import { BivectorN, MatN, Rotor4 } from '@holotope/core';
export type OrientationTrivialization4 = 'world-left' | 'body-right';
export interface BivectorPairCoordinates4 {
    readonly left: Float64Array;
    readonly right: Float64Array;
}
export interface OrientationBranchToken4 {
    readonly pairSign: 1 | -1;
    readonly guardAtSelection: number;
}
export interface RelativeOrientationOptions4 {
    readonly trivialization?: OrientationTrivialization4;
    readonly previousBranch?: OrientationBranchToken4;
    /** Guard on `|wL + wR|`; zero is the SO(4) logarithm cut locus. */
    readonly cutLocusTolerance?: number;
    /** Retain a previous pair lift while its signed `wL + wR` guard is above `-hysteresis`. */
    readonly branchHysteresis?: number;
}
export type RelativeOrientationCoordinates4 = {
    readonly status: 'regular';
    readonly error: BivectorN;
    readonly branch: OrientationBranchToken4;
    readonly cutLocusGuard: number;
    readonly shortestPairSign: 1 | -1;
    readonly usesShortestLift: boolean;
} | {
    readonly status: 'cut-locus';
    readonly branch: OrientationBranchToken4;
    readonly cutLocusGuard: number;
    readonly shortestPairSign: 1 | -1;
};
/**
 * Split a lexicographic R4 bivector `(01,02,03,12,13,23)` into the exact
 * quaternion-log coordinates consumed by `Rotor4.fromBivector`.
 */
export declare function splitBivectorPair4(bivector: BivectorN): BivectorPairCoordinates4;
/** Inverse of `splitBivectorPair4` in the shipped Rotor4 convention. */
export declare function combineBivectorPair4(pair: BivectorPairCoordinates4): BivectorN;
/**
 * Relative SO(4) logarithm with an explicit shortest-lift theorem, cut-locus
 * result, and optional pair-level hysteresis token.
 */
export declare function relativeOrientationCoordinates4(current: Rotor4, target: Rotor4, options?: RelativeOrientationOptions4): RelativeOrientationCoordinates4;
/**
 * Differential of the SO(4) exponential in lexicographic bivector
 * coordinates. Factor blocks use the quaternion-log scale of Rotor4.
 */
export declare function orientationDexp4(error: BivectorN, trivialization?: OrientationTrivialization4): MatN;
/** Analytic inverse of `orientationDexp4` on the regular chart. */
export declare function orientationDlog4(error: BivectorN, trivialization?: OrientationTrivialization4): MatN;
/** Tight Euclidean operator norm of the 4x4 skew angular-velocity map. */
export declare function angularVelocityOperatorNorm4(omega: BivectorN): number;
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