import { type ExactValue } from '../coxeter/exact.js';
import { ConvexWindow, FlatN, LatticeN, type CoefficientBoxSampleOptions, type ModelPoint, type WindowBoundaryPolicy } from './model-set.js';
/**
 * Two exact ring values: a point of the internal plane, or a phason offset
 * expressed in it. Kept exact so window membership is decided without a
 * rounding decision.
 */
export type ExactPair = readonly [ExactValue, ExactValue];
export type PenroseCoefficients = readonly [bigint, bigint, bigint, bigint];
export type PenroseWindowClass = 1 | 2 | 3 | 4;
export type PenrosePhasonOffset = readonly [ExactValue, ExactValue];
export interface PenroseModelSetOptions {
    boundaryPolicy?: WindowBoundaryPolicy;
    /**
     * Exact internal translation in seventh-coordinate units. The default
     * `[1,1]` is globally nonsingular; `[0,0]` is the symmetric singular cut.
     */
    phasonOffsetSevenths?: PenrosePhasonOffset;
}
export interface PenroseModelPoint extends ModelPoint {
    /** Discrete C5 component selecting one of the four pentagonal windows. */
    readonly windowClass: PenroseWindowClass;
}
export interface PenroseModelSetPatch {
    readonly points: readonly PenroseModelPoint[];
    readonly candidateCount: number;
    readonly boundaryCount: number;
}
export interface PenrosePatchOptions {
    /** Inclusive cyclotomic coefficient radius. Default 7. */
    coefficientRadius?: number;
    /** Euclidean radius in the unit-edge physical plane. Default 9. */
    physicalRadius?: number;
    /** Exact internal translation in seventh-coordinate units. Default `[1,1]`. */
    phasonOffsetSevenths?: PenrosePhasonOffset;
    /** Boundary policy. Default `error`; use `include` for the singular centered cut. */
    boundaryPolicy?: WindowBoundaryPolicy;
}
export interface PenrosePatch {
    readonly points: readonly PenroseModelPoint[];
    /** Tiling edges between accepted points at one of the five unit directions. */
    readonly edges: Uint32Array;
    /** Direction 0...4 for each edge pair, corresponding to powers of zeta_5. */
    readonly edgeDirections: Uint8Array;
    readonly boundaryCount: number;
    readonly candidateCount: number;
}
export interface PenroseVertexStarCensusOptions {
    /** Only vertices within this Euclidean radius are counted. */
    interiorRadius: number;
}
/** Exact vertices of one native-scale pentagonal acceptance window. */
export declare function penroseWindowVertices(windowClass: PenroseWindowClass): readonly ExactPair[];
/**
 * Penrose's rank-four cyclotomic cut-and-project scheme. The discrete C5
 * component routes every point to P, -phi P, phi P, or -P.
 */
export declare class PenroseModelSet {
    readonly lattice: LatticeN;
    readonly flat: FlatN;
    readonly windows: ReadonlyMap<PenroseWindowClass, ConvexWindow>;
    readonly boundaryPolicy: WindowBoundaryPolicy;
    constructor({ boundaryPolicy, phasonOffsetSevenths }?: PenroseModelSetOptions);
    sample({ coefficientRanges, maxCandidates }: CoefficientBoxSampleOptions): PenroseModelSetPatch;
}
export declare function createPenroseModelSet(options?: PenroseModelSetOptions): PenroseModelSet;
/** Convert exact {1,zeta_5}-basis coordinates to an orthonormal Cartesian plane. */
export declare function penroseCartesian(exactCoordinates: readonly ExactValue[]): Float64Array;
/** Multiplication by zeta_5, an exact 72-degree rotation of provenance. */
export declare function penroseRotate72([h, j, k, l]: PenroseCoefficients): PenroseCoefficients;
/**
 * A finite radial patch of the unit-edge rhombic Penrose tiling.
 *
 * @param options - Coefficient bound, physical crop, phason, and boundary policy.
 */
export declare function penrosePatch(options?: PenrosePatchOptions): PenrosePatch;
/** Canonical ten-ray vertex-star key modulo the full local dihedral action. */
export declare function penroseVertexStarKey(mask: number): string;
/** Census of complete local edge stars away from a radial patch boundary. */
export declare function penroseVertexStarCensus(patch: PenrosePatch, { interiorRadius }: PenroseVertexStarCensusOptions): ReadonlyMap<string, number>;
/** Native regular pentagon, useful for internal-space renderers. */
export declare const penroseUnitPentagon: readonly ExactPair[];
/** Default offset numerator and common denominator of the regular cut. */
export declare const penroseDefaultPhason: {
    readonly numerator: PenrosePhasonOffset;
    readonly denominator: ExactValue;
};
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