quat.ts

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

import { CCClass } from '../data/class';
import { ValueType } from '../value-types/value-type';
import { Mat3 } from './mat3';
import { IQuatLike, IVec3Like } from './type-define';
import { EPSILON, toDegree } from './utils';
import { Vec3 } from './vec3';
import { legacyCC } from '../global-exports';

/**
 * @en quaternion
 * @zh 四元数
 */
export class Quat extends ValueType {

    public static IDENTITY = Object.freeze(new Quat());

    /**
     * @en Obtain a copy of the given quaternion
     * @zh 获得指定四元数的拷贝
     */
    public static clone<Out extends IQuatLike> (a: Out) {
        return new Quat(a.x, a.y, a.z, a.w);
    }

    /**
     * @en Copy the given quaternion to the out quaternion
     * @zh 复制目标四元数
     */
    public static copy<Out extends IQuatLike, QuatLike extends IQuatLike> (out: Out, a: QuatLike) {
        out.x = a.x;
        out.y = a.y;
        out.z = a.z;
        out.w = a.w;
        return out;
    }

    /**
     * @en Sets the out quaternion with values of each component
     * @zh 设置四元数值
     */
    public static set<Out extends IQuatLike> (out: Out, x: number, y: number, z: number, w: number) {
        out.x = x;
        out.y = y;
        out.z = z;
        out.w = w;
        return out;
    }

    /**
     * @en Sets the out quaternion to an identity quaternion
     * @zh 将目标赋值为单位四元数
     */
    public static identity<Out extends IQuatLike> (out: Out) {
        out.x = 0;
        out.y = 0;
        out.z = 0;
        out.w = 1;
        return out;
    }

    /**
     * @en Sets the out quaternion with the shortest path orientation between two vectors, considering both vectors normalized
     * @zh 设置四元数为两向量间的最短路径旋转，默认两向量都已归一化
     */
    public static rotationTo<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, a: VecLike, b: VecLike) {
        const dot = Vec3.dot(a, b);
        if (dot < -0.999999) {
            Vec3.cross(v3_1, Vec3.UNIT_X, a);
            if (v3_1.length() < 0.000001) {
                Vec3.cross(v3_1, Vec3.UNIT_Y, a);
            }
            Vec3.normalize(v3_1, v3_1);
            Quat.fromAxisAngle(out, v3_1, Math.PI);
            return out;
        } else if (dot > 0.999999) {
            out.x = 0;
            out.y = 0;
            out.z = 0;
            out.w = 1;
            return out;
        } else {
            Vec3.cross(v3_1, a, b);
            out.x = v3_1.x;
            out.y = v3_1.y;
            out.z = v3_1.z;
            out.w = 1 + dot;
            return Quat.normalize(out, out);
        }
    }

    /**
     * @en Gets the rotation axis and the arc of rotation from the quaternion
     * @zh 获取四元数的旋转轴和旋转弧度
     * @param outAxis output axis
     * @param q input quaternion
     * @return radius of rotation
     */
    public static getAxisAngle<Out extends IQuatLike, VecLike extends IVec3Like> (outAxis: VecLike, q: Out) {
        const rad = Math.acos(q.w) * 2.0;
        const s = Math.sin(rad / 2.0);
        if (s !== 0.0) {
            outAxis.x = q.x / s;
            outAxis.y = q.y / s;
            outAxis.z = q.z / s;
        } else {
            // If s is zero, return any axis (no rotation - axis does not matter)
            outAxis.x = 1;
            outAxis.y = 0;
            outAxis.z = 0;
        }
        return rad;
    }

    /**
     * @en Quaternion multiplication and save the results to out quaternion
     * @zh 四元数乘法
     */
    public static multiply<Out extends IQuatLike, QuatLike_1 extends IQuatLike, QuatLike_2 extends IQuatLike> (out: Out, a: QuatLike_1, b: QuatLike_2) {
        const x = a.x * b.w + a.w * b.x + a.y * b.z - a.z * b.y;
        const y = a.y * b.w + a.w * b.y + a.z * b.x - a.x * b.z;
        const z = a.z * b.w + a.w * b.z + a.x * b.y - a.y * b.x;
        const w = a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z;
        out.x = x;
        out.y = y;
        out.z = z;
        out.w = w;
        return out;
    }

    /**
     * @en Quaternion scalar multiplication and save the results to out quaternion
     * @zh 四元数标量乘法
     */
    public static multiplyScalar<Out extends IQuatLike> (out: Out, a: Out, b: number) {
        out.x = a.x * b;
        out.y = a.y * b;
        out.z = a.z * b;
        out.w = a.w * b;
        return out;
    }

    /**
     * @en Quaternion multiplication and addition: A + B * scale
     * @zh 四元数乘加：A + B * scale
     */
    public static scaleAndAdd<Out extends IQuatLike> (out: Out, a: Out, b: Out, scale: number) {
        out.x = a.x + b.x * scale;
        out.y = a.y + b.y * scale;
        out.z = a.z + b.z * scale;
        out.w = a.w + b.w * scale;
        return out;
    }

    /**
     * @en Sets the out quaternion to represent a radian rotation around x axis
     * @zh 绕 X 轴旋转指定四元数
     * @param rad radius of rotation
     */
    public static rotateX<Out extends IQuatLike> (out: Out, a: Out, rad: number) {
        rad *= 0.5;

        const bx = Math.sin(rad);
        const bw = Math.cos(rad);
        const { x, y, z, w } = a;

        out.x = x * bw + w * bx;
        out.y = y * bw + z * bx;
        out.z = z * bw - y * bx;
        out.w = w * bw - x * bx;
        return out;
    }

    /**
     * @en Sets the out quaternion to represent a radian rotation around y axis
     * @zh 绕 Y 轴旋转指定四元数
     * @param rad radius of rotation
     */
    public static rotateY<Out extends IQuatLike> (out: Out, a: Out, rad: number) {
        rad *= 0.5;

        const by = Math.sin(rad);
        const bw = Math.cos(rad);
        const { x, y, z, w } = a;

        out.x = x * bw - z * by;
        out.y = y * bw + w * by;
        out.z = z * bw + x * by;
        out.w = w * bw - y * by;
        return out;
    }

    /**
     * @en Sets the out quaternion to represent a radian rotation around z axis
     * @zh 绕 Z 轴旋转指定四元数
     * @param rad radius of rotation
     */
    public static rotateZ<Out extends IQuatLike> (out: Out, a: Out, rad: number) {
        rad *= 0.5;

        const bz = Math.sin(rad);
        const bw = Math.cos(rad);
        const { x, y, z, w } = a;

        out.x = x * bw + y * bz;
        out.y = y * bw - x * bz;
        out.z = z * bw + w * bz;
        out.w = w * bw - z * bz;
        return out;
    }

    /**
     * @en Sets the out quaternion to represent a radian rotation around a given rotation axis in world space
     * @zh 绕世界空间下指定轴旋转四元数
     * @param axis axis of rotation, normalized by default
     * @param rad radius of rotation
     */
    public static rotateAround<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, rot: Out, axis: VecLike, rad: number) {
        // get inv-axis (local to rot)
        Quat.invert(qt_1, rot);
        Vec3.transformQuat(v3_1, axis, qt_1);
        // rotate by inv-axis
        Quat.fromAxisAngle(qt_1, v3_1, rad);
        Quat.multiply(out, rot, qt_1);
        return out;
    }

    /**
     * @en Sets the out quaternion to represent a radian rotation around a given rotation axis in local space
     * @zh 绕本地空间下指定轴旋转四元数
     * @param axis axis of rotation
     * @param rad radius of rotation
     */
    public static rotateAroundLocal<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, rot: Out, axis: VecLike, rad: number) {
        Quat.fromAxisAngle(qt_1, axis, rad);
        Quat.multiply(out, rot, qt_1);
        return out;
    }

    /**
     * @en Calculates the w component with xyz components, considering the given quaternion normalized
     * @zh 根据 xyz 分量计算 w 分量，默认已归一化
     */
    public static calculateW<Out extends IQuatLike> (out: Out, a: Out) {

        out.x = a.x;
        out.y = a.y;
        out.z = a.z;
        out.w = Math.sqrt(Math.abs(1.0 - a.x * a.x - a.y * a.y - a.z * a.z));
        return out;
    }

    /**
     * @en Quaternion dot product (scalar product)
     * @zh 四元数点积（数量积）
     */
    public static dot<Out extends IQuatLike> (a: Out, b: Out) {
        return a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
    }

    /**
     * @en Element by element linear interpolation: A + t * (B - A)
     * @zh 逐元素线性插值： A + t * (B - A)
     */
    public static lerp<Out extends IQuatLike> (out: Out, a: Out, b: Out, t: number) {
        out.x = a.x + t * (b.x - a.x);
        out.y = a.y + t * (b.y - a.y);
        out.z = a.z + t * (b.z - a.z);
        out.w = a.w + t * (b.w - a.w);
        return out;
    }

    /**
     * @en Spherical quaternion interpolation
     * @zh 四元数球面插值
     */
    public static slerp<Out extends IQuatLike, QuatLike_1 extends IQuatLike, QuatLike_2 extends IQuatLike>
        (out: Out, a: QuatLike_1, b: QuatLike_2, t: number) {
        // benchmarks:
        //    http://jsperf.com/quaternion-slerp-implementations

        let scale0 = 0;
        let scale1 = 0;
        let bx = b.x;
        let by = b.y;
        let bz = b.z;
        let bw = b.w;

        // calc cosine
        let cosom = a.x * b.x + a.y * b.y + a.z * b.z + a.w * b.w;
        // adjust signs (if necessary)
        if (cosom < 0.0) {
            cosom = -cosom;
            bx = -bx;
            by = -by;
            bz = -bz;
            bw = -bw;
        }
        // calculate coefficients
        if ((1.0 - cosom) > 0.000001) {
            // standard case (slerp)
            const omega = Math.acos(cosom);
            const sinom = Math.sin(omega);
            scale0 = Math.sin((1.0 - t) * omega) / sinom;
            scale1 = Math.sin(t * omega) / sinom;
        } else {
            // "from" and "to" quaternions are very close
            //  ... so we can do a linear interpolation
            scale0 = 1.0 - t;
            scale1 = t;
        }
        // calculate final values
        out.x = scale0 * a.x + scale1 * bx;
        out.y = scale0 * a.y + scale1 * by;
        out.z = scale0 * a.z + scale1 * bz;
        out.w = scale0 * a.w + scale1 * bw;

        return out;
    }

    /**
     * @en Spherical quaternion interpolation with two control points
     * @zh 带两个控制点的四元数球面插值
     */
    public static sqlerp<Out extends IQuatLike> (out: Out, a: Out, b: Out, c: Out, d: Out, t: number) {
        Quat.slerp(qt_1, a, d, t);
        Quat.slerp(qt_2, b, c, t);
        Quat.slerp(out, qt_1, qt_2, 2 * t * (1 - t));
        return out;
    }

    /**
     * @en Sets the inverse of the given quaternion to out quaternion
     * @zh 四元数求逆
     */
    public static invert<Out extends IQuatLike, QuatLike extends IQuatLike> (out: Out, a: QuatLike) {
        const dot = a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w;
        const invDot = dot ? 1.0 / dot : 0;

        // TODO: Would be faster to return [0,0,0,0] immediately if dot == 0

        out.x = -a.x * invDot;
        out.y = -a.y * invDot;
        out.z = -a.z * invDot;
        out.w = a.w * invDot;
        return out;
    }

    /**
     * @en Conjugating a quaternion, it's equivalent to the inverse of the unit quaternion, but more efficient
     * @zh 求共轭四元数，对单位四元数与求逆等价，但更高效
     */
    public static conjugate<Out extends IQuatLike> (out: Out, a: Out) {
        out.x = -a.x;
        out.y = -a.y;
        out.z = -a.z;
        out.w = a.w;
        return out;
    }

    /**
     * @en Calculates the length of the quaternion
     * @zh 求四元数长度
     */
    public static len<Out extends IQuatLike> (a: Out) {
        return Math.sqrt(a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w);
    }

    /**
     * @en Calculates the squared length of the quaternion
     * @zh 求四元数长度平方
     */
    public static lengthSqr<Out extends IQuatLike> (a: Out) {
        return a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w;
    }

    /**
     * @en Normalize the given quaternion
     * @zh 归一化四元数
     */
    public static normalize<Out extends IQuatLike> (out: Out, a: Out) {
        let len = a.x * a.x + a.y * a.y + a.z * a.z + a.w * a.w;
        if (len > 0) {
            len = 1 / Math.sqrt(len);
            out.x = a.x * len;
            out.y = a.y * len;
            out.z = a.z * len;
            out.w = a.w * len;
        }
        return out;
    }

    /**
     * @en Calculated the quaternion represents the given coordinates, considering all given vectors are normalized and mutually perpendicular
     * @zh 根据本地坐标轴朝向计算四元数，默认三向量都已归一化且相互垂直
     */
    public static fromAxes<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, xAxis: VecLike, yAxis: VecLike, zAxis: VecLike) {
        Mat3.set(m3_1,
            xAxis.x, xAxis.y, xAxis.z,
            yAxis.x, yAxis.y, yAxis.z,
            zAxis.x, zAxis.y, zAxis.z,
        );
        return Quat.normalize(out, Quat.fromMat3(out, m3_1));
    }

    /**
     * @en Calculates the quaternion with the up direction and the direction of the viewport
     * @zh 根据视口的前方向和上方向计算四元数
     * @param view The view direction, it`s must be normalized.
     * @param up The view up direction, it`s must be normalized, default value is (0, 1, 0).
     */
    public static fromViewUp<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, view: VecLike, up?: Vec3) {
        Mat3.fromViewUp(m3_1, view, up);
        return Quat.normalize(out, Quat.fromMat3(out, m3_1));
    }

    /**
     * @en Calculates the quaternion from a given rotary shaft and a radian rotation around it.
     * @zh 根据旋转轴和旋转弧度计算四元数
     */
    public static fromAxisAngle<Out extends IQuatLike, VecLike extends IVec3Like> (out: Out, axis: VecLike, rad: number) {
        rad = rad * 0.5;
        const s = Math.sin(rad);
        out.x = s * axis.x;
        out.y = s * axis.y;
        out.z = s * axis.z;
        out.w = Math.cos(rad);
        return out;
    }

    /**
     * @en Calculates the quaternion with the three-dimensional transform matrix, considering no scale included in the matrix
     * @zh 根据三维矩阵信息计算四元数，默认输入矩阵不含有缩放信息
     */
    public static fromMat3<Out extends IQuatLike> (out: Out, m: Mat3) {
        const {
            m00: m00, m03: m01, m06: m02,
            m01: m10, m04: m11, m07: m12,
            m02: m20, m05: m21, m08: m22,
        } = m;

        const trace = m00 + m11 + m22;

        if (trace > 0) {
            const s = 0.5 / Math.sqrt(trace + 1.0);

            out.w = 0.25 / s;
            out.x = (m21 - m12) * s;
            out.y = (m02 - m20) * s;
            out.z = (m10 - m01) * s;

        } else if ((m00 > m11) && (m00 > m22)) {
            const s = 2.0 * Math.sqrt(1.0 + m00 - m11 - m22);

            out.w = (m21 - m12) / s;
            out.x = 0.25 * s;
            out.y = (m01 + m10) / s;
            out.z = (m02 + m20) / s;

        } else if (m11 > m22) {
            const s = 2.0 * Math.sqrt(1.0 + m11 - m00 - m22);

            out.w = (m02 - m20) / s;
            out.x = (m01 + m10) / s;
            out.y = 0.25 * s;
            out.z = (m12 + m21) / s;

        } else {
            const s = 2.0 * Math.sqrt(1.0 + m22 - m00 - m11);

            out.w = (m10 - m01) / s;
            out.x = (m02 + m20) / s;
            out.y = (m12 + m21) / s;
            out.z = 0.25 * s;
        }

        return out;
    }

    /**
     * @en Calculates the quaternion with Euler angles, the rotation order is YZX
     * @zh 根据欧拉角信息计算四元数，旋转顺序为 YZX
     */
    public static fromEuler<Out extends IQuatLike> (out: Out, x: number, y: number, z: number) {
        x *= halfToRad;
        y *= halfToRad;
        z *= halfToRad;

        const sx = Math.sin(x);
        const cx = Math.cos(x);
        const sy = Math.sin(y);
        const cy = Math.cos(y);
        const sz = Math.sin(z);
        const cz = Math.cos(z);

        out.x = sx * cy * cz + cx * sy * sz;
        out.y = cx * sy * cz + sx * cy * sz;
        out.z = cx * cy * sz - sx * sy * cz;
        out.w = cx * cy * cz - sx * sy * sz;

        return out;
    }

    /**
     * @en Calculates the quaternion with given 2D angle (0, 0, z).
     * @zh 根据 2D 角度（0, 0, z）计算四元数
     *
     * @param out Output quaternion
     * @param z Angle to rotate around Z axis in degrees.
     */
    public static fromAngleZ<Out extends IQuatLike>(out: Out, z: number) {
        z *= halfToRad;
        out.x = out.y = 0;
        out.z = Math.sin(z);
        out.w = Math.cos(z);
        return out;
    }

    /**
     * @en This returns the X-axis vector of the quaternion
     * @zh 返回定义此四元数的坐标系 X 轴向量
     */
    public static toAxisX (out: IVec3Like, q: IQuatLike) {
        const fy = 2.0 * q.y;
        const fz = 2.0 * q.z;
        out.x = 1.0 - fy * q.y - fz * q.z;
        out.y = fy * q.x + fz * q.w;
        out.z = fz * q.x + fy * q.w;

        return out;
    }

    /**
     * @en This returns the Y-axis vector of the quaternion
     * @zh 返回定义此四元数的坐标系 Y 轴向量
     */
    public static toAxisY (out: IVec3Like, q: IQuatLike) {
        const fx = 2.0 * q.x;
        const fy = 2.0 * q.y;
        const fz = 2.0 * q.z;
        out.x = fy * q.x - fz * q.w;
        out.y = 1.0 - fx * q.x - fz * q.z;
        out.z = fz * q.y + fx * q.w;

        return out;
    }

    /**
     * @en This returns the Z-axis vector of the quaternion
     * @zh 返回定义此四元数的坐标系 Z 轴向量
     */
    public static toAxisZ (out: IVec3Like, q: IQuatLike) {
        const fx = 2.0 * q.x;
        const fy = 2.0 * q.y;
        const fz = 2.0 * q.z;
        out.x = fz * q.x - fy * q.w;
        out.y = fz * q.y - fx * q.w;
        out.z = 1.0 - fx * q.x - fy * q.y;

        return out;
    }

    /**
     * @en Converts the quaternion to angles, result angle x, y in the range of [-180, 180], z in the range of [-90, 90] interval, the rotation order is YZX
     * @zh 根据四元数计算欧拉角，返回角度 x, y 在 [-180, 180] 区间内, z 默认在 [-90, 90] 区间内，旋转顺序为 YZX
     * @param outerZ change z value range to [-180, -90] U [90, 180]
     */
    public static toEuler (out: IVec3Like, q: IQuatLike, outerZ?: boolean) {
        const { x, y, z, w } = q;
        let bank = 0;
        let heading = 0;
        let attitude = 0;
        const test = x * y + z * w;
        if (test > 0.499999) {
            bank = 0; // default to zero
            heading = toDegree(2 * Math.atan2(x, w));
            attitude = 90;
        } else if (test < -0.499999) {
            bank = 0; // default to zero
            heading = -toDegree(2 * Math.atan2(x, w));
            attitude = -90;
        } else {
            const sqx = x * x;
            const sqy = y * y;
            const sqz = z * z;
            bank = toDegree(Math.atan2(2 * x * w - 2 * y * z, 1 - 2 * sqx - 2 * sqz));
            heading = toDegree(Math.atan2(2 * y * w - 2 * x * z, 1 - 2 * sqy - 2 * sqz));
            attitude = toDegree(Math.asin(2 * test));
            if (outerZ) {
                bank = -180 * Math.sign(bank + 1e-6) + bank;
                heading = -180 * Math.sign(heading + 1e-6) + heading;
                attitude = 180 * Math.sign(attitude + 1e-6) - attitude;
            }
        }
        out.x = bank; out.y = heading; out.z = attitude;
        return out;
    }

    /**
     * @en Converts quaternion to an array
     * @zh 四元数转数组
     * @param ofs Array Start Offset
     */
    public static toArray<Out extends IWritableArrayLike<number>> (out: Out, q: IQuatLike, ofs = 0) {
        out[ofs + 0] = q.x;
        out[ofs + 1] = q.y;
        out[ofs + 2] = q.z;
        out[ofs + 3] = q.w;
        return out;
    }

    /**
     * @en Array to a quaternion
     * @zh 数组转四元数
     * @param ofs Array Start Offset
     */
    public static fromArray (out: IQuatLike, arr: IWritableArrayLike<number>, ofs = 0) {
        out.x = arr[ofs + 0];
        out.y = arr[ofs + 1];
        out.z = arr[ofs + 2];
        out.w = arr[ofs + 3];
        return out;
    }

    /**
     * @en Check whether two quaternions are equal
     * @zh 四元数等价判断
     */
    public static strictEquals (a: IQuatLike, b: IQuatLike) {
        return a.x === b.x && a.y === b.y && a.z === b.z && a.w === b.w;
    }

    /**
     * @en Check whether two quaternions are approximately equal
     * @zh 排除浮点数误差的四元数近似等价判断
     */
    public static equals (a: IQuatLike, b: IQuatLike, 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)) &&
            Math.abs(a.z - b.z) <= epsilon * Math.max(1.0, Math.abs(a.z), Math.abs(b.z)) &&
            Math.abs(a.w - b.w) <= epsilon * Math.max(1.0, Math.abs(a.w), Math.abs(b.w)));
    }

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

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

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

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

    constructor (other: Quat);

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

    constructor (x?: number | IQuatLike, y?: number, z?: number, w?: number) {
        super();
        if (x && typeof x === 'object') {
            this.x = x.x;
            this.y = x.y;
            this.z = x.z;
            this.w = x.w;
        } else {
            this.x = x || 0;
            this.y = y || 0;
            this.z = z || 0;
            this.w = w ?? 1;
        }
    }

    /**
     * @en clone the current Quat
     * @zh 克隆当前四元数。
     */
    public clone () {
        return new Quat(this.x, this.y, this.z, this.w);
    }

    /**
     * @en Set values with another quaternion
     * @zh 设置当前四元数使其与指定四元数相等。
     * @param other Specified quaternion
     * @returns `this`
     */
    public set (other: Quat): Quat;

    /**
     * @en Set the value of each component of the current quaternion
     * @zh 设置当前四元数指定元素值。
     * @returns `this`
     */
    public set (x?: number, y?: number, z?: number, w?: number): Quat;

    public set (x?: number | Quat, y?: number, z?: number, w?: number) {
        if (x && typeof x === 'object') {
            this.x = x.x;
            this.y = x.y;
            this.z = x.z;
            this.w = x.w;
        } else {
            this.x = x || 0;
            this.y = y || 0;
            this.z = z || 0;
            this.w = w ?? 1;
        }
        return this;
    }

    /**
     * @en Check whether the quaternion approximately equals another one
     * @zh 判断当前四元数是否在误差范围内与指定向量相等。
     * @param other Comparative quaternion
     * @param epsilon The error allowed. It`s should be a non-negative number.
     * @returns Returns `true' when the components of the two quaternions are equal within the specified error range; otherwise, returns `false'.
     */
    public equals (other: Quat, 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)) &&
            Math.abs(this.z - other.z) <= epsilon * Math.max(1.0, Math.abs(this.z), Math.abs(other.z)) &&
            Math.abs(this.w - other.w) <= epsilon * Math.max(1.0, Math.abs(this.w), Math.abs(other.w)));
    }

    /**
     * @en Check whether the current quaternion strictly equals other quaternion
     * @zh 判断当前四元数是否与指定四元数相等。
     * @param other Comparative quaternion
     * @returns Returns `true' when the components of the two quaternions are equal within the specified error range; otherwise, returns `false'.
     */
    public strictEquals (other: Quat) {
        return other && this.x === other.x && this.y === other.y && this.z === other.z && this.w === other.w;
    }

    /**
     * @en Convert quaternion to Euler angles
     * @zh 将当前四元数转化为欧拉角（x-y-z）并赋值给出口向量。
     * @param out the output vector
     */
    public getEulerAngles (out: Vec3) {
        return Quat.toEuler(out, this);
    }

    /**
     * @en Calculate the linear interpolation result between this quaternion and another one with given ratio
     * @zh 根据指定的插值比率，从当前四元数到目标四元数之间做线性插值。
     * @param to The target quaternion
     * @param ratio The interpolation coefficient. The range is [0,1].
     */
    public lerp (to: Quat, ratio: number) {
        this.x = this.x + ratio * (to.x - this.x);
        this.y = this.y + ratio * (to.y - this.y);
        this.z = this.z + ratio * (to.z - this.z);
        this.w = this.w + ratio * (to.w - this.w);
        return this;
    }

    /**
     * @en Calculates the spherical interpolation result between this quaternion and another one with the given ratio
     * @zh 根据指定的插值比率，从当前四元数到目标四元数之间做球面插值。
     * @param to The target quaternion
     * @param ratio The interpolation coefficient. The range is [0,1].
     */
    public slerp (to: Quat, ratio: number) {
        return Quat.slerp(this, this, to, ratio);
    }

    /**
     * @en Calculates the length of the quaternion
     * @zh 求四元数长度
     */
    public length () {
        return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w);
    }

    /**
     * @en Calculates the squared length of the quaternion
     * @zh 求四元数长度平方
     */
    public lengthSqr () {
        return this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w;
    }
}

const qt_1 = new Quat();
const qt_2 = new Quat();
const v3_1 = new Vec3();
const m3_1 = new Mat3();
const halfToRad = 0.5 * Math.PI / 180.0;

CCClass.fastDefine('cc.Quat', Quat, { x: 0, y: 0, z: 0, w: 1 });
legacyCC.Quat = Quat;

export function quat (other: Quat): Quat;
export function quat (x?: number, y?: number, z?: number, w?: number): Quat;

export function quat (x: number | Quat = 0, y: number = 0, z: number = 0, w: number = 1) {
    return new Quat(x as any, y, z, w);
}

legacyCC.quat = quat;