import { vec2 } from 'linearly';
import { SegmentLocation } from './Location.js';
import { Path, VertexC } from './Path.js';
import { SegmentC } from './Segment.js';
import { PartialBy } from './utils.js';
/**
 * Almost equivalent to {@link SegmentC}, but the redundant `command` field can be ommited. Used for the argument of CubicBezier functions.
 */
type SimpleSegmentC = PartialBy<SegmentC, 'command'>;
/**
 * A collection of functions to handle a cubic bezier represented with {@link SimpleSegment}.
 * @category Modules
 */
export declare namespace CubicBezier {
    function of(start: vec2, control1: vec2, control2: vec2, point: vec2): {
        command: string;
        start: vec2;
        args: vec2[];
        point: vec2;
    };
    const toPaperBezier: (arg: SimpleSegmentC) => paper.Curve;
    function fromQuadraticBezier(start: vec2, control: vec2, point: vec2): SegmentC;
    /**
     * Calculates the length of the Bezier curve. Length is calculated using numerical approximation, specifically the Legendre-Gauss quadrature algorithm.
     */
    const length: (arg: SimpleSegmentC) => number;
    /**
     * Calculates the rect of this Bezier curve.
     */
    const bounds: (arg: SimpleSegmentC) => [vec2, vec2];
    function toTime(bezier: SimpleSegmentC, loc: SegmentLocation): number;
    /**
     * Calculates the point on the curve at the specified `t` value.
     */
    function point(bezier: SimpleSegmentC, loc: SegmentLocation): vec2;
    /**
     * Calculates the curve tangent at the specified `t` value. Note that this yields a not-normalized vector.
     */
    function derivative(bezier: SimpleSegmentC, loc: SegmentLocation): vec2;
    /**
     * Calculates the curve tangent at the specified `t` value. Unlike {@link derivative}, this yields a normalized vector.
     */
    function tangent(bezier: SimpleSegmentC, loc: SegmentLocation): vec2;
    /**
     * Calculates the curve normal at the specified `t` value. Note that this yields a normalized vector.
     */
    function normal(bezier: SimpleSegmentC, loc: SegmentLocation): vec2;
    /**
     * Finds the on-curve point closest to the specific off-curve point
     */
    function project(bezier: SimpleSegmentC, origin: vec2): {
        position: vec2;
        t?: number;
        distance?: number;
    };
    function trim(bezier: SimpleSegmentC, start: SegmentLocation, end: SegmentLocation): SegmentC;
    function divideAtTimes(segment: SimpleSegmentC, times: Iterable<number>): VertexC[];
    function isZero(bezier: SimpleSegmentC): boolean;
    function isStraight(bezier: SimpleSegmentC): boolean;
    function offset(bezier: SimpleSegmentC, distance: number): Path;
}
export {};
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