/** Point-like object with x, y and optional z components. */
interface CurvePoint {
    x: number;
    y: number;
    z?: number;
    equals?(other: CurvePoint): boolean;
}
/** Abstract base class for parametric curves. */
export declare class Curve {
    #private;
    type: string;
    arcLengthDivisions: number;
    /**
     * Returns the point on the curve at parameter t.
     * Abstract - subclasses must override.
     */
    getPoint(_t: number, _target?: CurvePoint): CurvePoint | undefined;
    /** Returns the point on the curve at arc-length fraction u. */
    getPointAt(u: number, target?: CurvePoint): CurvePoint | undefined;
    /** Returns an array of (divisions + 1) points evenly spaced by parameter. */
    getPoints(divisions?: number): Array<CurvePoint | undefined>;
    /** Returns an array of (divisions + 1) points evenly spaced by arc length. */
    getSpacedPoints(divisions?: number): Array<CurvePoint | undefined>;
    /** Returns the total arc length of the curve. */
    getLength(): number;
    /** Computes and caches cumulative arc lengths at each subdivision. */
    getLengths(divisions?: number): number[];
    /** Invalidates the arc length cache, forcing recomputation on next call. */
    updateArcLengths(): void;
    /** Maps a uniform arc-length fraction u (or absolute distance) to curve parameter t. */
    getUtoTmapping(u: number, distance?: number): number;
    /** Returns the unit tangent vector at parameter t using numerical differentiation. */
    getTangent(t: number, target?: CurvePoint): CurvePoint | undefined;
    /** Returns the unit tangent vector at arc-length fraction u. */
    getTangentAt(u: number, target?: CurvePoint): CurvePoint | undefined;
    /** Returns a new Curve with the same properties. */
    clone(): Curve;
    /** Copies properties from source into this curve. */
    copy(source: Curve): this;
    /** Returns a plain JSON representation of this curve. */
    toJSON(): Record<string, unknown>;
    /** Restores this curve from a plain JSON object. */
    fromJSON(json: Record<string, unknown>): this;
}
export {};
//# sourceMappingURL=Curve.d.ts.map