
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* <zh/> 计算向量与 x 轴正方向的夹角（弧度制）
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*
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* <en/> The angle between the vector and the positive direction of the x-axis (radians)
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* @param a - <zh/> 向量 | <en/> The vector
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* @returns <zh/> 弧度值 | <en/> The angle in radians
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*/
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export function rad(a) {
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const [x, y] = a;
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if (!x && !y)
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return 0;
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return Math.atan2(y, x);
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}
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/**
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* <zh/> 旋转向量（角度制）
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*
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* <en/> Rotational vector (Angle system)
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* @param a - <zh/> 向量 | <en/> The vector
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* @param angle - <zh/> 旋转角度 | <en/> The rotation angle
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* @returns <zh/> 向量 | <en/> The vector
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*/
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export function rotate(a, angle) {
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const [dx, dy] = a;
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if (angle % 360 === 0)
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return [dx, dy];
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const rad = (angle * Math.PI) / 180;
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const cos = Math.cos(rad);
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const sin = Math.sin(rad);
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return [dx * cos - dy * sin, dx * sin + dy * cos];
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}
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//# sourceMappingURL=vector.js.map
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