import { type ExactValue } from '../coxeter/exact.js';
import { ModelSet, type ModelPoint, type WindowBoundaryPolicy } from './model-set.js';
export type AmmannBeenkerCoefficients = readonly [bigint, bigint, bigint, bigint];
export type AmmannBeenkerPhasonOffset = readonly [ExactValue, ExactValue];
export interface AmmannBeenkerModelSetOptions {
    boundaryPolicy?: WindowBoundaryPolicy;
    /** Exact internal offset in quarter-coordinate units. Default zero. */
    phasonOffsetQuarters?: AmmannBeenkerPhasonOffset;
}
/** Canonical Z[zeta_8] Ammann–Beenker model set with a unit-edge octagonal window. */
export declare function createAmmannBeenkerModelSet(options?: WindowBoundaryPolicy | AmmannBeenkerModelSetOptions): ModelSet;
/** Multiplication by zeta_8: exact 45-degree rotation of lattice provenance. */
export declare function ammannBeenkerRotate45([n0, n1, n2, n3]: AmmannBeenkerCoefficients): AmmannBeenkerCoefficients;
/**
 * Silver-mean inflation. In physical space this multiplies by 1+sqrt2;
 * in internal space its star image multiplies by 1-sqrt2.
 */
export declare function ammannBeenkerInflate([n0, n1, n2, n3]: AmmannBeenkerCoefficients): AmmannBeenkerCoefficients;
export interface AmmannBeenkerPatchOptions {
    /** Inclusive lattice coefficient radius. Default 6. */
    coefficientRadius?: number;
    /** Euclidean radius in standard unit-edge physical coordinates. Default 8. */
    physicalRadius?: number;
    /** Exact internal offset in quarter-coordinate units. Default zero. */
    phasonOffsetQuarters?: AmmannBeenkerPhasonOffset;
}
export interface AmmannBeenkerPatch {
    readonly points: readonly ModelPoint[];
    /** Tiling edges between accepted points whose provenance differs by one basis vector. */
    readonly edges: Uint32Array;
    readonly boundaryCount: number;
    readonly candidateCount: number;
}
/**
 * A radial finite patch of the canonical Ammann–Beenker vertex set.
 *
 * @param options - Coefficient bound, physical crop, and exact phason offset.
 */
export declare function ammannBeenkerPatch(options?: AmmannBeenkerPatchOptions): AmmannBeenkerPatch;
/** Exact silver-mean factors, exposed for invariant checks and dynamics. */
export declare const ammannBeenkerInflationFactors: {
    readonly parallel: ExactValue;
    readonly perpendicular: ExactValue;
};
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