/**
 * @import { Mat4 } from './mat4.js'
 */
/**
 * A quaternion representing rotation in 3D space. Quaternions are typically used to represent
 * rotations in 3D applications, offering advantages over Euler angles including no gimbal lock and
 * more efficient interpolation.
 *
 * @category Math
 */
export class Quat {
    /**
     * A constant quaternion set to [0, 0, 0, 1] (the identity). Represents no rotation.
     *
     * @type {Quat}
     * @readonly
     */
    static readonly IDENTITY: Quat;
    /**
     * A constant quaternion set to [0, 0, 0, 0].
     *
     * @type {Quat}
     * @readonly
     */
    static readonly ZERO: Quat;
    /**
     * Creates a new Quat instance.
     *
     * @overload
     * @param {number} [x] - The x value. Defaults to 0.
     * @param {number} [y] - The y value. Defaults to 0.
     * @param {number} [z] - The z value. Defaults to 0.
     * @param {number} [w] - The w value. Defaults to 1.
     * @example
     * const q1 = new pc.Quat(); // defaults to 0, 0, 0, 1
     * const q2 = new pc.Quat(1, 2, 3, 4);
     */
    constructor(x?: number, y?: number, z?: number, w?: number);
    /**
     * Creates a new Quat instance.
     *
     * @overload
     * @param {number[]} arr - The array to set the vector values from.
     * @example
     * const q = new pc.Quat([1, 2, 3, 4]);
     */
    constructor(arr: number[]);
    /**
     * The x component of the quaternion.
     *
     * @type {number}
     */
    x: number;
    /**
     * The y component of the quaternion.
     *
     * @type {number}
     */
    y: number;
    /**
     * The z component of the quaternion.
     *
     * @type {number}
     */
    z: number;
    /**
     * The w component of the quaternion.
     *
     * @type {number}
     */
    w: number;
    /**
     * Returns an identical copy of the specified quaternion.
     *
     * @returns {this} A new quaternion identical to this one.
     * @example
     * const q = new pc.Quat(-0.11, -0.15, -0.46, 0.87);
     * const qclone = q.clone();
     *
     * console.log("The result of the cloning is: " + qclone.toString());
     */
    clone(): this;
    /**
     * Conjugates a quaternion.
     *
     * @param {Quat} [src] - The quaternion to conjugate. If not set, the operation is done in place.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat(1, 2, 3, 4);
     * q.conjugate();
     * // q is now [-1, -2, -3, 4]
     * @ignore
     */
    conjugate(src?: Quat): Quat;
    /**
     * Copies the contents of a source quaternion to a destination quaternion.
     *
     * @param {Quat} rhs - The quaternion to be copied.
     * @returns {Quat} Self for chaining.
     * @example
     * const src = new pc.Quat();
     * const dst = new pc.Quat();
     * dst.copy(src);
     * console.log("The two quaternions are " + (src.equals(dst) ? "equal" : "different"));
     */
    copy(rhs: Quat): Quat;
    /**
     * Calculates the dot product of two quaternions.
     *
     * @param {Quat} other - The quaternion to calculate the dot product with.
     * @returns {number} The dot product of the two quaternions.
     * @example
     * const a = new pc.Quat(1, 0, 0, 0);
     * const b = new pc.Quat(0, 1, 0, 0);
     * console.log("Dot product: " + a.dot(b)); // Outputs 0
     */
    dot(other: Quat): number;
    /**
     * Reports whether two quaternions are equal.
     *
     * @param {Quat} rhs - The quaternion to be compared against.
     * @returns {boolean} True if the quaternions are equal and false otherwise.
     * @example
     * const a = new pc.Quat();
     * const b = new pc.Quat();
     * console.log("The two quaternions are " + (a.equals(b) ? "equal" : "different"));
     */
    equals(rhs: Quat): boolean;
    /**
     * Reports whether two quaternions are equal using an absolute error tolerance.
     *
     * @param {Quat} rhs - The quaternion to be compared against.
     * @param {number} [epsilon] - The maximum difference between each component of the two
     * quaternions. Defaults to 1e-6.
     * @returns {boolean} True if the quaternions are equal and false otherwise.
     * @example
     * const a = new pc.Quat();
     * const b = new pc.Quat();
     * console.log("The two quaternions are approximately " + (a.equalsApprox(b, 1e-9) ? "equal" : "different"));
     */
    equalsApprox(rhs: Quat, epsilon?: number): boolean;
    /**
     * Gets the rotation axis and angle for a given quaternion. If a quaternion is created with
     * `setFromAxisAngle`, this method will return the same values as provided in the original
     * parameter list OR functionally equivalent values.
     *
     * @param {Vec3} axis - The 3-dimensional vector to receive the axis of rotation.
     * @returns {number} Angle, in degrees, of the rotation.
     * @example
     * const q = new pc.Quat();
     * q.setFromAxisAngle(new pc.Vec3(0, 1, 0), 90);
     * const v = new pc.Vec3();
     * const angle = q.getAxisAngle(v);
     * // Outputs 90
     * console.log(angle);
     * // Outputs [0, 1, 0]
     * console.log(v.toString());
     */
    getAxisAngle(axis: Vec3): number;
    /**
     * Converts this quaternion to Euler angles, specified in degrees. The decomposition uses an
     * **intrinsic XYZ** order, representing the angles required to achieve the quaternion's
     * orientation by rotating sequentially: first around the X-axis, then around the newly
     * transformed Y-axis, and finally around the resulting Z-axis.
     *
     * @param {Vec3} [eulers] - An optional 3-dimensional vector to receive the calculated
     * Euler angles (output parameter). If not provided, a new Vec3 object will be allocated
     * and returned.
     * @returns {Vec3} The 3-dimensional vector holding the Euler angles in degrees. This will be
     * the same object passed in as the `eulers` parameter (if one was provided).
     * @example
     * const q = new pc.Quat();
     * q.setFromAxisAngle(pc.Vec3.UP, 90);
     * const e = new pc.Vec3();
     * q.getEulerAngles(e);
     * // Outputs [0, 90, 0]
     * console.log(e.toString());
     */
    getEulerAngles(eulers?: Vec3): Vec3;
    /**
     * Generates the inverse of the specified quaternion.
     *
     * @param {Quat} [src] - The quaternion to invert. If not set, the operation is done in place.
     * @returns {Quat} Self for chaining.
     * @example
     * // Create a quaternion rotated 180 degrees around the y-axis
     * const rot = new pc.Quat().setFromEulerAngles(0, 180, 0);
     *
     * // Invert in place
     * rot.invert();
     */
    invert(src?: Quat): Quat;
    /**
     * Returns the magnitude of the specified quaternion.
     *
     * @returns {number} The magnitude of the specified quaternion.
     * @example
     * const q = new pc.Quat(0, 0, 0, 5);
     * const len = q.length();
     * // Outputs 5
     * console.log("The length of the quaternion is: " + len);
     */
    length(): number;
    /**
     * Returns the magnitude squared of the specified quaternion.
     *
     * @returns {number} The magnitude squared of the quaternion.
     * @example
     * const q = new pc.Quat(3, 4, 0, 0);
     * const lenSq = q.lengthSq();
     * // Outputs 25
     * console.log("The length squared of the quaternion is: " + lenSq);
     */
    lengthSq(): number;
    /**
     * Performs a linear interpolation between two quaternions. The result of the interpolation
     * is written to the quaternion calling the function.
     *
     * @param {Quat} lhs - The quaternion to interpolate from.
     * @param {Quat} rhs - The quaternion to interpolate to.
     * @param {number} alpha - The value controlling the interpolation in relation to the two input
     * quaternions. The value is in the range 0 to 1, 0 generating q1, 1 generating q2 and anything
     * in between generating a linear interpolation between the two.
     * @returns {Quat} Self for chaining.
     * @example
     * const q1 = new pc.Quat(-0.11, -0.15, -0.46, 0.87);
     * const q2 = new pc.Quat(-0.21, -0.21, -0.67, 0.68);
     *
     * const result = new pc.Quat();
     * result.lerp(q1, q2, 0);   // Return q1
     * result.lerp(q1, q2, 0.5); // Return the midpoint interpolant
     * result.lerp(q1, q2, 1);   // Return q2
     */
    lerp(lhs: Quat, rhs: Quat, alpha: number): Quat;
    /**
     * Returns the result of multiplying the specified quaternions together.
     *
     * @param {Quat} rhs - The quaternion used as the second multiplicand of the operation.
     * @returns {Quat} Self for chaining.
     * @example
     * const a = new pc.Quat().setFromEulerAngles(0, 30, 0);
     * const b = new pc.Quat().setFromEulerAngles(0, 60, 0);
     *
     * // a becomes a 90 degree rotation around the Y axis
     * // In other words, a = a * b
     * a.mul(b);
     *
     * console.log("The result of the multiplication is: " + a.toString());
     */
    mul(rhs: Quat): Quat;
    /**
     * Multiplies each element of a quaternion by a number.
     *
     * @param {number} scalar - The number to multiply by.
     * @param {Quat} [src] - The quaternion to scale. If not set, the operation is done in place.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat(1, 2, 3, 4);
     * q.mulScalar(2);
     * // q is now [2, 4, 6, 8]
     */
    mulScalar(scalar: number, src?: Quat): Quat;
    /**
     * Returns the result of multiplying the specified quaternions together.
     *
     * @param {Quat} lhs - The quaternion used as the first multiplicand of the operation.
     * @param {Quat} rhs - The quaternion used as the second multiplicand of the operation.
     * @returns {Quat} Self for chaining.
     * @example
     * const a = new pc.Quat().setFromEulerAngles(0, 30, 0);
     * const b = new pc.Quat().setFromEulerAngles(0, 60, 0);
     * const r = new pc.Quat();
     *
     * // r is set to a 90 degree rotation around the Y axis
     * // In other words, r = a * b
     * r.mul2(a, b);
     */
    mul2(lhs: Quat, rhs: Quat): Quat;
    /**
     * Normalizes the specified quaternion.
     *
     * @param {Quat} [src] - The quaternion to normalize. If not set, the operation is done in place.
     * @returns {Quat} The result of the normalization.
     * @example
     * const v = new pc.Quat(0, 0, 0, 5);
     * v.normalize();
     * // Outputs [0, 0, 0, 1]
     * console.log(v.toString());
     */
    normalize(src?: Quat): Quat;
    /**
     * Sets the specified quaternion to the supplied numerical values.
     *
     * @param {number} x - The x component of the quaternion.
     * @param {number} y - The y component of the quaternion.
     * @param {number} z - The z component of the quaternion.
     * @param {number} w - The w component of the quaternion.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat();
     * q.set(1, 0, 0, 0);
     *
     * // Outputs 1, 0, 0, 0
     * console.log("The result of the vector set is: " + q.toString());
     */
    set(x: number, y: number, z: number, w: number): Quat;
    /**
     * Sets a quaternion from an angular rotation around an axis.
     *
     * @param {Vec3} axis - World space axis around which to rotate. Should be normalized.
     * @param {number} angle - Angle to rotate around the given axis in degrees.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat();
     * q.setFromAxisAngle(pc.Vec3.UP, 90);
     */
    setFromAxisAngle(axis: Vec3, angle: number): Quat;
    /**
     * Sets this quaternion to represent a rotation specified by Euler angles in degrees.
     * The rotation is applied using an **intrinsic XYZ** order: first around the X-axis, then
     * around the newly transformed Y-axis, and finally around the resulting Z-axis.
     *
     * @param {number|Vec3} ex - The angle to rotate around the X-axis in degrees, or a Vec3
     * object containing the X, Y, and Z angles in degrees in its respective components (`ex.x`,
     * `ex.y`, `ex.z`).
     * @param {number} [ey] - The angle to rotate around the Y-axis in degrees. This parameter is
     * only used if `ex` is provided as a number.
     * @param {number} [ez] - The angle to rotate around the Z-axis in degrees. This parameter is
     * only used if `ex` is provided as a number.
     * @returns {Quat} The quaternion itself (this), now representing the orientation from the
     * specified XYZ Euler angles. Allows for method chaining.
     * @example
     * // Create a quaternion from 3 individual Euler angles (interpreted as X, Y, Z order)
     * const q1 = new pc.Quat();
     * q1.setFromEulerAngles(45, 90, 180); // 45 deg around X, then 90 deg around Y', then 180 deg around Z''
     * console.log("From numbers:", q1.toString());
     * @example
     * // Create the same quaternion from a Vec3 containing the angles (X, Y, Z)
     * const anglesVec = new pc.Vec3(45, 90, 180);
     * const q2 = new pc.Quat();
     * q2.setFromEulerAngles(anglesVec);
     * console.log("From Vec3:", q2.toString()); // Should match q1
     */
    setFromEulerAngles(ex: number | Vec3, ey?: number, ez?: number): Quat;
    /**
     * Converts the specified 4x4 matrix to a quaternion. Note that since a quaternion is purely a
     * representation for orientation, only the rotational part of the matrix is used.
     *
     * @param {Mat4} m - The 4x4 matrix to convert.
     * @returns {Quat} Self for chaining.
     * @example
     * // Create a 4x4 rotation matrix of 180 degrees around the y-axis
     * const rot = new pc.Mat4().setFromAxisAngle(pc.Vec3.UP, 180);
     *
     * // Convert to a quaternion
     * const q = new pc.Quat().setFromMat4(rot);
     */
    setFromMat4(m: Mat4): Quat;
    /**
     * Set the quaternion that represents the shortest rotation from one direction to another.
     *
     * @param {Vec3} from - The direction to rotate from. It should be normalized.
     * @param {Vec3} to - The direction to rotate to. It should be normalized.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat();
     * const from = new pc.Vec3(0, 0, 1);
     * const to = new pc.Vec3(0, 1, 0);
     * q.setFromDirections(from, to);
     */
    setFromDirections(from: Vec3, to: Vec3): Quat;
    /**
     * Performs a spherical interpolation between two quaternions. The result of the interpolation
     * is written to the quaternion calling the function.
     *
     * @param {Quat} lhs - The quaternion to interpolate from.
     * @param {Quat} rhs - The quaternion to interpolate to.
     * @param {number} alpha - The value controlling the interpolation in relation to the two input
     * quaternions. The value is in the range 0 to 1, 0 generating q1, 1 generating q2 and anything
     * in between generating a spherical interpolation between the two.
     * @returns {Quat} Self for chaining.
     * @example
     * const q1 = new pc.Quat(-0.11, -0.15, -0.46, 0.87);
     * const q2 = new pc.Quat(-0.21, -0.21, -0.67, 0.68);
     *
     * const result = new pc.Quat();
     * result.slerp(q1, q2, 0);   // Return q1
     * result.slerp(q1, q2, 0.5); // Return the midpoint interpolant
     * result.slerp(q1, q2, 1);   // Return q2
     */
    slerp(lhs: Quat, rhs: Quat, alpha: number): Quat;
    /**
     * Transforms a 3-dimensional vector by the specified quaternion.
     *
     * @param {Vec3} vec - The 3-dimensional vector to be transformed.
     * @param {Vec3} [res] - An optional 3-dimensional vector to receive the result of the transformation.
     * @returns {Vec3} The transformed vector (res if specified, otherwise a new Vec3).
     * @example
     * // Create a 3-dimensional vector
     * const v = new pc.Vec3(1, 2, 3);
     *
     * // Create a quaternion rotation
     * const q = new pc.Quat().setFromEulerAngles(10, 20, 30);
     *
     * const tv = q.transformVector(v);
     */
    transformVector(vec: Vec3, res?: Vec3): Vec3;
    /**
     * Set the values of the quaternion from an array.
     *
     * @param {number[]|ArrayBufferView} arr - The array to set the quaternion values from.
     * @param {number} [offset] - The zero-based index at which to start copying elements from the
     * array. Default is 0.
     * @returns {Quat} Self for chaining.
     * @example
     * const q = new pc.Quat();
     * q.fromArray([20, 10, 5, 0]);
     * // q is set to [20, 10, 5, 0]
     */
    fromArray(arr: number[] | ArrayBufferView, offset?: number): Quat;
    /**
     * Converts the quaternion to string form.
     *
     * @returns {string} The quaternion in string form.
     * @example
     * const q = new pc.Quat(0, 0, 0, 1);
     * // Outputs [0, 0, 0, 1]
     * console.log(q.toString());
     */
    toString(): string;
    /**
     * @overload
     * @param {number[]} [arr] - The array to populate with the quaternion's number
     * components. If not specified, a new array is created.
     * @param {number} [offset] - The zero-based index at which to start copying elements to the
     * array. Default is 0.
     * @returns {number[]} The quaternion as an array.
     */
    toArray(arr?: number[], offset?: number): number[];
    /**
     * @overload
     * @param {ArrayBufferView} arr - The array to populate with the quaternion's number
     * components. If not specified, a new array is created.
     * @param {number} [offset] - The zero-based index at which to start copying elements to the
     * array. Default is 0.
     * @returns {ArrayBufferView} The quaternion as an array.
     */
    toArray(arr: ArrayBufferView, offset?: number): ArrayBufferView;
}
import { Vec3 } from './vec3.js';
import type { Mat4 } from './mat4.js';