import type { CoxeterDiagram } from './diagram.js';
import type { ExactValue } from './exact.js';
/**
 * Float64 realization of mirror-distance tuples as Cartesian points.
 *
 * With G the Gram matrix of the unit mirror normals (Gᵢᵢ = 1,
 * Gᵢⱼ = −cos(π/mᵢⱼ)) and N a matrix whose rows are the normals, a point
 * x has mirror distances d = N·x. Choosing N = L from the Cholesky
 * factorization G = L·Lᵀ fixes a deterministic frame; realizing a tuple
 * is one forward-substitution solve x = L⁻¹·d. Exact tuples convert to
 * Float64 exactly once, here at the boundary.
 */
export declare class CoxeterRealization {
    readonly rank: number;
    /** Lower-triangular Cholesky factor of the Gram matrix, row-major. */
    readonly choleskyL: Float64Array;
    constructor(diagram: CoxeterDiagram);
    /** Solves L·x = d (forward substitution); writes and returns `out`. */
    realizeDistances(d: readonly number[], out?: Float64Array): Float64Array;
}
/**
 * Realizes a whole orbit of exact tuples as packed Float64 Cartesian
 * positions (rank coordinates per point).
 */
export declare function realizeOrbit(diagram: CoxeterDiagram, tuples: ReadonlyArray<ReadonlyArray<ExactValue>>): Float64Array;
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