/**
 * NURBS surface evaluation and operations.
 * Implements algorithms from "The NURBS Book" (Piegl & Tiller), Chapters 4, 6.
 */
import { NurbsCurve } from "./curve";
import type { SurfaceData } from "./types";
export declare class NurbsSurface {
    private _degreeU;
    private _degreeV;
    private _knotsU;
    private _knotsV;
    private _controlPoints;
    private _weights;
    constructor(data: SurfaceData);
    static byKnotsControlPointsWeights(degreeU: number, degreeV: number, knotsU: number[], knotsV: number[], controlPoints: number[][][], weights: number[][]): NurbsSurface;
    static byLoftingCurves(curves: NurbsCurve[], degreeV: number): NurbsSurface;
    static byCorners(p0: number[], p1: number[], p2: number[], p3: number[]): NurbsSurface;
    /**
     * Evaluate surface point at (u, v) — Algorithm A4.3 (rational tensor product).
     */
    point(u: number, v: number): number[];
    /**
     * Compute surface normal at (u, v) as cross product of partial derivatives.
     */
    normal(u: number, v: number): number[];
    /**
     * Compute partial derivatives of the rational surface at (u, v).
     * Returns ders[k][l] = mixed partial derivative ∂^(k+l)S / ∂u^k ∂v^l.
     * Algorithm A4.4 adapted for rational surfaces (Eq. 4.20 generalized).
     */
    derivatives(u: number, v: number, numDerivs: number): number[][][];
    /**
     * Find closest UV parameters to a 3D point.
     * Implements the surface point projection from "The NURBS Book" Section 6.1.
     *
     * Phase 1: Initial guess via closest control point (Greville abscissa)
     *          + grid refinement near the best candidate.
     * Phase 2: Newton iteration with four convergence criteria:
     *   (1) Point coincidence:  ||S(u,v) - P|| < eps1
     *   (2) Zero cosine (U):   |S_u · (S - P)| / (|S_u| · |S - P|) < eps2
     *   (2) Zero cosine (V):   |S_v · (S - P)| / (|S_v| · |S - P|) < eps2
     *   (3) Parameter correction: |Δu·S_u + Δv·S_v| < eps1
     *   (4) Domain bounds
     */
    closestParam(point: number[]): number[];
    /**
     * Extract an iso-parametric curve from the surface.
     * If useV=false: fix u=param, extract curve in V direction.
     * If useV=true: fix v=param, extract curve in U direction.
     */
    /**
     * Extract an iso-parametric curve from the surface.
     * If useV=true: fix v=param, extract curve in U direction.
     * If useV=false: fix u=param, extract curve in V direction.
     *
     * Works in homogeneous coordinates: for each row/column, blend the
     * homogeneous control points (w*P, w) using basis functions, then
     * store the result as the new curve's control points and weights.
     */
    isocurve(param: number, useV: boolean): NurbsCurve;
    degreeU(): number;
    degreeV(): number;
    knotsU(): number[];
    knotsV(): number[];
    controlPoints(): number[][][];
    weights(): number[][];
    asData(): SurfaceData;
}