/**
 * NURBS modification operations.
 * Implements Algorithms A5.1, A5.4, A5.9 from "The NURBS Book" (Piegl & Tiller).
 */
import type { CurveData, SurfaceData } from "./types";
/**
 * Insert a single knot u into a curve r times.
 * Uses Boehm's algorithm, operating on control points and weights separately.
 */
export declare function curveKnotInsert(curve: CurveData, u: number, r: number): CurveData;
/**
 * Refine a curve by inserting multiple knots (Algorithm A5.4).
 */
export declare function curveKnotRefine(curve: CurveData, knotsToInsert: number[]): CurveData;
/**
 * Refine a surface by inserting knots in U or V direction.
 */
export declare function surfaceKnotRefine(surface: SurfaceData, knotsToInsert: number[], useV: boolean): SurfaceData;
/**
 * Elevate the degree of a curve (simplified approach: insert all interior knots
 * to get Bezier segments, elevate each, then remove unnecessary knots).
 * For the initial implementation, we use a simpler approach via knot insertion.
 */
export declare function curveElevateDegree(curve: CurveData, finalDegree: number): CurveData;
/**
 * Unify knot vectors across multiple curves:
 * 1. Elevate all to the maximum degree
 * 2. Merge all knot vectors and refine each curve to the union
 */
export declare function unifyCurveKnots(curves: CurveData[]): CurveData[];