cocos/core/math/vec2.ts

/*
 Copyright (c) 2013-2016 Chukong Technologies Inc.
 Copyright (c) 2017-2020 Xiamen Yaji Software Co., Ltd.

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/**
 * @packageDocumentation
 * @module core/math
 */

import { CCClass } from '../data/class';
import { ValueType } from '../value-types/value-type';
import { Mat4 } from './mat4';
import { IMat3Like, IMat4Like, IVec2Like } from './type-define';
import { clamp, EPSILON, random } from './utils';

import { Vec3 } from './vec3';
import { legacyCC } from '../global-exports';

/**
 * @en Representation of 2D vectors and points.
 * @zh 二维向量。
 */
export class Vec2 extends ValueType {
    public static ZERO = Object.freeze(new Vec2(0, 0));
    public static ONE = Object.freeze(new Vec2(1, 1));
    public static NEG_ONE = Object.freeze(new Vec2(-1, -1));
    public static UNIT_X = Object.freeze(new Vec2(1, 0));
    public static UNIT_Y = Object.freeze(new Vec2(0, 1));

    /**
     * @en Obtains a clone of the given vector object
     * @zh 获得指定向量的拷贝
     */
    public static clone <Out extends IVec2Like> (a: Out) {
        return new Vec2(a.x, a.y);
    }

    /**
     * @en Copy the target vector and save the results to out vector object
     * @zh 复制目标向量
     */
    public static copy <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = a.x;
        out.y = a.y;
        return out;
    }

    /**
     * @en Sets the out vector with the given x and y values
     * @zh 设置向量值
     */
    public static set <Out extends IVec2Like> (out: Out, x: number, y: number) {
        out.x = x;
        out.y = y;
        return out;
    }

    /**
     * @en Element-wise vector addition and save the results to out vector object
     * @zh 逐元素向量加法
     */
    public static add <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = a.x + b.x;
        out.y = a.y + b.y;
        return out;
    }

    /**
     * @en Element-wise vector subtraction and save the results to out vector object
     * @zh 逐元素向量减法
     */
    public static subtract <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = a.x - b.x;
        out.y = a.y - b.y;
        return out;
    }

    /**
     * @en Element-wise vector multiplication and save the results to out vector object
     * @zh 逐元素向量乘法
     */
    public static multiply <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = a.x * b.x;
        out.y = a.y * b.y;
        return out;
    }

    /**
     * @en Element-wise vector division and save the results to out vector object
     * @zh 逐元素向量除法
     */
    public static divide <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = a.x / b.x;
        out.y = a.y / b.y;
        return out;
    }

    /**
     * @en Rounds up by elements of the vector and save the results to out vector object
     * @zh 逐元素向量向上取整
     */
    public static ceil <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = Math.ceil(a.x);
        out.y = Math.ceil(a.y);
        return out;
    }

    /**
     * @en Element-wise rounds down of the current vector and save the results to the out vector
     * @zh 逐元素向量向下取整
     */
    public static floor <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = Math.floor(a.x);
        out.y = Math.floor(a.y);
        return out;
    }

    /**
     * @en Calculates element-wise minimum values and save to the out vector
     * @zh 逐元素向量最小值
     */
    public static min <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = Math.min(a.x, b.x);
        out.y = Math.min(a.y, b.y);
        return out;
    }

    /**
     * @en Calculates element-wise maximum values and save to the out vector
     * @zh 逐元素向量最大值
     */
    public static max <Out extends IVec2Like> (out: Out, a: Out, b: Out) {
        out.x = Math.max(a.x, b.x);
        out.y = Math.max(a.y, b.y);
        return out;
    }

    /**
     * @en Calculates element-wise round results and save to the out vector
     * @zh 逐元素向量四舍五入取整
     */
    public static round <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = Math.round(a.x);
        out.y = Math.round(a.y);
        return out;
    }

    /**
     * @en Vector scalar multiplication and save the results to out vector object
     * @zh 向量标量乘法
     */
    public static multiplyScalar <Out extends IVec2Like> (out: Out, a: Out, b: number) {
        out.x = a.x * b;
        out.y = a.y * b;
        return out;
    }

    /**
     * @en Element-wise multiplication and addition with the equation: a + b * scale
     * @zh 逐元素向量乘加: A + B * scale
     */
    public static scaleAndAdd <Out extends IVec2Like> (out: Out, a: Out, b: Out, scale: number) {
        out.x = a.x + (b.x * scale);
        out.y = a.y + (b.y * scale);
        return out;
    }

    /**
     * @en Calculates the euclidean distance of two vectors
     * @zh 求两向量的欧氏距离
     */
    public static distance <Out extends IVec2Like> (a: Out, b: Out) {
        const x = b.x - a.x;
        const y = b.y - a.y;
        return Math.sqrt(x * x + y * y);
    }

    /**
     * @en Calculates the squared euclidean distance of two vectors
     * @zh 求两向量的欧氏距离平方
     */
    public static squaredDistance <Out extends IVec2Like> (a: Out, b: Out) {
        const x = b.x - a.x;
        const y = b.y - a.y;
        return x * x + y * y;
    }

    /**
     * @en Calculates the length of the vector
     * @zh 求向量长度
     */
    public static len <Out extends IVec2Like> (a: Out) {
        const x = a.x;
        const y = a.y;
        return Math.sqrt(x * x + y * y);
    }

    /**
     * @en Calculates the squared length of the vector
     * @zh 求向量长度平方
     */
    public static lengthSqr <Out extends IVec2Like> (a: Out) {
        const x = a.x;
        const y = a.y;
        return x * x + y * y;
    }

    /**
     * @en Sets each element to its negative value
     * @zh 逐元素向量取负
     */
    public static negate <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = -a.x;
        out.y = -a.y;
        return out;
    }

    /**
     * @en Sets each element to its inverse value, zero value will become Infinity
     * @zh 逐元素向量取倒数，接近 0 时返回 Infinity
     */
    public static inverse <Out extends IVec2Like> (out: Out, a: Out) {
        out.x = 1.0 / a.x;
        out.y = 1.0 / a.y;
        return out;
    }

    /**
     * @en Sets each element to its inverse value, zero value will remain zero
     * @zh 逐元素向量取倒数，接近 0 时返回 0
     */
    public static inverseSafe <Out extends IVec2Like> (out: Out, a: Out) {
        const x = a.x;
        const y = a.y;

        if (Math.abs(x) < EPSILON) {
            out.x = 0;
        } else {
            out.x = 1.0 / x;
        }

        if (Math.abs(y) < EPSILON) {
            out.y = 0;
        } else {
            out.y = 1.0 / y;
        }

        return out;
    }

    /**
     * @en Sets the normalized vector to the out vector
     * @zh 归一化向量
     */
    public static normalize <Out extends IVec2Like, Vec2Like extends IVec2Like> (out: Out, a: Vec2Like) {
        const x = a.x;
        const y = a.y;
        let len = x * x + y * y;
        if (len > 0) {
            len = 1 / Math.sqrt(len);
            out.x = x * len;
            out.y = y * len;
        }
        return out;
    }

    /**
     * @en Calculates the dot product of the vector
     * @zh 向量点积（数量积）
     */
    public static dot <Out extends IVec2Like> (a: Out, b: Out) {
        return a.x * b.x + a.y * b.y;
    }

    /**
     * @en Calculates the cross product of the vector
     * @zh 向量叉积（向量积），注意二维向量的叉积为与 Z 轴平行的三维向量
     */
    public static cross <Out extends IVec2Like> (out: Vec3, a: Out, b: Out) {
        out.x = out.y = 0;
        out.z = a.x * b.y - a.y * b.x;
        return out;
    }

    /**
     * @en Calculates the linear interpolation between two vectors with a given ratio
     * @zh 逐元素向量线性插值： A + t * (B - A)
     */
    public static lerp <Out extends IVec2Like> (out: Out, a: Out, b: Out, t: number) {
        const x = a.x;
        const y = a.y;
        out.x = x + t * (b.x - x);
        out.y = y + t * (b.y - y);
        return out;
    }

    /**
     * @en Generates a uniformly distributed random vector points from center to the surface of the unit sphere
     * @zh 生成一个在单位圆上均匀分布的随机向量
     * @param scale vector length
     */
    public static random <Out extends IVec2Like> (out: Out, scale?: number) {
        scale = scale || 1.0;
        const r = random() * 2.0 * Math.PI;
        out.x = Math.cos(r) * scale;
        out.y = Math.sin(r) * scale;
        return out;
    }

    /**
     * @en Vector and third order matrix multiplication, will complete the vector with a third value as one
     * @zh 向量与三维矩阵乘法，默认向量第三位为 1。
     */
    public static transformMat3 <Out extends IVec2Like, MatLike extends IMat3Like> (out: Out, a: Out, m: IMat3Like) {
        const x = a.x;
        const y = a.y;
        out.x = m.m00 * x + m.m03 * y + m.m06;
        out.y = m.m01 * x + m.m04 * y + m.m07;
        return out;
    }

    /**
     * @en Vector and third order matrix multiplication, will complete the vector with a third and a fourth element as one
     * @zh 向量与四维矩阵乘法，默认向量第三位为 0，第四位为 1。
     */
    public static transformMat4 <Out extends IVec2Like, MatLike extends IMat4Like> (out: Out, a: Out, m: IMat4Like) {
        const x = a.x;
        const y = a.y;
        out.x = m.m00 * x + m.m04 * y + m.m12;
        out.y = m.m01 * x + m.m05 * y + m.m13;
        return out;
    }

    /**
     * @en Gets the string representation of the given vector
     * @zh 返回向量的字符串表示
     */
    public static str <Out extends IVec2Like> (a: Out) {
        return `Vec2(${a.x}, ${a.y})`;
    }

    /**
     * @en Converts the given vector to an array
     * @zh 向量转数组
     * @param ofs Array Start Offset
     */
    public static toArray <Out extends IWritableArrayLike<number>> (out: Out, v: IVec2Like, ofs = 0) {
        out[ofs + 0] = v.x;
        out[ofs + 1] = v.y;
        return out;
    }

    /**
     * @en Converts the given array to a vector
     * @zh 数组转向量
     * @param ofs Array Start Offset
     */
    public static fromArray <Out extends IVec2Like> (out: Out, arr: IWritableArrayLike<number>, ofs = 0) {
        out.x = arr[ofs + 0];
        out.y = arr[ofs + 1];
        return out;
    }

    /**
     * @en Check the equality of the two given vectors
     * @zh 向量等价判断
     */
    public static strictEquals <Out extends IVec2Like> (a: Out, b: Out) {
        return a.x === b.x && a.y === b.y;
    }

    /**
     * @en Check whether the two given vectors are approximately equivalent
     * @zh 排除浮点数误差的向量近似等价判断
     */
    public static equals <Out extends IVec2Like> (a: Out, b: Out,  epsilon = EPSILON) {
        return (
            Math.abs(a.x - b.x)
            <= epsilon * Math.max(1.0, Math.abs(a.x), Math.abs(b.x))
            && Math.abs(a.y - b.y)
            <= epsilon * Math.max(1.0, Math.abs(a.y), Math.abs(b.y))
        );
    }

    /**
     * @en Calculates the radian angle between two vectors
     * @zh 求两向量夹角弧度
     */
    public static angle <Out extends IVec2Like> (a: Out, b: Out) {
        Vec2.normalize(v2_1, a);
        Vec2.normalize(v2_2, b);
        const cosine = Vec2.dot(v2_1, v2_2);
        if (cosine > 1.0) {
            return 0;
        }
        if (cosine < -1.0) {
            return Math.PI;
        }
        return Math.acos(cosine);
    }

    /**
     * @en x component.
     * @zh x 分量。
     */
    public declare x: number;

    /**
     * @en y component.
     * @zh y 分量。
     */
    public declare y: number;

    constructor (other: Vec2);

    constructor (x?: number, y?: number);

    constructor (x?: number | Vec2, y?: number) {
        super();
        if (x && typeof x === 'object') {
            this.x = x.x;
            this.y = x.y;
        } else {
            this.x = x || 0;
            this.y = y || 0;
        }
    }

    /**
     * @en clone a Vec2 value
     * @zh 克隆当前向量。
     */
    public clone () {
        return new Vec2(this.x, this.y);
    }

    /**
     * @en Set the current vector value with the given vector.
     * @zh 设置当前向量使其与指定向量相等。
     * @param other Specified vector
     * @return `this`
     */
    public set (other: Vec2);

    /**
     * @en Set the value of each component of the current vector.
     * @zh 设置当前向量的具体分量值。
     * @param x x value
     * @param y y value
     * @return `this`
     */
    public set (x?: number, y?: number);

    public set (x?: number | Vec2, y?: number) {
        if (x && typeof x === 'object') {
            this.x = x.x;
            this.y = x.y;
        } else {
            this.x = x || 0;
            this.y = y || 0;
        }
        return this;
    }

    /**
     * @en Check whether the vector approximately equals another one.
     * @zh 判断当前向量是否在误差范围内与指定向量相等。
     * @param other Specified vector
     * @param epsilon The error allowed. It`s should be a non-negative number.
     * @return Returns `true` when the components of both vectors are equal within the specified range of error; otherwise it returns `false`.
     */
    public equals (other: Vec2, epsilon = EPSILON) {
        return (
            Math.abs(this.x - other.x)
            <= epsilon * Math.max(1.0, Math.abs(this.x), Math.abs(other.x))
            && Math.abs(this.y - other.y)
            <= epsilon * Math.max(1.0, Math.abs(this.y), Math.abs(other.y))
        );
    }

    /**
     * @en Check whether the vector approximately equals another one.
     * @zh 判断当前向量是否在误差范围内与指定分量的向量相等。
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     * @param epsilon The error allowed. It`s should be a non-negative number.
     * @return Returns `true` when the components of both vectors are equal within the specified range of error; otherwise it returns `false`.
     */
    public equals2f (x: number, y: number, epsilon = EPSILON) {
        return (
            Math.abs(this.x - x)
            <= epsilon * Math.max(1.0, Math.abs(this.x), Math.abs(x))
            && Math.abs(this.y - y)
            <= epsilon * Math.max(1.0, Math.abs(this.y), Math.abs(y))
        );
    }

    /**
     * @en Check whether the current vector strictly equals another Vec2.
     * @zh 判断当前向量是否与指定向量相等。
     * @param other specified vector
     * @return Returns `true` when the components of both vectors are equal within the specified range of error; otherwise it returns `false`.
     */
    public strictEquals (other: Vec2) {
        return other && this.x === other.x && this.y === other.y;
    }

    /**
     * @en Check whether the current vector strictly equals another Vec2.
     * @zh 判断当前向量是否与指定分量的向量相等。
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     * @return Returns `true` when the components of both vectors are equal within the specified range of error; otherwise it returns `false`.
     */
    public strictEquals2f (x: number, y: number) {
        return this.x === x && this.y === y;
    }

    /**
     * @en Transform to string with vector information.
     * @zh 返回当前向量的字符串表示。
     * @returns The string with vector information
     */
    public toString () {
        return `(${this.x.toFixed(2)}, ${this.y.toFixed(2)})`;
    }

    /**
     * @en Calculate linear interpolation result between this vector and another one with given ratio.
     * @zh 根据指定的插值比率，从当前向量到目标向量之间做插值。
     * @param to Target vector
     * @param ratio The interpolation coefficient.The range is [0,1].
     */
    public lerp (to: Vec2, ratio: number) {
        const x = this.x;
        const y = this.y;
        this.x = x + ratio * (to.x - x);
        this.y = y + ratio * (to.y - y);
        return this;
    }

    /**
     * @en Clamp the vector between minInclusive and maxInclusive.
     * @zh 设置当前向量的值，使其各个分量都处于指定的范围内。
     * @param minInclusive Minimum value allowed
     * @param maxInclusive Maximum value allowed
     * @return `this`
     */
    public clampf (minInclusive: Vec2, maxInclusive: Vec2) {
        this.x = clamp(this.x, minInclusive.x, maxInclusive.x);
        this.y = clamp(this.y, minInclusive.y, maxInclusive.y);
        return this;
    }

    /**
     * @en Adds the current vector with another one and return this
     * @zh 向量加法。将当前向量与指定向量的相加
     * @param other specified vector
     */
    public add (other: Vec2) {
        this.x += other.x;
        this.y += other.y;
        return this;
    }

    /**
     * @en Adds the current vector with another one and return this
     * @zh 向量加法。将当前向量与指定分量的向量相加
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     */
    public add2f (x: number, y: number) {
        this.x += x;
        this.y += y;
        return this;
    }

    /**
     * @en Subtracts one vector from this, and returns this.
     * @zh 向量减法。将当前向量减去指定向量
     * @param other specified vector
     */
    public subtract (other: Vec2) {
        this.x -= other.x;
        this.y -= other.y;
        return this;
    }

    /**
     * @en Subtracts one vector from this, and returns this.
     * @zh 向量减法。将当前向量减去指定分量的向量
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     */
    public subtract2f (x: number, y: number) {
        this.x -= x;
        this.y -= y;
        return this;
    }

    /**
     * @en Multiplies the current vector with a number, and returns this.
     * @zh 向量数乘。将当前向量数乘指定标量
     * @param scalar scalar number
     */
    public multiplyScalar (scalar: number) {
        if (typeof scalar === 'object') { console.warn('should use Vec2.multiply for vector * vector operation'); }
        this.x *= scalar;
        this.y *= scalar;
        return this;
    }

    /**
     * @en Multiplies the current vector with another one and return this
     * @zh 向量乘法。将当前向量乘以与指定向量的结果赋值给当前向量。
     * @param other specified vector
     */
    public multiply (other: Vec2) {
        if (typeof other !== 'object') { console.warn('should use Vec2.scale for vector * scalar operation'); }
        this.x *= other.x;
        this.y *= other.y;
        return this;
    }

    /**
     * @en Multiplies the current vector with another one and return this
     * @zh 向量乘法。将当前向量与指定分量的向量相乘的结果赋值给当前向量。
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     */
    public multiply2f (x: number, y: number) {
        this.x *= x;
        this.y *= y;
        return this;
    }

    /**
     * @en Element-wisely divides this vector with another one, and return this.
     * @zh 向量逐元素相除。将当前向量与指定分量的向量相除的结果赋值给当前向量。
     * @param other specified vector
     */
    public divide (other: Vec2) {
        this.x /= other.x;
        this.y /= other.y;
        return this;
    }

    /**
     * @en Element-wisely divides this vector with another one, and return this.
     * @zh 向量逐元素相除。将当前向量与指定分量的向量相除的结果赋值给当前向量。
     * @param x The x value of specified vector
     * @param y The y value of specified vector
     */
    public divide2f (x: number, y: number) {
        this.x /= x;
        this.y /= y;
        return this;
    }

    /**
     * @en Sets each component of this vector with its negative value
     * @zh 将当前向量的各个分量取反
     */
    public negative () {
        this.x = -this.x;
        this.y = -this.y;
        return this;
    }

    /**
     * @en Calculates the dot product with another vector
     * @zh 向量点乘。
     * @param other specified vector
     * @return The result of calculates the dot product with another vector
     */
    public dot (other: Vec2) {
        return this.x * other.x + this.y * other.y;
    }

    /**
     * @en Calculates the cross product with another vector.
     * @zh 向量叉乘。
     * @param other specified vector
     * @return `out`
     */
    public cross (other: Vec2) {
        return this.x * other.y - this.y * other.x;
    }

    /**
     * @en Returns the length of this vector.
     * @zh 计算向量的长度（模）。
     * @return Length of vector
     */
    public length () {
        return Math.sqrt(this.x * this.x + this.y * this.y);
    }

    /**
     * @en Returns the squared length of this vector.
     * @zh 计算向量长度（模）的平方。
     * @return the squared length of this vector
     */
    public lengthSqr () {
        return this.x * this.x + this.y * this.y;
    }

    /**
     * @en Normalize the current vector.
     * @zh 将当前向量归一化。
     */
    public normalize () {
        const x = this.x;
        const y = this.y;
        let len = x * x + y * y;
        if (len > 0) {
            len = 1 / Math.sqrt(len);
            this.x *= len;
            this.y *= len;
        }
        return this;
    }

    /**
     * @en Calculates radian angle between two vectors
     * @zh 获取当前向量和指定向量之间的角度。
     * @param other specified vector
     * @return The angle between the current vector and the specified vector (in radians); if there are zero vectors in the current vector and the specified vector, 0 is returned.
     */
    public angle (other: Vec2) {
        const magSqr1 = this.lengthSqr();
        const magSqr2 = other.lengthSqr();

        if (magSqr1 === 0 || magSqr2 === 0) {
            console.warn('Can\'t get angle between zero vector');
            return 0.0;
        }

        const dot = this.dot(other);
        let theta = dot / (Math.sqrt(magSqr1 * magSqr2));
        theta = clamp(theta, -1.0, 1.0);
        return Math.acos(theta);
    }

    /**
     * @en Get angle in radian between this and vector with direction.
     * @zh 获取当前向量和指定向量之间的有符号角度。<br/>
     * 有符号角度的取值范围为 (-180, 180]，当前向量可以通过逆时针旋转有符号角度与指定向量同向。<br/>
     * @param other specified vector
     * @return The signed angle between the current vector and the specified vector (in radians); if there is a zero vector in the current vector and the specified vector, 0 is returned.
     */
    public signAngle (other: Vec2) {
        const angle = this.angle(other);
        return this.cross(other) < 0 ? -angle : angle;
    }

    /**
     * @en Rotates the current vector by an angle in radian value
     * @zh 将当前向量的旋转
     * @param radians radius of rotation
     */
    public rotate (radians: number) {
        const x = this.x;
        const y = this.y;

        const sin = Math.sin(radians);
        const cos = Math.cos(radians);
        this.x = cos * x - sin * y;
        this.y = sin * x + cos * y;
        return this;
    }

    /**
     * @en Projects the current vector on another one
     * @zh 计算当前向量在指定向量上的投影向量。
     * @param other specified vector
     */
    public project (other: Vec2) {
        const scalar = this.dot(other) / other.dot(other);
        this.x = other.x * scalar;
        this.y = other.y * scalar;
        return this;
    }

    /**
     * @en Transforms the vec2 with a mat4. 3rd vector component is implicitly '0', 4th vector component is implicitly '1'
     * @zh 将当前向量视为 z 分量为 0、w 分量为 1 的四维向量，<br/>
     * 应用四维矩阵变换到当前矩阵<br/>
     * @param matrix matrix to transform with
     */
    public transformMat4 (matrix: Mat4) {
        const x = this.x;
        const y = this.y;
        this.x = matrix.m00 * x + matrix.m04 * y + matrix.m12;
        this.y = matrix.m01 * x + matrix.m05 * y + matrix.m13;
        return this;
    }
}

const v2_1 = new Vec2();
const v2_2 = new Vec2();

CCClass.fastDefine('cc.Vec2', Vec2, { x: 0, y: 0 });
legacyCC.Vec2 = Vec2;

export function v2 (other: Vec2): Vec2;
export function v2 (x?: number, y?: number): Vec2;

export function v2 (x?: number | Vec2, y?: number) {
    return new Vec2(x as any, y);
}

legacyCC.v2 = v2;