import { type FaceLattice } from './face-lattice.js';
/**
 * A tetrahedralization of a face lattice's 3-cells, with full provenance:
 * the derived object every slicer, picker, and per-cell material reads.
 */
export interface Tetrahedralization {
    /** Source vertices followed by one centroid helper vertex per 3-cell. */
    readonly positions: Float64Array;
    /** Four vertex indices per tetrahedron, emitted cell-major. */
    readonly indices: Uint32Array;
    /** Canonical rank-3 face (cell) ID of each tetrahedron. */
    readonly tetToCell: Uint32Array;
    /** Global 2-face whose triangulation generated each tetrahedron. */
    readonly tetToFace: Uint32Array;
    /** Cell c owns tets [cellTetOffsets[c], cellTetOffsets[c+1]). */
    readonly cellTetOffsets: Uint32Array;
    /** Helper centroid vertex index of each cell. */
    readonly cellCentroidVertex: Uint32Array;
    /** Vertex count before helpers were appended. */
    readonly sourceVertexCount: number;
}
/**
 * Centroid-fan tetrahedralization of every 3-cell of a convex polytope's
 * face lattice: each cell's centroid (strictly interior, being a positive
 * combination of its vertices) cones over its boundary polygons, and each
 * polygon is fan-triangulated **once globally** — adjacent cells reuse the
 * same triangles, so slices stay continuous across cell boundaries.
 *
 * Tetrahedra are emitted cell-major and positively oriented in each
 * cell's outward-oriented tangent frame; a degenerate (near-zero volume)
 * tetrahedron throws rather than silently corrupting downstream volume
 * or slicing invariants. Float64 is appropriate here: orientation
 * validates known topology, it does not determine incidence.
 */
export declare function tetrahedralizeLattice(lattice: FaceLattice, positions: Float64Array): Tetrahedralization;
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