import { Rotor4 } from '../math/rotor4.js';
import type { VecN } from '../math/vecn.js';
/** A time-parameterized rotation, sampled per frame. */
export type RotorMotion = (t: number) => Rotor4;
/** Constant-rate rotation in one coordinate plane. */
export declare function spin(i: number, j: number, rate: number): RotorMotion;
/**
 * Double rotation in two disjoint coordinate planes with independent
 * rates. Disjoint-plane bivectors commute, so the exponential of the
 * sum is exact — no ordering ambiguity.
 */
export declare function doubleSpin(planeA: [number, number], rateA: number, planeB: [number, number], rateB: number): RotorMotion;
/**
 * Isoclinic rotation: equal-angle double rotation in a plane and its
 * orthogonal complement — every point of the 3-sphere moves at equal
 * speed along Clifford-parallel circles. In the paired-quaternion
 * split, 'left' chirality drives only the left factor and 'right' only
 * the right; torque-free 4D rigid bodies relax toward exactly these
 * motions, so they are the natural idle/ambient spins.
 */
export declare function isoclinicSpin(rate: number, chirality?: 'left' | 'right'): RotorMotion;
/**
 * Removes the component of `rotor` that moves the axis `up`: peels off
 * the minimal plane rotation taking R·u back to u, leaving a rotation
 * that stabilizes u (the swing–twist split taken at the vector
 * stabilizer). The result is the roll-free constraint for cameras and
 * walk controllers: with u fixed, the admissible motion is the SO(3)
 * of the orthogonal 3-space.
 */
export declare function constrainUp(rotor: Rotor4, up: VecN): Rotor4;
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