import { VecN } from '../math/vecn.js';
/** One source-simplex vertex and its valid or invalid homogeneous image. */
export interface HomogeneousSimplexVertexN {
    readonly sourcePoint: VecN;
    readonly coordinates: ArrayLike<number>;
    readonly valid: boolean;
}
export interface HomogeneousSimplexLiftOptions {
    /** Scale-relative geometric and barycentric tolerance. Default `1e-9`. */
    readonly tolerance?: number;
}
export type HomogeneousSimplexLiftFailureReason = 'unsupported-projection' | 'invalid-projection-vertex' | 'invalid-homogeneous-denominator' | 'degenerate-simplex' | 'point-off-simplex' | 'point-outside-simplex' | 'singular-source-weights';
export interface ExactHomogeneousSimplexLiftN {
    readonly kind: 'exact';
    readonly point: VecN;
    /** Affine weights in the rendered segment or triangle. */
    readonly representationWeights: Float64Array;
    /** Perspective-correct affine weights in the source simplex. */
    readonly sourceWeights: Float64Array;
    readonly minAbsQ: number;
    /** One for a segment; normalized Gram determinant in `[0,1]` for a triangle. */
    readonly simplexConditioning: number;
    readonly representationResidual: number;
}
export interface UnavailableHomogeneousSimplexLiftN {
    readonly kind: 'unavailable';
    readonly reason: HomogeneousSimplexLiftFailureReason;
    readonly details: Readonly<Record<string, number | boolean>>;
}
export type HomogeneousSimplexLiftN = ExactHomogeneousSimplexLiftN | UnavailableHomogeneousSimplexLiftN;
/**
 * Lifts a point on a rendered segment or triangle through a homogeneous map.
 *
 * The representation-space affine weights `lambda_i` become source weights
 * `mu_i = (lambda_i / q_i) / sum_j(lambda_j / q_j)`. A result is exact only
 * when every vertex is inside the projection domain, the representation
 * simplex is nondegenerate, and the supplied point lies on that simplex.
 */
export declare function liftHomogeneousSimplexPointN(vertices: readonly HomogeneousSimplexVertexN[], point3: ArrayLike<number>, options?: HomogeneousSimplexLiftOptions): HomogeneousSimplexLiftN;
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