import { EdgeType } from './types';
/**
 * A vertex of a 3D graph.
 */
export type Vertex3D = {
    /** Horizontal coordinate. */
    x: number;
    /** Vertical coordinate. */
    y: number;
    /** Depthwise coordinate. */
    z: number;
    /** Index to input array. */
    index?: number;
};
/**
 * An edge connecting two vertices of a 3D graph.
 */
export type Edge3D = {
    /** First horizontal coordinate. */
    x1: number;
    /** First vertical coordinate. */
    y1: number;
    /** First depthwise coordinate. */
    z1: number;
    /** Second horizontal coordinate. */
    x2: number;
    /** Second vertical coordinate. */
    y2: number;
    /** Second depthwise coordinate. */
    z2: number;
    /** Type of connection. */
    type: EdgeType;
};
/**
 * Options for {@link spanLattice3D}.
 */
export type LatticeOptions3D = {
    /** Mapping for prime x-coordinates. */
    horizontalCoordinates: number[];
    /** Mapping for prime y-coordinates. */
    verticalCoordinates: number[];
    /** Mapping for prime z-coordinates. */
    depthwiseCoordinates: number[];
    /** Maximum prime-wise distance for connecting two inputs. */
    maxDistance?: number;
    /** Prime-count vectors of connections in addition the the primes. */
    edgeMonzos?: number[][];
    /** Flag to merge short edges into a long ones wherever possible. */
    mergeEdges?: boolean;
};
/**
 * Combine edges that share an endpoint and slope into longer ones.
 * @param edges Large number of short edges to merge.
 * @returns Smaller number of long edges.
 */
export declare function mergeEdges3D(edges: Edge3D[]): Edge3D[];
/**
 * Compute vertices and edges for a 2D graph representing the lattice of a musical scale in just intonation.
 * @param monzos Prime exponents of the musical intervals in the scale.
 * @param options Options for connecting vertices in the graph.
 * @returns Vertices and edges of the graph.
 */
export declare function spanLattice3D(monzos: number[][], options: LatticeOptions3D): {
    vertices: Vertex3D[];
    edges: Edge3D[];
};
/**
 * Get Wilson-Grady-Pakkanen coordinates for the first 9 primes.
 * @param equaveIndex Index of the prime to use as the interval of equivalence.
 * @returns An array of horizontal coordinates for each prime and the same for vertical and depthwise coordinates.
 */
export declare function WGP9(equaveIndex?: number): LatticeOptions3D;
/**
 * Compute coordinates based on sizes of primes that lie on the surface of a sphere offset on the x-axis.
 * @param equaveIndex Index of the prime to use as the interval of equivalence.
 * @param logs Logarithms of (formal) primes with the prime of equivalence first. Defaults to the first 24 actual primes.
 * @param searchResolution Search resolution for optimizing orthogonality of the resulting set.
 * @returns An array of horizontal coordinates for each prime and the same for vertical and depthwise coordinates.
 */
export declare function primeSphere(equaveIndex?: number, logs?: number[], searchResolution?: number): {
    horizontalCoordinates: number[];
    verticalCoordinates: number[];
    depthwiseCoordinates: number[];
};