import { type PageMesh } from './mesh';
import type { CurlAnchor } from './types';
/**
 * Silk — hand-turned S-curve page.
 *
 * This is not a traveling contact wave (`leaf`), not a cone wrap (`cone`), not a
 * cylinder roll (`roll`), and not a single-mode inertial cantilever (`flick`).
 *
 * Real paper turned by hand takes an S-shaped cross-section: a main bend through
 * the near half and a reverse bend through the far half (the flap over the
 * fingers). The sheet is a developable strip clamped at the spine and driven
 * through a base rotation ρ(t) = πt. Along the width the tangent is:
 *
 *   θ(u) = ρ + env·S·sin(2πu) + peel(t)·u²
 *
 * where:
 *  - sin(2πu) is a full-period S (zero net at spine and free edge, opposite
 *    bends in the two halves) — a true inflection that none of the other
 *    models produce mid-turn,
 *  - u² is an early peel lead that lifts the free edge first, then releases.
 *
 * env = sin(πt) holds the S through the middle and forces exact flat rests.
 * Rows far from the tap lag so a corner grab draws a living diagonal.
 * Arc length is integrated with the unit tangent (trapezoid per grid cell), so
 * the paper never stretches.
 */
export declare function deformSilk(mesh: PageMesh, W: number, H: number, t: number, anchor: CurlAnchor): void;