import type { CellComplex } from '../geometry/cell-complex.js';
import type { TransformN } from '../math/transform.js';
import type { HyperplaneSlice4 } from '../projection/slice.js';
import type { RepresentationCellChartN, RepresentationChartSourceCellResolutionN } from './chart-source-cell-types.js';
/**
 * Construct the exact triangulated chart of an affine R4 section.
 *
 * The returned record carries per-triangle source-cell references and an exact
 * chart lift. It is renderer-independent and can therefore be consumed by
 * headless experiments, Three.js adapters, or tests through the same resolver.
 *
 * @param complex - R4 source with simplex 3-cells.
 * @param slice - Affine hyperplane and its retained 3D chart.
 * @param options - Optional source pose and marching tolerance.
 */
export declare function createAffineSectionCellChart4N(complex: CellComplex, slice: HyperplaneSlice4, options?: {
    /** Source pose applied before sectioning. Must be R4. */
    readonly transform?: TransformN;
    /** Signed-distance degeneracy tolerance. Default `1e-9`. */
    readonly epsilon?: number;
}): RepresentationCellChartN;
/**
 * Resolve a point in a triangulated representation chart to its source cell.
 *
 * Containment chooses a rendered triangle, retained provenance chooses the
 * source cell, and an exact chart lift is projected onto that source simplex
 * to produce a local barycentric coordinate. No inverse is invented for a
 * projection: the cell remains resolved from its retained record while
 * `sourceCoordinate` reports `projection-ambiguous`.
 */
export declare function resolveRepresentationChartPointToSourceCellN(chart: RepresentationCellChartN, point: ArrayLike<number>, options?: {
    /**
     * Known rendered triangle, such as a Three.js `faceIndex`. Supplying it
     * disambiguates points on a boundary shared by multiple source cells.
     */
    readonly triangleIndex?: number;
    /**
     * Chart-space containment tolerance. Defaults to the chart-owned value,
     * or `1e-6` when the chart does not declare one.
     */
    readonly chartTolerance?: number;
    /**
     * Source-space coordinate residual tolerance. Defaults to the chart-owned
     * value, or `1e-9` when the chart does not declare one.
     */
    readonly sourceTolerance?: number;
}): RepresentationChartSourceCellResolutionN;
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