import type { CubicPath2d } from '../path/cubic2d.ts';
import type { Pipeable } from '../utils.ts';
import type { Vector2 } from '../vector/vector2.ts';
import type { Basis2dTypeId } from './basis2d.internal.ts';
import type { Bezier2d } from './bezier2d.ts';
/**
 * A Basis Spline (uniform cubic B-spline) in 2D space.
 *
 * All fields are readonly and immutable, and all operations create new instances.
 *
 * The characteristic matrix that identifies this spline family lives in the
 * `characteristic` module as `Characteristic.cubicBasisSpline`.
 *
 * @since 1.0.0
 */
export interface Basis2d extends Pipeable {
    readonly [Basis2dTypeId]: Basis2dTypeId;
    [Symbol.iterator](): Iterator<Vector2>;
}
/**
 * Checks if a value is a `Basis2d`.
 *
 * @param p - The value to check.
 * @returns `true` if the value is a `Basis2d`, `false` otherwise.
 * @since 1.0.0
 */
export declare const isBasis2d: (p: unknown) => p is Basis2d;
/**
 * Creates a new `Basis2d` instance.
 *
 * @param p0 - The first control point.
 * @param p1 - The second control point.
 * @param p2 - The third control point.
 * @param p3 - The fourth control point.
 * @returns A new `Basis2d` instance.
 * @since 1.0.0
 */
export declare const make: (p0: Vector2, p1: Vector2, p2: Vector2, p3: Vector2) => Basis2d;
/**
 * Creates a new `Basis2d` instance from an array of control points.
 *
 * @param points - The control points.
 * @returns A new `Basis2d` instance.
 * @since 1.0.0
 */
export declare const fromArray: (points: ReadonlyArray<Vector2>) => Basis2d;
/**
 * Creates a new `Basis2d` from an array of `[x, y]` tuples.
 *
 * @param tuples - The control points as `[x, y]` tuples.
 * @returns A new `Basis2d` instance.
 * @since 2.0.0
 */
export declare const fromTuples: (tuples: ReadonlyArray<readonly [number, number]>) => Basis2d;
export declare const append: {
    /**
     * Appends control points to a `Basis2d`.
     *
     * @param points - The control points to append.
     * @returns A function that takes a `Basis2d` and returns a new `Basis2d` instance with the appended control points.
     * @since 1.0.0
     */
    (...points: ReadonlyArray<Vector2>): (p: Basis2d) => Basis2d;
    /**
     * Appends control points to a `Basis2d`.
     *
     * @param p - The `Basis2d` to append the control points to.
     * @param points - The control points to append.
     * @returns A new `Basis2d` instance with the appended control points.
     * @since 1.0.0
     */
    (p: Basis2d, ...points: ReadonlyArray<Vector2>): Basis2d;
};
export declare const prepend: {
    /**
     * Prepends control points to a `Basis2d`.
     *
     * @param points - The control points to prepend.
     * @returns A function that takes a `Basis2d` and returns a new `Basis2d` instance with the prepended control points.
     * @since 1.0.0
     */
    (...points: ReadonlyArray<Vector2>): (p: Basis2d) => Basis2d;
    /**
     * Prepends control points to a `Basis2d`.
     *
     * @param p - The `Basis2d` to prepend the control points to.
     * @param points - The control points to prepend.
     * @returns A new `Basis2d` instance with the prepended control points.
     * @since 1.0.0
     */
    (p: Basis2d, ...points: ReadonlyArray<Vector2>): Basis2d;
};
/**
 * Triplicates the endpoints of a `Basis2d`.
 *
 * This is useful for creating a closed loop spline.
 *
 * @param p - The `Basis2d` to triplicate the endpoints of.
 * @returns A new `Basis2d` instance with the triplicated endpoints.
 * @since 1.0.0
 */
export declare const withTriplicatedEndpoints: (p: Basis2d) => Basis2d;
/**
 * Creates a new `Path2d` from a `Basis2d`.
 *
 * @param p - The `Basis2d` to convert to a `Path2d`.
 * @returns A new `Path2d` instance.
 * @since 1.0.0
 */
export declare const toPath: (p: Basis2d) => CubicPath2d;
/**
 * Converts a `Basis2d` to a `Bezier2d`.
 *
 * @param p - The `Basis2d` to convert.
 * @returns A new `Bezier2d` instance.
 * @since 1.0.0
 */
export declare const toBezier: (p: Basis2d) => Bezier2d;