import { VecN } from '@holotope/core';
import { type GjkFeaturePair, type GjkOptions, type GjkResult } from './gjk.js';
import type { SupportShapeN } from './support-shape.js';
export interface EpaOptions4 {
    /** GJK intersection policy used to enter EPA. */
    readonly gjkOptions?: GjkOptions;
    /** Expansion steps after the seed contains the origin. Default 96. */
    readonly maxIterations?: number;
    /** Support expansions allowed while enclosing the origin. Default 32. */
    readonly maxSeedIterations?: number;
    /** Hard tetrahedral-facet budget. Default 4096. */
    readonly maxFacets?: number;
    /** Relative support-gap termination tolerance. Default 1e-10. */
    readonly relativeTolerance?: number;
    /** World-space support-gap/contact tolerance. Default 1e-10. */
    readonly absoluteTolerance?: number;
    /** Scale-relative affine-rank and facet-volume band. Default 1e-12. */
    readonly degeneracyTolerance?: number;
    /** Scale-relative facet visibility band. Default 1e-12. */
    readonly visibilityTolerance?: number;
    /** Dimensionless tetrahedral barycentric band. Default 1e-10. */
    readonly barycentricTolerance?: number;
    /** Retain one compact record per expansion. Default false. */
    readonly recordTrace?: boolean;
}
export type EpaStatus4 = 'separated' | 'touching' | 'penetrating' | 'indeterminate';
export type EpaTerminationReason4 = 'gjk-separated' | 'gjk-iteration-limit' | 'support-gap' | 'duplicate-support' | 'degenerate-seed' | 'seed-iteration-limit' | 'seed-stalled' | 'degenerate-facet' | 'non-manifold-horizon' | 'invalid-hull' | 'invalid-closest-facet' | 'facet-limit' | 'iteration-limit';
export interface EpaFacetCertificate4 {
    readonly vertexIndices: readonly [number, number, number, number];
    readonly featurePairs: readonly GjkFeaturePair[];
    /** Convex weights aligned with vertexIndices and featurePairs. */
    readonly weights: Float64Array;
    /** Outward normal of the Minkowski-difference boundary facet. */
    readonly minkowskiNormal: VecN;
    readonly distance: number;
    readonly conditionEstimate: number;
    readonly projectionConditionEstimate: number;
    readonly witnessResidual: number;
}
/** Single ordered EPA witness; deliberately not a persistent manifold type. */
export interface EpaPointContactPatch4 {
    readonly kind: 'point';
    readonly normal: VecN;
    readonly pointA: VecN;
    readonly pointB: VecN;
    readonly alignmentShift: number;
    readonly translationA: VecN;
    readonly resolvedPoint: VecN;
    readonly penetrationDepth: number;
}
export interface EpaTraceEntry4 {
    readonly iteration: number;
    readonly facetCount: number;
    readonly supportCount: number;
    readonly lowerBound: number;
    readonly upperBound: number;
    readonly supportGap: number;
    readonly visibleFacetCount: number;
    readonly horizonTriangleCount: number;
}
export interface EpaTerminationCertificate4 {
    readonly reason: EpaTerminationReason4;
    readonly supportGap: number | null;
    readonly threshold: number | null;
    readonly seedIterations: number;
    readonly expansionIterations: number;
    readonly supportCount: number;
    readonly facetCount: number;
    readonly maxFacetCount: number;
}
export interface EpaPenetrationResult4 {
    readonly status: EpaStatus4;
    readonly intersects: boolean | null;
    /** Minimum-translation magnitude when convergence is certified. */
    readonly penetrationDepth: number | null;
    /** Unit direction from ordered B toward ordered A. */
    readonly normal: VecN | null;
    readonly pointA: VecN | null;
    readonly pointB: VecN | null;
    readonly patch: EpaPointContactPatch4 | null;
    /** Inner-polytope lower bound on penetration magnitude. */
    readonly lowerBound: number | null;
    /** Support-plane upper bound along the selected direction. */
    readonly upperBound: number | null;
    readonly errorBound: number | null;
    readonly facet: EpaFacetCertificate4 | null;
    readonly gjk: GjkResult;
    readonly termination: EpaTerminationCertificate4;
    readonly trace?: readonly EpaTraceEntry4[];
}
/**
 * Auditable Float64 EPA fallback for full-dimensional compact convex shapes
 * in R4. It returns one minimum-translation witness, not a persistent contact
 * manifold. Every numerical failure remains an explicit indeterminate result.
 */
export declare function epaPenetration4(shapeA: SupportShapeN, shapeB: SupportShapeN, options?: EpaOptions4): EpaPenetrationResult4;
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