import { CellComplex } from '../geometry/cell-complex.js';
export interface HopfFiberOptions {
    /** Base point on S² (normalized internally; must be nonzero). */
    base: [number, number, number];
    /** Radius of the 3-sphere carrying the fiber. Default 1. */
    radius?: number;
    /** Polyline segments. Default 96. */
    segments?: number;
}
/**
 * One fiber of the Hopf fibration S³ → S²: the great circle of the
 * 3-sphere sitting over a base point.
 *
 * With the Hopf map written as
 *
 *   h(x₀,x₁,x₂,x₃) = (2(x₀x₂ + x₁x₃), 2(x₁x₂ − x₀x₃), x₂²+x₃² − x₀²−x₁²),
 *
 * each output component is invariant under the simultaneous equal-angle
 * rotation of the (x₀,x₁) and (x₂,x₃) planes — so that isoclinic flow
 * *is* the fiber direction, and every fiber is a Clifford circle. A
 * preimage of the unit base (a,b,c) with c ≠ 1 is obtained by setting
 * x₁ = 0: x₀ = √((1−c)/2), x₂ = a/2x₀, x₃ = −b/2x₀; the north pole's
 * fiber is the (x₂,x₃)-plane circle.
 *
 * Returns a closed polyline CellComplex (1-cells), renderable by
 * ProjectedEdges3D. Projecting with PerspectiveProjection at
 * viewDistance = radius is exactly stereographic projection from the
 * pole, under which every fiber maps to a perfect circle (or a line
 * through the pole) and any two fibers are linked once.
 */
export declare function createHopfFiber(options: HopfFiberOptions): CellComplex;
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