import { MatN, VecN } from '@holotope/core';
export type SimplexOrientationChangeN = {
    readonly kind: 'embedded';
} | {
    readonly kind: 'full-dimensional';
    readonly signedMeasureRatio: number;
    readonly state: 'preserved' | 'inverted' | 'collapsed';
};
/** Intrinsic affine deformation of one k-simplex embedded in RN. */
export interface SimplexMetricDeformationN {
    readonly ambientDimension: number;
    readonly simplexDimension: number;
    /** Rest edge Gram matrix `Dm^T Dm`. */
    readonly restMetric: MatN;
    /** Current edge Gram matrix `Ds^T Ds`. */
    readonly currentMetric: MatN;
    /** Current metric in the deterministic orthonormal rest-material basis. */
    readonly rightCauchyGreen: MatN;
    /** `(rightCauchyGreen - I) / 2`. */
    readonly greenLagrangeStrain: MatN;
    /** Square roots of the metric eigenvalues, in ascending order. */
    readonly principalStretches: Float64Array;
    /** Intrinsic current/rest k-measure ratio. */
    readonly measureRatio: number;
    /** Smallest/largest singular-value ratio of the rest edge matrix. */
    readonly restConditioning: number;
    readonly strainFrobeniusNorm: number;
    /** Maximum absolute eigenpair residual for `rightCauchyGreen`. */
    readonly spectralResidual: number;
    readonly orientationChange: SimplexOrientationChangeN;
}
/**
 * Evaluates intrinsic affine strain between matching rest/current simplices.
 *
 * The Cholesky material basis makes this valid for any `1 <= k <= N`, without
 * an ambient cross product or normal. Full-dimensional orientation is reported
 * separately through the signed determinant ratio.
 */
export declare function evaluateSimplexMetricDeformationN(restPositions: readonly VecN[], currentPositions: readonly VecN[]): SimplexMetricDeformationN;
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