import { CellComplex } from '../geometry/cell-complex.js';
export interface CliffordCurveOptions {
    /** Windings in the xy plane. Default 2. */
    p?: number;
    /** Windings in the zw plane. Default 3. */
    q?: number;
    /** Circumradius: every vertex lies on the 3-sphere of this radius. Default 1. */
    radius?: number;
    /**
     * Ratio of the zw circle radius to the xy circle radius. 1 puts the
     * curve on the square Clifford torus. Default 1.
     */
    radiusRatio?: number;
    /** Number of polyline segments. Default 256. */
    segments?: number;
}
/**
 * The (p, q) curve on a Clifford torus in S³:
 *
 *   γ(θ) = (r₁·cos pθ, r₁·sin pθ, r₂·cos qθ, r₂·sin qθ),  θ ∈ [0, 2π)
 *
 * with r₁² + r₂² = radius², so the whole curve lies on the 3-sphere. For
 * coprime p and q this is the (p, q) torus knot — but flat, living on the
 * flat Clifford torus, with none of the pinching a torus embedded in R³
 * forces on it. It is exactly the vertex path of the p×q duoprism made
 * continuous.
 *
 * Under the equal-speed double rotation (xy and zw together — a Clifford
 * displacement) the curve slides along itself: the isoclinic flow of S³
 * is tangent to it everywhere.
 *
 * Returns a closed polyline: a CellComplex with 1-cells only, ready for
 * ProjectedEdges3D.
 */
export declare function createCliffordCurve(options?: CliffordCurveOptions): CellComplex;
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